This paper presents a real-world case study of optimizing waste collection in Sweden. The problem, involving approximately 17,000 garbage bins served by three bin lorries, is approached as a travelling salesman problem and solved using simulation-based optimization and an evolutionary algorithm. To improve the performance of the evolutionary algorithm, it is enhanced with a repair function that adjusts its genome values so that shorter routes are found more quickly. The algorithm is tested using two crossover operators, i.e., the order crossover and heuristic crossover, combined with different mutation rates. The results indicate that the order crossover is superior to the heuristics crossover, but that the driving force of the search process is the mutation operator combined with the repair function.
A HYBRID COA-DEA METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS ijcsa
The Cuckoo optimization algorithm (COA) is developed for solving single-objective problems and it cannot be used for solving multi-objective problems. So the multi-objective cuckoo optimization algorithm based on data envelopment analysis (DEA) is developed in this paper and it can gain the efficient Pareto frontiers. This algorithm is presented by the CCR model of DEA and the output-oriented approach of it.The selection criterion is higher efficiency for next iteration of the proposed hybrid method. So the profit function of the COA is replaced by the efficiency value that is obtained from DEA. This algorithm is
compared with other methods using some test problems. The results shows using COA and DEA approach for solving multi-objective problems increases the speed and the accuracy of the generated solutions.
THE NEW HYBRID COAW METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...BRNSS Publication Hub
In this paper, a proposed method, namely, zero average method is used for solving fuzzy transportation problems by assuming that a decision-maker is uncertain about the precise values of the transportation costs, demand, and supply of the product. In the proposed method, transportation costs, demand, and supply are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed method, a numerical example is solved. The proposed method is easy to understand and apply to real-life transportation problems for the decision-makers.
Additive Smoothing for Relevance-Based Language Modelling of Recommender Syst...Daniel Valcarce
Slides of the presentation given at CERI 2016 for the following paper:
Daniel Valcarce, Javier Parapar, Alvaro Barreiro: Additive Smoothing for Relevance-Based Language Modelling of Recommender Systems. CERI 2016: Article 9.
http://dx.doi.org/10.1145/2934732.2934737
A HYBRID COA-DEA METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS ijcsa
The Cuckoo optimization algorithm (COA) is developed for solving single-objective problems and it cannot be used for solving multi-objective problems. So the multi-objective cuckoo optimization algorithm based on data envelopment analysis (DEA) is developed in this paper and it can gain the efficient Pareto frontiers. This algorithm is presented by the CCR model of DEA and the output-oriented approach of it.The selection criterion is higher efficiency for next iteration of the proposed hybrid method. So the profit function of the COA is replaced by the efficiency value that is obtained from DEA. This algorithm is
compared with other methods using some test problems. The results shows using COA and DEA approach for solving multi-objective problems increases the speed and the accuracy of the generated solutions.
THE NEW HYBRID COAW METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...BRNSS Publication Hub
In this paper, a proposed method, namely, zero average method is used for solving fuzzy transportation problems by assuming that a decision-maker is uncertain about the precise values of the transportation costs, demand, and supply of the product. In the proposed method, transportation costs, demand, and supply are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed method, a numerical example is solved. The proposed method is easy to understand and apply to real-life transportation problems for the decision-makers.
Additive Smoothing for Relevance-Based Language Modelling of Recommender Syst...Daniel Valcarce
Slides of the presentation given at CERI 2016 for the following paper:
Daniel Valcarce, Javier Parapar, Alvaro Barreiro: Additive Smoothing for Relevance-Based Language Modelling of Recommender Systems. CERI 2016: Article 9.
http://dx.doi.org/10.1145/2934732.2934737
A performance analysis of metaheuristics and hybrid metaheuristics for the travel salesman problem is presented. Four single classical metaheuristics (genetic algorithm, memetic algorithm, iterated local search, and simulated annealing) were used. In addition, hybrid variations using nine different heuristic techniques for the local search, the mutation, and the intensification were used. The performance analysis was made using the Friedman test, and for the simulated annealing and local search algorithms statistical evidence was found that hybridization provides a difference in performance, while no evidence was found for the genetic and memetic algorithms. Up to six combinations were found to improve performance, five of them based on local search and one more based on simulated annealing.
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
AUTOMATIC TRANSFER RATE ADJUSTMENT FOR TRANSFER REINFORCEMENT LEARNINGgerogepatton
This paper proposes a novel parameter for transfer reinforcement learning to avoid over-fitting when an
agent uses a transferred policy from a source task. Learning robot systems have recently been studied for
many applications, such as home robots, communication robots, and warehouse robots. However, if the
agent reuses the knowledge that has been sufficiently learned in the source task, deadlock may occur and
appropriate transfer learning may not be realized. In the previous work, a parameter called transfer rate
was proposed to adjust the ratio of transfer, and its contribution include avoiding dead lock in the target
task. However, adjusting the parameter depends on human intuition and experiences. Furthermore, the
method for deciding transfer rate has not discussed. Therefore, an automatic method for adjusting the
transfer rate is proposed in this paper using a sigmoid function. Further, computer simulations are used to
evaluate the effectiveness of the proposed method to improve the environmental adaptation performance in
a target task, which refers to the situation of reusing knowledge.
Hybrid Genetic Algorithms and Simulated Annealing for Multi-trip Vehicle Rout...IJECEIAES
Vehicle routing problem with time windows (VRPTW) is one of NP-hard problem. Multi-trip is approach to solve the VRPTW that looking trip scheduling for gets best result. Even though there are various algorithms for the problem, there is opportunity to improve the existing algorithms in order gaining a better result. In this research, genetic algoritm is hybridized with simulated annealing algoritm to solve the problem. Genetic algoritm is employed to explore global search area and simulated annealing is employed to exploit local search area. Four combination types of genetic algorithm and simulated annealing (GA-SA) are tested to get the best solution. The computational experiment shows that GA-SA1 and GA-SA4 can produced the most optimal fitness average values with each value was 1.0888 and 1.0887. However GA-SA4 can found the best fitness chromosome faster than GA-SA1.
A Fuzzy Mean-Variance-Skewness Portfolioselection Problem.inventionjournals
A fuzzy number is a normal and convex fuzzy subsetof the real line. In this paper, based on membership function, we redefine the concepts of mean and variance for fuzzy numbers. Furthermore, we propose the concept of skewness and prove some desirable properties. A fuzzy mean-variance-skewness portfolio se-lection model is formulated and two variations are given, which are transformed to nonlinear optimization models with polynomial ob-jective and constraint functions such that they can be solved analytically. Finally, we present some numerical examples to demonstrate the effectiveness of the proposed models
Collocation Extraction Performance Ratings Using Fuzzy logicWaqas Tariq
The performance of Collocation extraction cannot quantified or properly express by a single dimension. It is very imprecise to interpret collocation extraction metrics without knowing what application (users) are involved. Most of the existing collocation extraction techniques are of Berry-Roughe, Church and Hanks, Kita, Shimohata, Blaheta and Johnson, and Pearce. The extraction techniques need to be frequently updated based on feedbacks from implementation of previous policies. These feedbacks are always stated in the form of ordinal ratings, e.g. “high speed”, “average performance”, “good condition”. Different people can describe different values to these ordinal ratings without a clear-cut reason or scientific basis. There is need for a way or means to transform vague ordinal ratings to more appreciable and precise numerical estimates. The paper transforms the ordinal performance ratings of some Collocation performance techniques to numerical ratings using Fuzzy logic. Keywords: Fuzzy Set Theory, collocation extraction, Transformation, performance Techniques, Criteria.
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
Antlion optimization algorithm for optimal non-smooth economic load dispatchIJECEIAES
This paper presents applications of Antlion optimization algorithm (ALO) for han- dling optimal economic load dispatch (OELD) problems. Electricity generation cost minimization by controlling power output of all available generating units is a major goal of the problem. ALO is a metaheuristic algorithm based on the hunting process of Antlions. The effect of ALO is investigated by solving a 10-unit system. Each studied case has different objective function and complex level of restraints. Three test cases are employed and arranged according to the complex level in which the first one only considers multi fuel sources while the second case is more complicated by taking valve point loading effects into account. And, the third case is the highest challenge to ALO since the valve effects together with ramp rate limits, prohibited operating zones and spinning reserve constraints are taken into consideration. The comparisons of the result obtained by ALO and other ones indicate the ALO algorithm is more potential than most methods on the solution, the stabilization, and the convergence velocity. Therefore, the ALO method is an effective and promising tool for systems with multi fuel sources and considering complicated constraints.
Study of relevancy, diversity, and novelty in recommender systemsChemseddine Berbague
In the next slides, we present our approach to tackling the conflicting recommendation quality in recommender systems using a genetic-based clustering algorithm. In our approach, we studied the users' tendencies toward diversity and proposed a pairwise similarity measure to amount it. Later, we used the new similarity within a fitness function to create overlapped clusters and to recommend balanced recommendations in terms of diversity and relevancy.
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
In recent years, consumers and legislation have been pushing companies to optimize their activities in such a way as to reduce negative environmental and social impacts more and more. In the other side, companies
must keep their total supply chain costs as low as possible to remain competitive.This work aims to develop a model to traveling salesman problem including environmental impacts and to identify, as far as possible, the contribution of genetic operator’s tuning and setting in the success and
efficiency of genetic algorithms for solving this problem with consideration of CO2 emission due to transport. This efficiency is calculated in terms of CPU time consumption and convergence of the solution. The best transportation policy is determined by finding a balance between financial and environmental
criteria.Empirically, we have demonstrated that the performance of the genetic algorithm undergo relevant
improvements during some combinations of parameters and operators which we present in our results part.
COMPARISON BETWEEN THE GENETIC ALGORITHMS OPTIMIZATION AND PARTICLE SWARM OPT...IAEME Publication
Close range photogrammetry network design is referred to the process of placing a set of
cameras in order to achieve photogrammetric tasks. The main objective of this paper is tried to find
the best location of two/three camera stations. The genetic algorithm optimization and Particle
Swarm Optimization are developed to determine the optimal camera stations for computing the three
dimensional coordinates. In this research, a mathematical model representing the genetic algorithm
optimization and Particle Swarm Optimization for the close range photogrammetry network is
developed. This paper gives also the sequence of the field operations and computational steps for this
task. A test field is included to reinforce the theoretical aspects.
A performance analysis of metaheuristics and hybrid metaheuristics for the travel salesman problem is presented. Four single classical metaheuristics (genetic algorithm, memetic algorithm, iterated local search, and simulated annealing) were used. In addition, hybrid variations using nine different heuristic techniques for the local search, the mutation, and the intensification were used. The performance analysis was made using the Friedman test, and for the simulated annealing and local search algorithms statistical evidence was found that hybridization provides a difference in performance, while no evidence was found for the genetic and memetic algorithms. Up to six combinations were found to improve performance, five of them based on local search and one more based on simulated annealing.
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
AUTOMATIC TRANSFER RATE ADJUSTMENT FOR TRANSFER REINFORCEMENT LEARNINGgerogepatton
This paper proposes a novel parameter for transfer reinforcement learning to avoid over-fitting when an
agent uses a transferred policy from a source task. Learning robot systems have recently been studied for
many applications, such as home robots, communication robots, and warehouse robots. However, if the
agent reuses the knowledge that has been sufficiently learned in the source task, deadlock may occur and
appropriate transfer learning may not be realized. In the previous work, a parameter called transfer rate
was proposed to adjust the ratio of transfer, and its contribution include avoiding dead lock in the target
task. However, adjusting the parameter depends on human intuition and experiences. Furthermore, the
method for deciding transfer rate has not discussed. Therefore, an automatic method for adjusting the
transfer rate is proposed in this paper using a sigmoid function. Further, computer simulations are used to
evaluate the effectiveness of the proposed method to improve the environmental adaptation performance in
a target task, which refers to the situation of reusing knowledge.
Hybrid Genetic Algorithms and Simulated Annealing for Multi-trip Vehicle Rout...IJECEIAES
Vehicle routing problem with time windows (VRPTW) is one of NP-hard problem. Multi-trip is approach to solve the VRPTW that looking trip scheduling for gets best result. Even though there are various algorithms for the problem, there is opportunity to improve the existing algorithms in order gaining a better result. In this research, genetic algoritm is hybridized with simulated annealing algoritm to solve the problem. Genetic algoritm is employed to explore global search area and simulated annealing is employed to exploit local search area. Four combination types of genetic algorithm and simulated annealing (GA-SA) are tested to get the best solution. The computational experiment shows that GA-SA1 and GA-SA4 can produced the most optimal fitness average values with each value was 1.0888 and 1.0887. However GA-SA4 can found the best fitness chromosome faster than GA-SA1.
A Fuzzy Mean-Variance-Skewness Portfolioselection Problem.inventionjournals
A fuzzy number is a normal and convex fuzzy subsetof the real line. In this paper, based on membership function, we redefine the concepts of mean and variance for fuzzy numbers. Furthermore, we propose the concept of skewness and prove some desirable properties. A fuzzy mean-variance-skewness portfolio se-lection model is formulated and two variations are given, which are transformed to nonlinear optimization models with polynomial ob-jective and constraint functions such that they can be solved analytically. Finally, we present some numerical examples to demonstrate the effectiveness of the proposed models
Collocation Extraction Performance Ratings Using Fuzzy logicWaqas Tariq
The performance of Collocation extraction cannot quantified or properly express by a single dimension. It is very imprecise to interpret collocation extraction metrics without knowing what application (users) are involved. Most of the existing collocation extraction techniques are of Berry-Roughe, Church and Hanks, Kita, Shimohata, Blaheta and Johnson, and Pearce. The extraction techniques need to be frequently updated based on feedbacks from implementation of previous policies. These feedbacks are always stated in the form of ordinal ratings, e.g. “high speed”, “average performance”, “good condition”. Different people can describe different values to these ordinal ratings without a clear-cut reason or scientific basis. There is need for a way or means to transform vague ordinal ratings to more appreciable and precise numerical estimates. The paper transforms the ordinal performance ratings of some Collocation performance techniques to numerical ratings using Fuzzy logic. Keywords: Fuzzy Set Theory, collocation extraction, Transformation, performance Techniques, Criteria.
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
Antlion optimization algorithm for optimal non-smooth economic load dispatchIJECEIAES
This paper presents applications of Antlion optimization algorithm (ALO) for han- dling optimal economic load dispatch (OELD) problems. Electricity generation cost minimization by controlling power output of all available generating units is a major goal of the problem. ALO is a metaheuristic algorithm based on the hunting process of Antlions. The effect of ALO is investigated by solving a 10-unit system. Each studied case has different objective function and complex level of restraints. Three test cases are employed and arranged according to the complex level in which the first one only considers multi fuel sources while the second case is more complicated by taking valve point loading effects into account. And, the third case is the highest challenge to ALO since the valve effects together with ramp rate limits, prohibited operating zones and spinning reserve constraints are taken into consideration. The comparisons of the result obtained by ALO and other ones indicate the ALO algorithm is more potential than most methods on the solution, the stabilization, and the convergence velocity. Therefore, the ALO method is an effective and promising tool for systems with multi fuel sources and considering complicated constraints.
Study of relevancy, diversity, and novelty in recommender systemsChemseddine Berbague
In the next slides, we present our approach to tackling the conflicting recommendation quality in recommender systems using a genetic-based clustering algorithm. In our approach, we studied the users' tendencies toward diversity and proposed a pairwise similarity measure to amount it. Later, we used the new similarity within a fitness function to create overlapped clusters and to recommend balanced recommendations in terms of diversity and relevancy.
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
In recent years, consumers and legislation have been pushing companies to optimize their activities in such a way as to reduce negative environmental and social impacts more and more. In the other side, companies
must keep their total supply chain costs as low as possible to remain competitive.This work aims to develop a model to traveling salesman problem including environmental impacts and to identify, as far as possible, the contribution of genetic operator’s tuning and setting in the success and
efficiency of genetic algorithms for solving this problem with consideration of CO2 emission due to transport. This efficiency is calculated in terms of CPU time consumption and convergence of the solution. The best transportation policy is determined by finding a balance between financial and environmental
criteria.Empirically, we have demonstrated that the performance of the genetic algorithm undergo relevant
improvements during some combinations of parameters and operators which we present in our results part.
COMPARISON BETWEEN THE GENETIC ALGORITHMS OPTIMIZATION AND PARTICLE SWARM OPT...IAEME Publication
Close range photogrammetry network design is referred to the process of placing a set of
cameras in order to achieve photogrammetric tasks. The main objective of this paper is tried to find
the best location of two/three camera stations. The genetic algorithm optimization and Particle
Swarm Optimization are developed to determine the optimal camera stations for computing the three
dimensional coordinates. In this research, a mathematical model representing the genetic algorithm
optimization and Particle Swarm Optimization for the close range photogrammetry network is
developed. This paper gives also the sequence of the field operations and computational steps for this
task. A test field is included to reinforce the theoretical aspects.
A MULTI-POPULATION BASED FROG-MEMETIC ALGORITHM FOR JOB SHOP SCHEDULING PROBLEMacijjournal
The Job Shop Scheduling Problem (JSSP) is a well known practical planning problem in the
manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this
paper, we develop a three-stage hybrid approach called JSFMA to solve the JSSP. In JSFMA,
considering a method similar to Shuffled Frog Leaping algorithm we divide the population in several sub
populations and then solve the problem using a Memetic algorithm. The proposed approach have been
compared with other algorithms for the Job Shop Scheduling and evaluated with satisfactory results on a
set of the JSSP instances derived from classical Job Shop Scheduling benchmarks. We have solved 20
benchmark problems from Lawrence’s datasets and compared the results obtained with the results of the
algorithms established in the literature. The experimental results show that JSFMA could gain the best
known makespan in 17 out of 20 problems.
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
An optimal design of current conveyors using a hybrid-based metaheuristic alg...IJECEIAES
This paper focuses on the optimal sizing of a positive second-generation current conveyor (CCII+), employing a hybrid algorithm named DE-ACO, which is derived from the combination of differential evolution (DE) and ant colony optimization (ACO) algorithms. The basic idea of this hybridization is to apply the DE algorithm for the ACO algorithm’s initialization stage. Benchmark test functions were used to evaluate the proposed algorithm’s performance regarding the quality of the optimal solution, robustness, and computation time. Furthermore, the DE-ACO has been applied to optimize the CCII+ performances. SPICE simulation is utilized to validate the achieved results, and a comparison with the standard DE and ACO algorithms is reported. The results highlight that DE-ACO outperforms both ACO and DE.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming ...Editor IJCATR
Branch and Bound technique (B&B) is commonly used for intelligent search in finding a set of integer solutions within a space of interest. The corresponding binary tree structure provides a natural parallelism allowing concurrent evaluation of sub-problems using parallel computing technology. Flower pollination Algorithm is a recently-developed method in the field of computational intelligence. In this paper is presented an improved version of Flower pollination Meta-heuristic Algorithm, (FPPSO), for solving integer programming problems. The proposed algorithm combines the standard flower pollination algorithm (FP) with the particle swarm optimization (PSO) algorithm to improve the searching accuracy. Numerical results show that the FPPSO is able to obtain the optimal results in comparison to traditional methods (branch and bound) and other harmony search algorithms. However, the benefits of this proposed algorithm is in its ability to obtain the optimal solution within less computation, which save time in comparison with the branch and bound algorithm.Branch and bound, flower pollination Algorithm; meta-heuristics; optimization; the particle swarm optimization; integer programming.
A Genetic Algorithm on Optimization Test FunctionsIJMERJOURNAL
ABSTRACT: Genetic Algorithms (GAs) have become increasingly useful over the years for solving combinatorial problems. Though they are generally accepted to be good performers among metaheuristic algorithms, most works have concentrated on the application of the GAs rather than the theoretical justifications. In this paper, we examine and justify the suitability of Genetic Algorithms in solving complex, multi-variable and multi-modal optimization problems. To achieve this, a simple Genetic Algorithm was used to solve four standard complicated optimization test functions, namely Rosenbrock, Schwefel, Rastrigin and Shubert functions. These functions are benchmarks to test the quality of an optimization procedure towards a global optimum. We show that the method has a quicker convergence to the global optima and that the optimal values for the Rosenbrock, Rastrigin, Schwefel and Shubert functions are zero (0), zero (0), -418.9829 and -14.5080 respectively
Optimizing Mobile Robot Path Planning and Navigation by Use of Differential E...IOSR Journals
Abstract: Path planning and navigation is essential for an autonomous robot which can move avoiding the
static obstacles in a real world and to reach the specific target. Optimizing path for the robot movement gives
the optimal distance from the source to the target and save precious time as well. With the development of
various evolutionary algorithms, the differential evolution is taking the pace in comparison to genetic algorithm.
Differential evolution has been deployed quite successfully for solving global optimization problem. Differential
evolution is a very simple yet powerful metaheuristics type problem solving method. In this paper we are
proposing a Differential Evolution based path navigation algorithm for mobile path navigation and analyze its
efficiency with other developed approaches. The proposed algorithm optimized the robot path and navigates the
robot to the proper target efficiently.
Performance Comparision of Machine Learning AlgorithmsDinusha Dilanka
In this paper Compare the performance of two
classification algorithm. I t is useful to differentiate
algorithms based on computational performance rather
than classification accuracy alone. As although
classification accuracy between the algorithms is similar,
computational performance can differ significantly and it
can affect to the final results. So the objective of this paper
is to perform a comparative analysis of two machine
learning algorithms namely, K Nearest neighbor,
classification and Logistic Regression. In this paper it
was considered a large dataset of 7981 data points and 112
features. Then the performance of the above mentioned
machine learning algorithms are examined. In this paper
the processing time and accuracy of the different machine
learning techniques are being estimated by considering the
collected data set, over a 60% for train and remaining
40% for testing. The paper is organized as follows. In
Section I, introduction and background analysis of the
research is included and in section II, problem statement.
In Section III, our application and data analyze Process,
the testing environment, and the Methodology of our
analysis are being described briefly. Section IV comprises
the results of two algorithms. Finally, the paper concludes
with a discussion of future directions for research by
eliminating the problems existing with the current
research methodology.
Optimal Allocation Policy for Fleet ManagementYogeshIJTSRD
The transportation problem is one of the biggest problem that face the fleet management, whereas the main objectives for the fleet management is reducing the operations cost besides improving the fleet efficiency. Therefore, this paper presents an application for a transportation technique on a company to distribute its products over a wide country by using its fleet. All the necessary data are collected from the company, analyzed and reformulated to become a suitable form to apply a transportation model to solve it. The results show that using this technique can be considered as powerful tool to improve the operation management for any fleet. Mohamed Khalil | Ibrahim Ahmed | Khaled Abdelwahed | Rania Ahmed | Elsayed Ellaimony "Optimal Allocation Policy for Fleet Management" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38673.pdf Paper URL: https://www.ijtsrd.com/management/operations-management/38673/optimal-allocation-policy-for-fleet-management/mohamed-khalil
Similar to Simulation-based Optimization of a Real-world Travelling Salesman Problem Using an Evolutionary Algorithm with a Repair Function (20)
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
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The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Simulation-based Optimization of a Real-world Travelling Salesman Problem Using an Evolutionary Algorithm with a Repair Function
1. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 27
Simulation-based Optimization of a Real-world Travelling
Salesman Problem Using an Evolutionary Algorithm with a
Repair Function
Anna Syberfeldt anna.syberfeldt@his.se
Engineering Science
University of Skövde
Skövde, SE-54148, Sweden
Joel Rogström joel.rogstrom@his.se
Engineering Science
University of Skövde
Skövde, SE-54148, Sweden
André Geertsen andre.geertsen@his.se
Engineering Science
University of Skövde
Skövde, SE-54148, Sweden
Abstract
This paper presents a real-world case study of optimizing waste collection in Sweden. The
problem, involving approximately 17,000 garbage bins served by three bin lorries, is approached
as a travelling salesman problem and solved using simulation-based optimization and an
evolutionary algorithm. To improve the performance of the evolutionary algorithm, it is enhanced
with a repair function that adjusts its genome values so that shorter routes are found more
quickly. The algorithm is tested using two crossover operators, i.e., the order crossover and
heuristic crossover, combined with different mutation rates. The results indicate that the order
crossover is superior to the heuristics crossover, but that the driving force of the search process
is the mutation operator combined with the repair function.
Keywords: Evolutionary Algorithm, Simulation-based Optimization, Travelling Salesman
Problem, Waste Collection, Real-world Case Study.
1. INTRODUCTION
In this paper, we present a study of optimizing waste collection from households in Sweden. The
study was undertaken in collaboration with the AÖS (www.aos.skovde.se) waste management
organization. AÖS is responsible for collecting household waste in seven municipalities in West
Sweden from a total of approximately 120,000 bins. Each bin is emptied once or several times
during a 14-day period according to a predefined schedule. Currently, the bin lorry routes and
their scheduling are specified manually by a transportation planner. Manually producing efficient
routes and schedules is very difficult due to the vast number of bins combined with the many
parameters to be considered. Parameters include driver working hours and breaks, truck capacity
(in terms of both weight and volume), and time windows at offload facilities. Due to the complexity
of producing efficient routes and schedules, AÖS has expressed a need to improve its current
process by introducing an optimization tool, motivating this study.
We approach the waste collection problem as a travelling salesman problem, defined as finding
the shortest possible route visiting each existing node exactly once and finally returning to the
starting node [1]. Finding the shortest route between several nodes might seem simple, but is
classified as NP-hard in its simplest form [2]. With an NP-hard problem, the time needed to solve
2. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 28
the problem grows exponentially with the problem size – in this case, the number of bins. Finding
the optimal route is possible, but might take a very long time because all possible routes must be
evaluated to find the best one. Even small travelling salesman problems involve a huge number
of possible routes. For example, for a problem with only 15 bins to visit, there are 6,227,020,800
possible routes. One can easily understand that manually optimizing the waste collection problem
is virtually impossible, at least within a reasonable timeframe.
Due to the complexity of routing problems, optimization techniques that are not guaranteed to find
the optimal solution, but a sufficiently good one in a short time, are often used rather than exact
methods [3]. Evolutionary algorithms are a class of such inexact optimization techniques usable
to approach routing problems [4], and an evolutionary algorithm is used here. In the study, we
enhance an ordinary evolutionary algorithm with a repair function that considerably improves the
optimization performance. Unlike repair functions previously suggested in the literature, the
suggested repair function does not aim to transform invalid into valid solutions but focuses solely
on improving performance. To ensure valid solutions, a non-destructive crossover operator is
used instead of a destructive one.
To evaluate the solutions generated by an evolutionary algorithm, a mathematical function
representing the travelling salesman problem is usually used. In this study, we instead use a
simulation that models the real-world waste collection scenario to evaluate solutions in order to
ensure that the obtained results are valid in practice. We believe that that the combinatorial
relationships, uncertainty factors, and nonlinearities present in the waste collection scenario –
and in real-world scenarios in general – are far too complex to be effectively modelled analytically
In the next section, the concepts of evolutionary algorithms and optimization using simulations,
so-called simulation-based optimization, are described in detail for the convenience of readers
unfamiliar with them. Section 3 outlines the simulation model developed for the waste collection
scenario considered here. Section 4 describes the evolutionary algorithm used for optimizations
and its repair function. Section 5 presents the optimization experiments and Section 6 finally
outlines the conclusions of the study and presents possibilities for future work.
2. THEORETICAL BACKGROUND
This section presents the fundamentals of evolutionary algorithms (Section 2.1) and simulation-
based optimization (Section 2.2).
2.1. Evolutionary Algorithms
The basic idea of evolutionary optimization is to use computational models of evolutionary
processes in designing and implementing problem solving applications [5]. Based on Darwin’s
“survival of the fittest” concept, candidate solutions to a problem are iteratively refined. Generally,
an evolutionary algorithm consists of a genetic representation of solutions, a population-based
solution approach, an iterative evolutionary process, and a guided random search. The genetic
representation defines an individual solution as a set of genes.
In evolving a population of solutions, evolutionary algorithms apply biologically inspired
operations for selection, crossover, and mutation. The operators are applied in a loop, an iteration
of the loop being called a generation. The following pseudo code presents the basic steps of this
evolutionary process:
Initialize population
Evaluate the fitness of solutions in the population
repeat
Select solutions to reproduce
Form a new generation of the population through crossover and mutation
Evaluate the new solutions
until terminating condition
3. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 29
The solutions in the initial population are usually generated randomly. In each generation, a
proportion of the solutions in the population is selected to breed offspring for the next generation
of the population. Solutions are selected based on their fitness, representing a quantification of
their optimality. Solutions with high fitness typically have a higher probability of being selected,
but to prevent premature convergence, it is common that a small proportion of solutions with
worse fitness is also selected. From the solutions selected, new solutions are created to form the
next generation of the population. To create each new solution, two parent solutions are chosen
and, through mating (called crossover), an offspring is produced (Figure 1).
3 7 5 1
B1 B2 B3 B4
6 2 5 7
B1 B2 B3 B4
Crossover point
3 7
B1 B2
5 7
B3 B4
6 2
B1 B2
5 1
B3 B4
Parents
Children
FIGURE 1: Example of a Crossover.
Occasionally, the new solution can undergo a small mutation in order to maintain high diversity in
the population and avoid local minima. A mutation usually involves changing an arbitrary part of a
solution with a certain probability, for example, slightly changing the size of the buffer in Figure 2.
FIGURE 2: Example of a Mutation.
When the new population is formed, the average fitness will have generally increased. The
process of evolving generations continues until a user-defined termination criterion has been
fulfilled, for example, that the best solutions in the last n generations have not changed or that a
certain time has passed.
2.2.Simulation-based Optimization
In simulation-based optimization, the evolutionary algorithm uses a simulation model to evaluate
the fitness of solutions [6]. The simulation model is a representation of the real-world scenario
that mimics reality as closely as possible, including stochastic events as well. Simulation-based
optimization is an iterative process (Figure 3): the evolutionary algorithm generates a solution (in
this case, a set of routes) and feeds it to the simulation model, which computes the fitness (in this
case, the driving time). Based on the evaluation feedback obtained from the simulation model, the
optimization algorithm generates a new set of parameter values and the generation–evaluation
process continues until a user-defined stopping criterion is satisfied. Such a criterion may, for
example, be that a certain amount of time has passed or that specific objective values have been
achieved.
4. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 30
FIGURE 3: Simulation–optimization Process.
The next section describes the simulation model developed for the waste collection scenario
considered here.
3. SIMULATION MODEL
To ensure that the optimized routes are valid in practice, a simulation is built that mimics the real-
world scenario as closely as possible. The simulation model is based on data from the Swedish
national road database, which holds information about all roads in Sweden. The information is
quite detailed and covers not only the length and speed limit of each road but also, for example,
traffic rules, road width, and whether the road is surfaced with asphalt or gravel. The database
also contains geographical information that makes it possible to render the roads graphically.
Although the Swedish national road database is huge, it is straightforward to use as it follows an
open standard that defines how to read and extract data [7].
The next two subsections outline the basic structure of the simulation model (Section 3.1) and
describe the graph used to navigate the roads in the model (Section 3.2).
3.1. Basic Structure
To represent the roads, the simulation model uses a road network. The road network comprises
two main elements, nodes and links. Nodes are the logical endpoints that connect links to each
other, while a link is a logical representation of a road. A link owns a set of link parts each of
which describes the link at different moments in time. If changes are made to a road, the link is
never changed; instead, the underlying link parts are replaced with newer parts that describe the
link from that moment on. Each link part owns a time interval that describes when this link part is
active.
To connect the nodes, links, and link parts, ports are used. A port is simply a connection between
two elements, and every node owns a set of node ports while every link owns a set of link ports.
A node connects to a link through a connection between one of its node ports and one of the
link’s link ports. A link’s various link parts connect to one another using the link’s link ports.
Furthermore, every link port holds information about its relative distance from the link’s starting
point. Note that a node does not have to connect to the end points of a link but only to a link port.
This concept is illustrated in Figure 4, in which three nodes each connect to the same link. The
concept of a link comprising its link parts is illustrated in Figure 5, in which the greyed-out link part
represents an older part of the road that has been removed. The link still represents the same
road, but its underlying representation has been changed. The figure also illustrates how the link
parts are connected through link ports.
5. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 31
FIGURE 4: Three nodes connecting to the same link using the port system.
FIGURE 5: A link and its underlying link parts.
3.2. Navigation Graph
To navigate the road network, a navigation graph is used in the simulator. This navigation graph
is a directed logical graph in which a set of nodes is connected to other nodes through edges. In
implementation, an edge can only be connected to two nodes. The edge’s beginning and ending
nodes denote the direction of the edge. As each link is connected to a node through a port, it is
straightforward to create edges between each port using the information contained in the link
part. In other words, each link part is converted to an edge between two nodes in the navigation
graph. This is illustrated in Figure 6, in which nodes A, B, and C are connected using edges
instead of links and link parts. A directed graph is used because not all nodes are connected to
each other in both directions. For instance, some roads allow traffic in only one direction. The
direction of travel is also important as some bin lorries can only empty receptacles on the right-
hand side of the road.
FIGURE 6: The same graph elements as in Figure 4, but in the navigation graph format.
An edge’s identity is defined by its beginning and ending nodes, its underlying link, and the port
ID used when connecting to its nodes. Using this approach makes it possible to separate two
edges that connect the same nodes, as they are constructed from different links and ports. It also
makes it possible to differentiate loops in different directions, as each loop will connect to different
beginning and ending ports. Examples of both scenarios are illustrated in Figure 7, in which
nodes A and B are connected through two different edges, and node A is connected to itself
through a loop. As every node is connected to a link through a port, and each port stores its
relative distance from the link’s beginning and end, it is possible to calculate the length of each
edge using the relative distance and the link’s entire length.
6. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 32
FIGURE 7: Examples of edge cases in the navigation graph.
The next section describes the evolutionary algorithm that uses the simulation model to evaluate
generated routes.
4. EVOLUTIONARY ALGORITHM
This section describes the configuration of the evolutionary algorithm implemented to solve the
optimization problem: first the genetic representation (Section 4.1), then the evolutionary
operators (Sections 4.2–4.4), and finally the repair function (Section 4.5) is described.
4.1. Genome
To represent solutions, a combinatorial genome is used. Combinatorial genomes are commonly
used when dealing with travelling salesman problems as they allow a simple, yet powerful,
genetic representation of the problems [8]. In the implemented genome, each gene represents an
edge to be visited by the bin lorry. All edges are visited in the order in which they appear in the
genome, making the genome a direct representation of a route. This implies that all genes of the
genome must be unique, and also that the crossover and mutation operators must never replace
or remove any genes.
As the route has specific beginning and ending points, they must be represented in the genome
and taken into account by the crossover and mutation operators. When building the genome, the
first entry is therefore always the starting point and the last entry is always the ending point. To
preserve these points, both the crossover and mutation operators operate on a subset of the
genome, ignoring the first and last entries.
4.2. Selection Operator
As the selection operator, binary tournament selection [9] is chosen. In binary tournament
selection, two lists are first created, each containing references to all individuals in the population.
Both lists are then shuffled, in the present case using the Fisher–Yates shuffle method [10]. By
comparing each element at the same index in both lists and choosing the best element, we select
individuals for recombination. This selection operator is used because it is fairly simple, fast and
easy to implement, and fair. The best solution in a population is guaranteed to be selected at
least once and at most twice.
4.3. Crossover Operator
Two crossover operators are implemented and tested for the problem: the ordered crossover [11]
and heuristic crossover [8]. Both operators are specifically designed for combinatorial problems
and therefore only change the order of the genes, never removing values or introducing new ones
into the genome. The ordered crossover is an older operator and is fairly simple. It is fast and
efficient, but it operates in a black box manner and uses no problem-specific information. The
heuristic crossover, in contrast, is more complex and uses problem-specific knowledge to guide
the crossover towards better results.
The order crossover works as follows: Two crossover points are randomly chosen in the parents.
The genes between the points in the first parent are copied into the second child, and the genes
from the second parent are copied into the first child. The remaining genes not covered by the
crossover are copied from the first parent into the first child in the order in which they appear. The
same is done for the second parent and second child. An example of an order crossover is given
in Figure 8.
7. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 33
Parent1 1 2 3 4 5 6
Parent2 4 6 5 2 3 1
Child1 1 6 5 2 3 4
Child2 6 2 3 4 5 1
FIGURE 8: Example of an order crossover.
The heuristic crossover (also known as the greedy crossover) uses a white box approach
employing problem knowledge. The crossover includes the following steps: First, a random gene
is chosen as the starting point for the crossover. The selected neighbouring genes in both parents
are then identified, and thereafter any neighbours already present in the child are sorted out. If
one or more neighbours remain, a heuristic is used to estimate the cost of travel between the
selected gene and the remaining neighbours. The lowest-cost neighbour is added to the child’s
genome and is set as the next selected gene. If all neighbours of the selected gene exist in the
child, one unvisited gene is randomly chosen as the next selected gene. The procedure is
repeated until the genome has been filled and the child is complete. This complete process is
repeated twice to produce two children.
4.4. Mutation Operator
As the mutation operator, the displacement operator [12] is used. This operator is well suited for
combinatorial problems as it manipulates only the order of elements in the genome. The
displacement operator works by randomly generating two offset points in the genome and then
shifting all the elements between the two points in a randomly selected number of steps. The
operator is demonstrated in Figure 9.
Displacement 1 2 3 4 5 6
1 5 6 2 3 4
FIGURE 9: The displacement operator demonstrated.
4.5. Repair Function
A pattern emerged when implementing and testing the evolutionary algorithm. Initially, the routes
resulting from the optimization often bypassed unvisited route stops on the way to other stops.
This led to various weaving patterns in which a route would bypass an unvisited stop several
times before it was finally visited (i.e., the bin was emptied). As it is not rational to drive past an
unvisited stop, a constraint was considered specifying that the sum of bypassed unvisited stops
must be zero. However, the act of detecting passed stops lends itself to fixing the problem, as we
know that travelling between stops can entail bypassing at least one unvisited stop. Instead of
adding a constraint, a solution was found in which the genome was reordered so that any
unvisited stop bypassed when travelling between two stops would be placed between these
stops. This approach was demonstrated to improve the performance of the optimization
significantly.
The repair function is illustrated in Figure 10. In the example, the genome is in form [1, 5, 4, 6, 8],
each number representing an edge in the graph. Asking the simulator for the shortest path
between the first and second genes would return the following path: [1, 3, 4, 5]. By iterating
through the path, we can find any unvisited stops bypassed. In the example given, the path
bypasses edge number four. To fix this, we can rearrange the genome in such a way that we visit
that edge before visiting edge number five. The genome after the fix would have the form [1, 4, 5,
6, 8] and the resulting route would be considerably shorter.
8. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 34
FIGURE 10: Graph illustrating the repair function.
It can be mentioned that repair functions have previously been described in several different
studies in the literature (see for example [13-17]). The difference between the existing functions
and the one suggested in this study is that the existing ones aim to transform invalid solutions into
valid ones, while the suggested one aims to improve the general performance of the algorithm.
The previously described repair functions are mainly used to compensate for a destructive
crossover, while in this study a non-destructive crossover is used and the problem of invalid
solutions is thereby eliminated.
The next section describes the results of optimizations using the evolutionary algorithm.
5. OPTIMIZATION
This section first describes the scope of the problem being optimized (Section 5.1), then presents
the exact algorithm configuration (Section 5.2), and finally outlines the optimization results
(Section 5.3).
5.1. Problem Scope
To test the optimization, one of the seven municipalities served by AÖS is selected. The selected
municipality includes approximately 17,000 unique bins spread over an area of approximately 40
× 50 kilometres. For the reader to grasp the problem, the geographical locations of the bins are
plotted on maps shown in Figures 11 and 12 (the latter zooms in on part of the former).
9. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 35
FIGURE 11: Garbage bins included in the optimization.
FIGURE 12: Zoomed-in view of the area corresponding to the black square in Figure 11.
10. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 36
Three trucks are available for emptying the selected bins, and each of them empties on average
approximately 550 bins per day. This means that a unique route should be created for each truck
and each workday during a 14-day period (excluding Saturdays and Sundays). If successful, the
optimization might free one or several trucks for one or several days, which would save the waste
management organization considerable money.
5.2. Algorithm Setup
The choice of parameters of an evolutionary algorithm has a distinct impact on the performance
of the algorithm and thereby also on the final results [18, 19]. No single set of parameter values is
universally optimal; rather, the parameters must be configured for each individual problem. In the
study we therefore evaluate various settings of the crossover and mutation operators, as
presented in the next subsection. In all presented experiments, the population size is set to 100
and the total number of iterations of the evolutionary algorithm is set to 10,000.
5.3. Results
The results of the experiments are presented in Table 1. Each combination of parameter values is
tested ten times, the presented results representing an average of these ten runs. As can be
seen in the table, the order crossover is superior to the heuristic crossover. It is also clear that the
higher the mutation rate, the better the results. The reasons for and implications of these results
are further discussed in Section 6. Due to lack of existing repair functions with equivalent focus, it
has not been possible to perform benchmarking against any other solution previously presented
in the literature. As mentioned in Chapter 4.5, existing repair functions have a completely different
purpose than the suggested one and a performance comparison is therefore not meaningful.
11. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 37
Crossover
Mutation
rate
Average minimum
fitness
Average minimum iterations
before local optimum is found
Order 1 2917.1 8920
Order 0.8 2938 8390
Order 0.9 2943.6 8460
Order 0.6 2958.1 9170
Order 0.7 2962.6 8490
Order 0.5 2977.8 9290
Order 0.4 3007.7 9380
Order 0.3 3034.4 8910
Order 0.2 3050.1 8930
Order 0.1 3160.8 9280
Heuristic 0.5 3163.2 6890
Heuristic 0.6 3167.5 3110
Heuristic 0.9 3168.6 5110
Heuristic 0.8 3182 5600
Heuristic 0.4 3194.5 4330
Heuristic 1 3211.5 5280
Heuristic 0.3 3218.7 1990
Heuristic 0.7 3223.1 6540
Heuristic 0.2 3230.6 2260
Heuristic 0.1 3249.6 3940
Heuristic 0 3260.4 610
Order 0 3885.9 100
TABLE 1: Results from experiments (ordered by average minimum fitness).
The routes resulting from the most successful optimization runs were presented to domain
experts in the waste management organization, who carefully studied and evaluated them. The
domain experts rated the improvement at about 25% when comparing the optimized routes with
the routes created manually by the transportation planner, who can instead concentrate on other
work tasks.
6. CONCLUSIONS AND FUTURE WORK
This study presented the optimization of waste collection, considering a problem including
approximately 17,000 garbage bins. The problem was approached using an evolutionary
algorithm and simulation-based optimization. To improve the performance of the evolutionary
algorithm, it was enhanced with a repair function that adjusts genome values so that shorter
routes are found more quickly. The algorithm was tested with two crossover operators, the order
crossover and heuristic crossover, combined with different mutation rates.
The results of the optimization experiments clearly indicate that the order crossover produces
much better results than does the heuristic crossover, at least as long as the mutation rate is
above zero. This is likely because the heuristic crossover does not introduce into the genome
changes as radical as does the order crossover. The order crossover, however, only works well
when the repair function is used, as the operator introduces many changes into the genome.
These changes might have negative effects, but these are immediately eliminated by the repair
12. Anna Syberfeldt, Joel Rogström & André Geertsen
International Journal of Artificial Intelligence and Expert Systems (IJAE), Volume (6) : Issue (3) : 2015 38
function. The repair function is therefore of great importance and significantly influences the
results. It can be noted that experiments with the repair function indicate that its importance
increases with the size of the routes, i.e., the more points to be visited, the more value it
produces.
Another interesting finding from the optimization experiments is that when the mutation rate is set
to zero and the order crossover is used, the search stagnates after only 100 iterations. This
indicates that the mutation rate has a much greater impact on the search than does the
crossover, likely because the repair algorithm overwrites many of the changes made by the
crossover. The repair algorithm tends to group together genes that are near each other, and as
the mutation operator shifts groups of genes around in the genome, these genes can be assumed
to work well together.
It is concluded from the study that the combination of mutation operator and repair function is the
most important factor for rapid search progress and successful optimization results. In the future,
it would be interesting to test additional crossover operators combined with the repair function to
see whether the optimization results can be improved even further.
It would also be interesting to consider a dynamic rather than static approach to garbage
collection. A problem is static if all transport requests are known when the routes are constructed
[20], which was the case here. In a situation in which transport requests may be added while
trucks are running the routes, meaning that routes have to be changed “on the fly”, the problem is
instead dynamic. In reality, the problem is already dynamic as customers often overfill their bins
and need immediate emptying outside the ordinary schedule. Dynamic problems are considerably
more difficult to tackle as the data change constantly and the optimizations must be performed in
real time, putting additional demands on the algorithm used.
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