This document proposes a new optimization algorithm called the Flower Pollination Algorithm (FPA) inspired by the pollination process of flowering plants. It first reviews the main characteristics of flower pollination including biotic and abiotic pollination, pollinators, flower constancy, and self-pollination vs cross-pollination. It then develops four rules to idealize these characteristics and uses them to design the FPA. The FPA is validated on standard test functions and compared to genetic algorithms and particle swarm optimization, showing it is more efficient. It is also applied to a nonlinear design problem with almost exponential convergence.
The document summarizes the flower pollination algorithm, a nature-inspired optimization technique. It describes how flower pollination occurs in nature through both biotic cross-pollination involving pollinators, and abiotic self-pollination involving wind and water. The algorithm mimics these processes to update solution populations towards optimization. It initializes a population randomly, then iteratively explores through global pollination modeled by Levy flights, and exploits through local pollination. Applications include engineering problems, neural networks, and scheduling.
Flower Pollination Algorithm: A Novel Approach for Multiobjective OptimizationXin-She Yang
This document summarizes a research paper that proposes a novel Flower Pollination Algorithm (FPA) approach for solving multiobjective optimization problems. The FPA is inspired by the natural flower pollination process and extends the previously developed single-objective FPA. It outlines four rules that mimic pollination characteristics like biotic cross-pollination, local pollination, flower constancy, and switching between local and global pollination. The proposed multi-objective FPA is tested on benchmark problems and engineering design problems with promising results, showing its efficiency in obtaining Pareto fronts.
Recent Advances in Flower Pollination AlgorithmEditor IJCATR
Flower Pollination Algorithm (FPA) is a nature inspired algorithm based on pollination process of plants. Recently, FPA
has become a popular algorithm in the evolutionary computation field due to its superiority to many other algorithms. As a
consequence, in this paper, FPA, its improvements, its hybridization and applications in many fields, such as operations research,
engineering and computer science, are discussed and analyzed. Based on its applications in the field of optimization it was seemed that
this algorithm has a better convergence speed compared to other algorithms. The survey investigates the difference between FPA
versions as well as its applications. To add to this, several future improvements are suggested.
Multi-objective Flower Algorithm for OptimizationXin-She Yang
The document proposes a multi-objective flower algorithm (MOFPA) for optimization. MOFPA extends the single-objective flower pollination algorithm (FPA) to solve multi-objective problems. MOFPA uses a weighted sum approach to combine multiple objectives into a single objective function. Random weights are used to find an accurate Pareto front with uniformly distributed solutions. MOFPA is tested on standard benchmark functions and shown to converge quickly, finding Pareto fronts accurately.
The document summarizes the flower pollination algorithm, a nature-inspired optimization technique. It describes how flower pollination occurs in nature through both biotic cross-pollination involving pollinators, and abiotic self-pollination involving wind and water. The algorithm mimics these processes to update solution populations towards optimization. It initializes a population randomly, then iteratively explores through global pollination modeled by Levy flights, and exploits through local pollination. Applications include engineering problems, neural networks, and scheduling.
محاضرات متقدمة تدرس لطلاب حاسبات بنى سويف السنة الثالثة لتنمية قدراتهم البحثية وهذة الموضوعات تدرس على مستوى الدكتوراة - - نريد تميز طلاب حاسبات ليتميزو فى البحث العلمى -
AUTOMATED TEST CASE GENERATION AND OPTIMIZATION: A COMPARATIVE REVIEWijcsit
Software testing is the primary phase, which is performed during software development and it is carried by a sequence of instructions of test inputs followed by expected output. Evolutionary algorithms are most popular in the computational field based on population. The test case generation process is used to identify
test cases with resources and also identifies critical domain requirements. The behavior of bees is based on
population and evolutionary method. Bee Colony algorithm (BCA) has gained superiority in comparison to other algorithms in the field of computation. The Harmony Search (HS) algorithm is based on the enhancement process of music. When musicians compose the harmony through different possible combinations of the music, at that time the pitches are stored in the harmony memory and the optimization
can be done by adjusting the input pitches and generate the perfect harmony. Particle Swarm Optimization (PSO) is an intelligence based meta-heuristic algorithm where each particle can locate their source of food at different position.. In this algorithm, the particles will search for a better food source position in the hope of getting a better result. In this paper, the role of Artificial Bee Colony, particle swarm optimization
and harmony search algorithms are analyzed in generating random test data and optimized those test data.
Test case generation and optimization through bee colony, PSO and harmony search (HS) algorithms which are applied through a case study, i.e., withdrawal operation in Bank ATM and it is observed that these algorithms are able to generate suitable automated test cases or test data in a client manner. This
section further gives the brief details and compares between HS, PSO, and Bee Colony (BC) Optimization
methods which are used for test case or test data generation and optimization.
The optimization of running queries in relational databases using ant colony ...ijdms
The issue of optimizing queries is a cost-sensitive
process and with respect to the number of associat
ed
tables in a query, its number of permutations grows
exponentially. On one hand, in comparison with oth
er
operators in relational database, join operator is
the most difficult and complicated one in terms of
optimization for reducing its runtime. Accordingly,
various algorithms have so far been proposed to so
lve
this problem. On the other hand, the success of any
database management system (DBMS) means
exploiting the query model. In the current paper, t
he heuristic ant algorithm has been proposed to sol
ve this
problem and improve the runtime of join operation.
Experiments and observed results reveal the efficie
ncy
of this algorithm compared to its similar algorithm
s.
The document summarizes the flower pollination algorithm, a nature-inspired optimization technique. It describes how flower pollination occurs in nature through both biotic cross-pollination involving pollinators, and abiotic self-pollination involving wind and water. The algorithm mimics these processes to update solution populations towards optimization. It initializes a population randomly, then iteratively explores through global pollination modeled by Levy flights, and exploits through local pollination. Applications include engineering problems, neural networks, and scheduling.
Flower Pollination Algorithm: A Novel Approach for Multiobjective OptimizationXin-She Yang
This document summarizes a research paper that proposes a novel Flower Pollination Algorithm (FPA) approach for solving multiobjective optimization problems. The FPA is inspired by the natural flower pollination process and extends the previously developed single-objective FPA. It outlines four rules that mimic pollination characteristics like biotic cross-pollination, local pollination, flower constancy, and switching between local and global pollination. The proposed multi-objective FPA is tested on benchmark problems and engineering design problems with promising results, showing its efficiency in obtaining Pareto fronts.
Recent Advances in Flower Pollination AlgorithmEditor IJCATR
Flower Pollination Algorithm (FPA) is a nature inspired algorithm based on pollination process of plants. Recently, FPA
has become a popular algorithm in the evolutionary computation field due to its superiority to many other algorithms. As a
consequence, in this paper, FPA, its improvements, its hybridization and applications in many fields, such as operations research,
engineering and computer science, are discussed and analyzed. Based on its applications in the field of optimization it was seemed that
this algorithm has a better convergence speed compared to other algorithms. The survey investigates the difference between FPA
versions as well as its applications. To add to this, several future improvements are suggested.
Multi-objective Flower Algorithm for OptimizationXin-She Yang
The document proposes a multi-objective flower algorithm (MOFPA) for optimization. MOFPA extends the single-objective flower pollination algorithm (FPA) to solve multi-objective problems. MOFPA uses a weighted sum approach to combine multiple objectives into a single objective function. Random weights are used to find an accurate Pareto front with uniformly distributed solutions. MOFPA is tested on standard benchmark functions and shown to converge quickly, finding Pareto fronts accurately.
The document summarizes the flower pollination algorithm, a nature-inspired optimization technique. It describes how flower pollination occurs in nature through both biotic cross-pollination involving pollinators, and abiotic self-pollination involving wind and water. The algorithm mimics these processes to update solution populations towards optimization. It initializes a population randomly, then iteratively explores through global pollination modeled by Levy flights, and exploits through local pollination. Applications include engineering problems, neural networks, and scheduling.
محاضرات متقدمة تدرس لطلاب حاسبات بنى سويف السنة الثالثة لتنمية قدراتهم البحثية وهذة الموضوعات تدرس على مستوى الدكتوراة - - نريد تميز طلاب حاسبات ليتميزو فى البحث العلمى -
AUTOMATED TEST CASE GENERATION AND OPTIMIZATION: A COMPARATIVE REVIEWijcsit
Software testing is the primary phase, which is performed during software development and it is carried by a sequence of instructions of test inputs followed by expected output. Evolutionary algorithms are most popular in the computational field based on population. The test case generation process is used to identify
test cases with resources and also identifies critical domain requirements. The behavior of bees is based on
population and evolutionary method. Bee Colony algorithm (BCA) has gained superiority in comparison to other algorithms in the field of computation. The Harmony Search (HS) algorithm is based on the enhancement process of music. When musicians compose the harmony through different possible combinations of the music, at that time the pitches are stored in the harmony memory and the optimization
can be done by adjusting the input pitches and generate the perfect harmony. Particle Swarm Optimization (PSO) is an intelligence based meta-heuristic algorithm where each particle can locate their source of food at different position.. In this algorithm, the particles will search for a better food source position in the hope of getting a better result. In this paper, the role of Artificial Bee Colony, particle swarm optimization
and harmony search algorithms are analyzed in generating random test data and optimized those test data.
Test case generation and optimization through bee colony, PSO and harmony search (HS) algorithms which are applied through a case study, i.e., withdrawal operation in Bank ATM and it is observed that these algorithms are able to generate suitable automated test cases or test data in a client manner. This
section further gives the brief details and compares between HS, PSO, and Bee Colony (BC) Optimization
methods which are used for test case or test data generation and optimization.
The optimization of running queries in relational databases using ant colony ...ijdms
The issue of optimizing queries is a cost-sensitive
process and with respect to the number of associat
ed
tables in a query, its number of permutations grows
exponentially. On one hand, in comparison with oth
er
operators in relational database, join operator is
the most difficult and complicated one in terms of
optimization for reducing its runtime. Accordingly,
various algorithms have so far been proposed to so
lve
this problem. On the other hand, the success of any
database management system (DBMS) means
exploiting the query model. In the current paper, t
he heuristic ant algorithm has been proposed to sol
ve this
problem and improve the runtime of join operation.
Experiments and observed results reveal the efficie
ncy
of this algorithm compared to its similar algorithm
s.
Flower patterns improve foraging efficiency in bumblebees by guiding approac...João Soares
Colourful patterns on flowers are thought to benefit both pollinators and the plants they visit, by increasing the plants’ pollination success via an increased foraging efficiency of the pollinators. This increased efficiency is assumed to result from a guidance effect of the flower patterns, correspondingly termed ‘nectar guides’, which indicate the position of the nectary to visiting pollinators, thus reducing their flower handling time. 2. Although it is well established that flower patterns play an important role in flower choice, the mechanisms by which they the foraging efficiency of flower-visiting insects remain poorly understood. 3. In this study, we quantified the contributions of patterns to all phases of flower interaction in the buff-tailed bumblebee (Bombus terrestris). We analysed the bees’flight paths, as well as landing positions and walking tracks on artificial flowers with different pattern types. 4. We reveal that flower patterns reduced the overall flower handling time of the bees by up to 30%, by guiding their approach flight, landing positions, and departure decisions. Surprisingly, we observed no improvement in nectary discovery time after the bee landed on the flower. 5. Since we tested experienced foragers, which represent the majority of insect pollinators active in nature, the newly described nectary-independent guidance effects of flower patterns are of high ecological relevance
THE BUTTERFLY-PARTICLE SWARM OPTIMIZATION (BUTTERFLY-PSO/BF-PSO) TECHNIQUE AN...ijscmcj
The new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm
Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all
optimization techniques. The proposed ‘Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)’ is
inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent
communication during the nectar search process. The BF-PSO introduces new parameters such as
sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying
probability coefficient (α). These parameters improve the searching ability, excellent convergence and the
overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented
for various functions with the multi-dimension problems.
The butterfly particle swarm optimization technique and its variablesijscmcj
he new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all optimization techniques. The proposed 'Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)' is inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent communication during the nectar search process. The BF-PSO introduces new parameters such as sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying probability coefficient (a). These parameters improve the searching ability, excellent convergence and the overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented for various functions with the multi-dimension problems.
THE BUTTERFLY-PARTICLE SWARM OPTIMIZATION (BUTTERFLY-PSO/BF-PSO) TECHNIQUE AN...ijscmcj
The new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all optimization techniques. The proposed ‘Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)’ is inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent communication during the nectar search process. The BF-PSO introduces new parameters such as sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying probability coefficient (α). These parameters improve the searching ability, excellent convergence and the overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented for various functions with the multi-dimension problems.
Physiological and molecular control of sinkactivity, partitioning efficiency ...manjupainkra
This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as roots, seeds and fruits. Photosynthates are transported from sources to sinks via the phloem. The harvest index is defined as the ratio of economic yield to biological yield, representing the efficiency of biomass partitioning. Crop yield is determined by interactions between yield components - including the number of reproductive units and grains - and environmental factors. Improving photosynthetic efficiency, source activity and sink strength will be key to increasing crop yields in the future.
This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as roots, seeds and fruits. Photosynthates are transported from sources to sinks via the phloem. The harvest index is defined as the ratio of economic yield to biological yield, representing the efficiency of biomass partitioning. Crop yield is determined by interactions between yield components - including the number of reproductive units and grains - and environmental factors. Improving photosynthetic efficiency, source activity, and sink strength will be key to increasing crop yields in the future.
Physiological and molecular control of sink activitymanjupainkra
This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as fruits. Sugars are transported from sources to sinks via phloem loading and unloading processes. Harvest index is defined as the ratio of economic yield to total biological yield, and crop yield can be increased by improving either factor or both. Yield components like number of reproductive units and grains per unit also influence overall yield.
This document summarizes research on homeotic genes controlling flower development in Antirrhinum majus (snapdragon). Through transposon mutagenesis, over 15 homeotic mutations were obtained. These were categorized into three types of genes: 1) genes like floricaula that control the transition from inflorescence to floral meristems, 2) genes that affect organ identity and number in floral whorls, and 3) genes that control differences between organs within a whorl. The floricaula gene was isolated and shown to be transiently expressed in specific floral primordia, suggesting it activates genes required for their development. The interactions between these three categories of genes are proposed to underlie
Importance of ecology and different foraging theoriesAaliya Afroz
This document discusses foraging theory and different optimal foraging models. It introduces optimal foraging theory, which predicts that animals will evolve foraging strategies that maximize energy intake per unit time. The optimal foraging model builds on this by generating quantitative predictions of how animals maximize fitness. Models discussed include the optimal diet model, marginal value theorem, and patch departure rules. The marginal value theorem predicts that animals should leave a patch when the marginal intake rate drops below the average habitat rate. The document also discusses various foraging strategies insects use to optimize nectar and pollen collection, such as specialization, learning, and scent marking.
The document describes a new optimization technique called Bees Colony Intelligence that is inspired by the foraging behavior of honey bees. The algorithm is developed to closely mimic how honey bees communicate food sources within the hive. It is then applied to the classical problem of designing a Power System Stabilizer (PSS) to improve power system stability. Simulation results validate that the bee colony algorithm can effectively design a PSS and provide damping over a wide range of operating points. The algorithm is derivative-free, efficient at locating global optima with few iterations, and robust in its convergence properties.
This document describes the development of a prototype pest management system using a wireless sensor network to monitor environmental parameters like temperature, humidity, and leaf wetness in apple and Kutki farms. The sensor data is transmitted wirelessly to a server to alert farmers when infection risk is high so they can take preventative measures and reduce unnecessary pesticide spraying. The system aims to improve crop growth and yield by monitoring conditions and notifying farmers to spray only when needed. The wireless sensor network allows for real-time monitoring across wide farm areas compared to traditional wired systems.
This document discusses insect monitoring techniques like pheromone and light traps. Pheromone traps use sex pheromones to attract specific insect species and are useful for tracking populations over time. Light traps attract a variety of insects. Data from these traps is used for pest forecasting through phenology models, which predict development timing based on temperature, and simulation models. The monitoring data and models help time management practices like pesticide applications and scouting.
This document presents a new meta-heuristic optimization algorithm called Cuckoo Search (CS) that is inspired by the brood parasitism of some cuckoo species and the Lévy flight behavior of some birds and insects. The CS algorithm is formulated based on three idealized rules: each cuckoo lays one egg in a randomly selected nest; the best nests with high-quality eggs are carried over to subsequent generations; and a portion of the worst nests are abandoned. New solutions in CS are generated through Lévy flights. The performance of CS is validated on benchmark test functions and compared to genetic algorithms and particle swarm optimization. Results show that CS can find global optima efficiently.
Pollination is the act of transferring pollen grains from the male anther of a flower to the female stigma. The goal of every living organism, including plants, is to create offspring for the next generation. One of the ways that plants can produce offspring is by making seeds.
Vision based entomology how to effectively exploit color and shape featurescseij
This document proposes an automatic insect identification framework using color and shape features. It extracts RGB color features and shape features from grasshopper and butterfly images. A support vector machine (SVM) classifier is trained on the extracted features to classify insects. The preliminary results demonstrate the effectiveness of using color and shape features for automatic insect identification of two insect classes. The framework could potentially be extended to identify other insect species.
This study investigated the effects of habitat restoration in 12 urban parks in Metro Vancouver on plant and pollinator communities. Restored plots had higher plant species richness and diversity compared to control plots, but similar plant abundance. Pollinator abundance, richness and diversity were not significantly different between restored and control plots. Network analysis found control plots had higher asymmetry, suggesting invasive plants increase network resilience. The results suggest that while restorations improved plant diversity, added native plants did not provide enough additional floral resources to significantly change pollinator communities compared to resources from invasive species in control plots. Managers should ensure alternative forage is available after invasive removal by planting generalist native species with overlapping blooms.
Insect Modeling by Muhammad Qasim, Aroj BashirMuhammad Qasim
Insect Modeling are used for a variety of purposes from study of the dynamics of the Insect population, determine the importance of factors of regulating of population, individual development of insects and future projections of insect development
AN OPTIMIZATION ALGORITHM BASED ON BACTERIA BEHAVIORijaia
Paradigms based on competition have shown to be useful for solving difficult problems. In this paper we present a new approach for solving hard problems using a collaborative philosophy. A collaborative philosophy can produce paradigms as interesting as the ones found in algorithms based on a competitive philosophy. Furthermore, we show that the performance - in problems associated to explosive combinatorial - is comparable to the performance obtained using a classic evolutive approach.
CROP MODELING IN VEGETABLES ( AABID AYOUB SKUAST-K).pptxAabidAyoub
crop modeling is future in agriculture to tackle changing environment conditions and increase food security in the world. These models incorporate various factors such as climate, soil characteristics, agronomic practices, and crop physiology to predict crop yields, water usage, nutrient uptake, and other important parameters. Crop modeling helps in understanding the complex interactions between different variables affecting crop growth and assists farmers, researchers, and policymakers in making informed decisions related to crop management, resource allocation, and risk assessment.
Role of AI in crop modeling: Artificial Intelligence (AI) plays a significant role in enhancing crop modeling by leveraging advanced computational techniques to improve model accuracy, efficiency, and scalability. One of the most important aspects of precision farming is sustainability. Using artificial neural networks (ANNs), a highly effective multilayer perceptron (MLP) model. The most common type in crop modeling is DSSAT , DSSAT (Decision Support System for Agro-technology Transfer).The Decision Support System for Agro-technology Transfer (DSSAT) is a software application program that comprises crop simulation models for over 42 crops (as of Version 4.8.2) as well as tools to facilitate effective use of the models. The tools include database management programs for soil, weather, crop management and experimental data, utilities, and application programs. The crop simulation models simulate growth, development and yield as a function of the soil-plant-atmosphere dynamics.DSSAT and its crop simulation models have been used for a wide range of applications at different spatial and temporal scales. This includes on-farm and precision management, regional assessments of the impact of climate variability and climate change, gene-based modeling and breeding selection, water use, greenhouse gas emissions, and long-term sustainability through the soil organic carbon and nitrogen balances.In conclusion, crop modeling stands as a crucial tool in modern agriculture, offering a systematic approach to understanding and predicting crop growth dynamics in diverse environmental conditions. By simulating the complex interactions between various factors influencing crop development, including climate, soil properties, agronomic practices, and genetic traits, crop models provide valuable insights for farmers, researchers, and policymakers.
Cuckoo Search Algorithm: An IntroductionXin-She Yang
This presentation explains the fundamental ideas of the standard Cuckoo Search (CS) algorithm, which also contains the links to the free Matlab codes at Mathswork file exchanges and the animations of numerical simulations (video at Youtube). An example of multi-objective cuckoo search (MOCS) is also given with link to the Matlab code.
Metaheuristic Algorithms: A Critical AnalysisXin-She Yang
The document discusses metaheuristic algorithms and their application to optimization problems. It provides an overview of several nature-inspired algorithms including particle swarm optimization, firefly algorithm, harmony search, and cuckoo search. It describes how these algorithms were inspired by natural phenomena like swarming behavior, flashing fireflies, and bird breeding. The document also discusses applications of these algorithms to engineering design problems like pressure vessel design and gear box design optimization.
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Flower patterns improve foraging efficiency in bumblebees by guiding approac...João Soares
Colourful patterns on flowers are thought to benefit both pollinators and the plants they visit, by increasing the plants’ pollination success via an increased foraging efficiency of the pollinators. This increased efficiency is assumed to result from a guidance effect of the flower patterns, correspondingly termed ‘nectar guides’, which indicate the position of the nectary to visiting pollinators, thus reducing their flower handling time. 2. Although it is well established that flower patterns play an important role in flower choice, the mechanisms by which they the foraging efficiency of flower-visiting insects remain poorly understood. 3. In this study, we quantified the contributions of patterns to all phases of flower interaction in the buff-tailed bumblebee (Bombus terrestris). We analysed the bees’flight paths, as well as landing positions and walking tracks on artificial flowers with different pattern types. 4. We reveal that flower patterns reduced the overall flower handling time of the bees by up to 30%, by guiding their approach flight, landing positions, and departure decisions. Surprisingly, we observed no improvement in nectary discovery time after the bee landed on the flower. 5. Since we tested experienced foragers, which represent the majority of insect pollinators active in nature, the newly described nectary-independent guidance effects of flower patterns are of high ecological relevance
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The new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm
Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all
optimization techniques. The proposed ‘Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)’ is
inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent
communication during the nectar search process. The BF-PSO introduces new parameters such as
sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying
probability coefficient (α). These parameters improve the searching ability, excellent convergence and the
overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented
for various functions with the multi-dimension problems.
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he new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all optimization techniques. The proposed 'Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)' is inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent communication during the nectar search process. The BF-PSO introduces new parameters such as sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying probability coefficient (a). These parameters improve the searching ability, excellent convergence and the overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented for various functions with the multi-dimension problems.
THE BUTTERFLY-PARTICLE SWARM OPTIMIZATION (BUTTERFLY-PSO/BF-PSO) TECHNIQUE AN...ijscmcj
The new presented Butterfly-PSO technique (or BF-PSO) is basically originated by Particle Swarm Optimization (PSO). The Butterfly-PSO technique (BF-PSO) appears as a new growing star among all optimization techniques. The proposed ‘Butterfly- Particle Swarm Optimization (Butterfly or BF-PSO)’ is inspired by butterfly natural intelligence, character, behavior, intelligent network and intelligent communication during the nectar search process. The BF-PSO introduces new parameters such as sensitivity of butterfly (s), probability of food (nectar) (p), the degree of the node and the time varying probability coefficient (α). These parameters improve the searching ability, excellent convergence and the overall performance of the Butterfly-PSO effectivly. The BF-PSO optimizations results have been presented for various functions with the multi-dimension problems.
Physiological and molecular control of sinkactivity, partitioning efficiency ...manjupainkra
This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as roots, seeds and fruits. Photosynthates are transported from sources to sinks via the phloem. The harvest index is defined as the ratio of economic yield to biological yield, representing the efficiency of biomass partitioning. Crop yield is determined by interactions between yield components - including the number of reproductive units and grains - and environmental factors. Improving photosynthetic efficiency, source activity and sink strength will be key to increasing crop yields in the future.
This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as roots, seeds and fruits. Photosynthates are transported from sources to sinks via the phloem. The harvest index is defined as the ratio of economic yield to biological yield, representing the efficiency of biomass partitioning. Crop yield is determined by interactions between yield components - including the number of reproductive units and grains - and environmental factors. Improving photosynthetic efficiency, source activity, and sink strength will be key to increasing crop yields in the future.
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This document discusses source-sink relationships in plants and factors that influence crop yield. It defines sources as regions where organic materials are synthesized, such as leaves, and sinks as non-photosynthetic organs that import photosynthates, such as fruits. Sugars are transported from sources to sinks via phloem loading and unloading processes. Harvest index is defined as the ratio of economic yield to total biological yield, and crop yield can be increased by improving either factor or both. Yield components like number of reproductive units and grains per unit also influence overall yield.
This document summarizes research on homeotic genes controlling flower development in Antirrhinum majus (snapdragon). Through transposon mutagenesis, over 15 homeotic mutations were obtained. These were categorized into three types of genes: 1) genes like floricaula that control the transition from inflorescence to floral meristems, 2) genes that affect organ identity and number in floral whorls, and 3) genes that control differences between organs within a whorl. The floricaula gene was isolated and shown to be transiently expressed in specific floral primordia, suggesting it activates genes required for their development. The interactions between these three categories of genes are proposed to underlie
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This document discusses foraging theory and different optimal foraging models. It introduces optimal foraging theory, which predicts that animals will evolve foraging strategies that maximize energy intake per unit time. The optimal foraging model builds on this by generating quantitative predictions of how animals maximize fitness. Models discussed include the optimal diet model, marginal value theorem, and patch departure rules. The marginal value theorem predicts that animals should leave a patch when the marginal intake rate drops below the average habitat rate. The document also discusses various foraging strategies insects use to optimize nectar and pollen collection, such as specialization, learning, and scent marking.
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Flower Pollination Algorithm for Global Optimization
1. arXiv:1312.5673v1 [math.OC] 19 Dec 2013
Flower Pollination Algorithm for Global Optimization
Xin-She Yang
Department of Engineering, University of Cambridge,
Trumpington Street, Cambridge CB2 1PZ, UK.
Abstract
Flower pollination is an intriguing process in the natural world. Its evolutionary
characteristics can be used to design new optimization algorithms. In this paper, we
propose a new algorithm, namely, flower pollination algorithm, inspired by the pollina-tion
process of flowers. We first use ten test functions to validate the new algorithm,
and compare its performance with genetic algorithms and particle swarm optimization.
Our simulation results show the flower algorithm is more efficient than both GA and
PSO. We also use the flower algorithm to solve a nonlinear design benchmark, which
shows the convergence rate is almost exponential.
Citation Details: Xin-She Yang, Flower pollination algorithm for global optimiza-tion,
in: Unconventional Computation and Natural Computation 2012, Lecture Notes in
Computer Science, Vol. 7445, pp. 240-249 (2012).
1 Introduction
Nature has been solving challenging problems over millions and billions of years, and many
biological systems have evolved with intriguing and surprising efficiency in maximizing their
evolutionary objectives such as reproduction. Based on the successfully characteristics of
biological systems, many nature-inspired algorithms have been developed over the last few
decades [18, 20]. For example, genetic algorithms were based on the Darwinian evolution of
biological systems [9] and particle swarm optimization was based on the swarm behaviour
of birds and fish [11, 12], which bat algorithm was based on the echolocation behaviour
of microbats [21] and firefly algorithm was based on the flashing light patterns of tropic
fireflies [18, 19]. All these algorithms have been applied to a wide range of applications.
In many design applications in engineering and industry, we have to try to find the
optimal solution to a given problem under highly complex constraints. Such constrained
optimization problems are often highly nonlinear, to find the optimal solutions is often a
very challenging task if it is not impossible. Most conventional optimization do not work well
for problems with nonlinearity and multimodality. Current trend is to use nature-inspired
metaheuristic algorithms to tackle such difficult problems, and it has been shown that
metaheuristics are surprisingly very efficient. For this reason, the literature of metaheuristics
has expanded tremendously in the last two decades [18, 20]. Up to now, researchers have
only use a very limited characateristics inspired by nature, and there is room for more
algorithm development.
In this paper, we will propose a new algorithm based on the flower pollination process of
flowering plants. We will first briefly review the main characteristics of flower pollination,
2. and thus idealize these characteristics into four rules. We will then use them to develop a
flower pollination algorithm (FPA), or the flower algorithm. Then, we validate it using a set
of well-known test functions and design benchmark. We analyze the simulations and make
comparison of its performance with genetic algorithm and particle swarm optimization.
Finally, we discuss further topics for extending this algorithm.
From the biological evolution point of view, the objective of the flower pollination is
the survival of the fittest and the optimal reproduction of plants in terms of numbers as
well as most fittest. This is in fact an optimization process of plant species. All the above
factors and processes of flower pollination interact so as to achieve optimal reproduction of
the flowering plants. Therefore, this can inspire to design new optimization algorithm. The
basic idea of flower pollination in the context of bees and clustering was investigated before
[10], but in this paper, we will design a completely new optimization solely based on the
flower pollination characteristics.
2 Characteristics of Flower Pollination
It is estimated that there are over a quarter of a million types of flowering plants in Nature
and that about 80% of all plant species are flowering species. It still remains partly a
mystery how flowering plants came to dominate the landscape from Cretaceous period
[16, 22]. Flowering plant has been evolving for more than 125 million years and flowers
have become so influential in evolution, we cannot image how the plant world would be
without flowers. The main purpose of a a flower is ultimately reproduction via pollination.
Flower pollination is typically associated with the transfer of pollen, and such transfer is
often linked with pollinators such as insects, birds, bats and other animals. In fact, some
flowers and insects have co-evolved into a very specialized flower-pollinator partnership. For
example, some flowers can only attract and can only depend on a specific species of insects
for successful pollination [7].
Pollination can take two major forms: abiotic and biotic. About 90% of flowering plants
belong to biotic pollination, that is, pollen is transferred by a pollinator such as insects and
animals. About 10% of pollination takes abiotic form which does not require any pollinators.
Wind and diffusion in water help pollination of such flowering plants and grass is a good
example [14, 7]. Pollinators, or sometimes called pollen vectors, can be very diverse. It is
estimate there are at least 200,000 variety of pollinators such as insects, bats and birds.
Honeybees are a good example of pollinator, and they can also developed the so-called
flower constancy [3]. That is, these pollinators tend to visit exclusive certain flower species
while bypassing other flower species. Such flower constancy may have evolutionary advan-tages
because this will maximize the transfer of flower pollen to the same or conspecific
plants, and thus maximizing the reproduction of the same flower species. Such flower con-stancy
may be advantageous for pollinators as well, because they can be sure that nectar
supply is available with their limited memory and minimum cost of learning or exploring.
Rather than focusing on some unpredictable but potentially more rewarding new flower
species, flower constancy may require minimum investment cost and more likely guaranteed
intake of nectar [17].
Pollination can be achieved by self-pollination or cross-pollination. Cross-pollination,
or allogamy, means pollination can occur from pollen of a flower of a different plant, while
self-pollination is the fertilization of one flower, such as peach flowers, from pollen of the
same flower or different flowers of the same plant, which often occurs when there is no
3. reliable pollinator available.
Biotic, cross-pollination may occur at long distance, and the pollinators such as bees,
bats, birds and flies can fly a long distance, thus they can considered as the global pollina-tion.
In addition, bees and birds may behave as L´evy flight behaviour [13], with jump or
fly distance steps obey a L´evy distribution. Furthermore, flower constancy can be used an
increment step using the similarity or difference of two flowers.
3 Flower Pollination Algorithm
Now we can idealize the above characteristics of pollination process, flower constancy and
pollinator behaviour as the following rules:
1. Biotic and cross-pollination is considered as global pollination process with pollen-carrying
pollinators performing L´evy flights.
2. Abiotic and self-pollination are considered as local pollination.
3. Flower constancy can be considered as the reproduction probability is proportional
to the similarity of two flowers involved.
4. Local pollination and global pollination is controlled by a switch probability p ∈ [0, 1].
Due to the physical proximity and other factors such as wind, local pollination can
have a significant fraction p in the overall pollination activities.
Obviously, in reality, each plant can have multiple flowers, and each flower patch often
release millions and even billions of pollen gametes. However, for simplicity, we also assume
that each plant only has one flower, and each flower only produce one pollen gamete. Thus,
there is no need to distinguish a pollen gamete, a flower, a plant or solution to a problem.
This simplicity means a solution xi is equivalent to a flower and/or a pollen gamete. In
future studies, we can easily extend to multiple pollen gametes for each flower and multiple
flowers for multiobjective optimization problems.
From the above discussions and the idealized characteristics, we can design a flower-based
on algorithm, namely, flower pollination algorithm (FPA). There are two key steps
in this algorithm, they are global pollination and local pollination.
In the global pollination step, flower pollens are carried by pollinators such as insects,
and pollens can travel over a long distance because insects can often fly and move in a much
longer range. This ensures the pollination and reproduction of the most fittest, and thus
we represent the most fittest as g. The first rule plus flower constancy can be represented
mathematically as
xt+1
i = xt
i + L(xt
i − g), (1)
where xtiis the pollen i or solution vector xi at iteration t, and g is the current best
solution found among all solutions at the current generation/iteration. The parameter L
is the strength of the pollination, which essentially is a step size. Since insects may move
over a long distance with various distance steps, we can use a L´evy flight to mimic this
characteristic efficiently [13, 15]. That is, we draw L 0 from a Levy distribution
L ∼
λ(λ) sin(πλ/2)
π
1
s1+ , (s ≫ s0 0). (2)
4. Flower Pollination Algorithm (or simply Flower Algorithm)
Objective min or max f(x), x = (x1, x2, ..., xd)
Initialize a population of n flowers/pollen gametes with random solutions
Find the best solution g in the initial population
Define a switch probability p ∈ [0, 1]
while (t MaxGeneration)
for i = 1 : n (all n flowers in the population)
if rand p,
Draw a (d-dimensional) step vector L which obeys a L´evy distribution
Global pollination via xt+1
i = xti
+ L(g − xti
)
else
Draw ǫ from a uniform distribution in [0,1]
Randomly choose j and k among all the solutions
Do local pollination via xt+1
i = xti
+ ǫ(xt
j − xt
k)
end if
Evaluate new solutions
If new solutions are better, update them in the population
end for
Find the current best solution g
end while
Figure 1: Pseudo code of the proposed Flower Pollination Algorithm (FPA).
Here (λ) is the standard gamma function, and this distribution is valid for large steps
s 0. In all our simulations below, we have used λ = 1.5.
The local pollination (Rule 2) and flower constancy can be represented as
xt+1
i = xt
i + ǫ(xt
j − xt
k), (3)
where xt
j and xt
k are pollens from the different flowers of the same plant species. This
essentially mimic the flower constancy in a limited neighborhood. Mathematically, if xt
j
and xt
k comes from the same species or selected from the same population, this become a
local random walk if we draw ǫ from a uniform distribution in [0,1].
Most flower pollination activities can occur at both local and global scale. In practice,
adjacent flower patches or flowers in the not-so-far-away neighborhood are more likely to be
pollinated by local flower pollens that those far away. For this, we use a switch probability
(Rule 4) or proximity probability p to switch between common global pollination to intensive
local pollination. To start with, we can use p = 0.5 as an initially value and then do a
parametric study to find the most appropriate parameter range. From our simulations, we
found that p = 0.8 works better for most applications.
The above two key steps plus the switch condition can be summarized in the pseudo
code shown in Fig. 1.
4 Numerical Results
Any new optimization should be extensively validated and comparison with other algo-rithms.
There are many test functions, at least over a hundred well-know test functions
However, there is no agreed set of test functions for validating new algorithms, though there
some review and literature [1, 5, 19]. In this paper, we will choose a diverse subset of such
test functions to validate our proposed Flower Pollination Algorithm (FPA).
5. In addition, we will also compare the performance of our algorithm with that of genetic
algorithms [8] and particle swarm optimization [11, 12]. Furthermore, we will also apply
FPA to solve a well-known pressure vessel design benchmark [2, 6].
4.1 Test Functions
The Ackley function can be written as
f(x) = −20 exp h −
1
5
vuut
1
d
d
Xi
=1
x2
i i − exp h1
d
d
Xi
=1
cos(2πxi)i + 20 + e, (4)
which has a global minimum f = 0 at (0, 0, ..., 0).
The simplest of De Jong’s functions is the so-called sphere function
f(x) =
n
Xi
=1
x2
i , −5.12 ≤ xi ≤ 5.12, (5)
whose global minimum is obviously f = 0 at (0, 0, ..., 0). This function is unimodal and
convex.
Easom’s function
f(x) = −cos(x) cos(y) exp h − (x − π)2 + (y − π)2i, (6)
whose global minimum is f = −1 at x = (π, π) within −100 ≤ x, y ≤ 100. It has many
local minima.
Griewangk’s function
f(x) =
1
4000
n
Xi
=1
x2
i −
n
Y
i=1
cos(
xi √i
) + 1, −600 ≤ xi ≤ 600, (7)
whose global minimum is f = 0 at x = (0, 0, ..., 0). This function is highly multimodal.
Michaelwicz’s function
f(x) = −
n
Xi
=1
sin(xi) · h sin(
ix2
i
π
)i2m
, (8)
where m = 10, and 0 ≤ xi ≤ π for i = 1, 2, ..., n. In 2D case, we have
f(x, y) = −sin(x) sin20(
x2
π
) − sin(y) sin20(
2y2
π
), (9)
where (x, y) ∈ [0, 5] × [0, 5]. This function has a global minimum f ≈ −1.8013 at
x = (x, y) = (2.20319, 1.57049).
Rastrigin’s function
f(x) = 10n +
n
Xi
=1
i − 10 cos(2πxi)i, −5.12 ≤ xi ≤ 5.12, (10)
hx2
whose global minimum is f = 0 at (0, 0, ..., 0). This function is highly multimodal.
6. Rosenbrock’s function
f(x) =
n−1
Xi
=1
h(xi − 1)2 + 100(xi+1 − x2
i )2i, (11)
whose global minimum f = 0 occurs at x = (1, 1, ..., 1) in the domain −5 ≤ xi ≤ 5 where
i = 1, 2, ..., n. In the 2D case, it is often written as
f(x, y) = (x − 1)2 + 100(y − x2)2, (12)
which is often referred to as the banana function.
Schwefel’s function
f(x) = −
n
Xi
=1
xi sin q|xi|, −500 ≤ xi ≤ 500, (13)
whose global minimum f ≈ −418.9829n occurs at xi = 420.9687 where i = 1, 2, ..., n.
Yang’s forest-like function [20]
f(x) =
d
=1 |xi| exp h −
Xi
d
Xi
=1
i )i, −2π ≤ xi ≤ 2π, (14)
sin(x2
has a global minimum f = 0 at (0, 0, ..., 0).
Shubert’s function
f(x) = h
n
Xi
=1
i cos i + (i + 1)xi · h
n
Xi
=1
i cos i + (i + 1)yi, (15)
which has 18 global minima f ≈ −186.7309 for n = 5 in the search domain −10 ≤ x, y ≤ 10.
Table 1: Comparison of algorithm performance in terms of number of iterations.
Functions/Algorithms GA PSO FPA
Michalewicz (d=16) 89325 ± 7914(95%) 6922 ± 537(98%) 3341 ± 649(100%)
Rosenbrock (d=16) 55723 ± 8901(90%) 32756 ± 5325(98%) 5532 ± 1464(100%)
De Jong (d=256) 25412 ± 1237(100%) 17040 ± 1123(100%) 4245 ± 545(100%)
Schwefel (d=128) 227329 ± 7572(95%) 14522 ± 1275(97%) 6851 ± 448(100%)
Ackley (d=128) 32720 ± 3327(90%) 23407 ± 4325(92%) 3357 ± 968(100%)
Rastrigin 110523 ± 5199(77%) 79491 ± 3715(90%) 10840 ± 2689(100%)
Easom 19239 ± 3307(92%) 17273 ± 2929(90%) 4017 ± 982(100%)
Griewank 70925 ± 7652(90%) 55970 ± 4223(92%) 4918 ± 1429(100%)
Yang (d = 16) 27923 ± 3025(83%) 14116 ± 2949(90%) 4254 ± 1839(100%)
Shubert(18 minima) 54077 ± 4997(89%) 23992 ± 3755(92%) 9271 ± 1758(100%)
For the above ten test functions, each function can have varied dimensions; then there
is an issue which dimensions should be used in the simulations. Research suggests that
higher-dimensional problems tend to be more challenging, and a new algorithm should be
7. tested against a wide range of functions in terms of function properties and dimensions.
Therefore, we tend to focus on problems with higher dimensions.
In addition, we have used three algorithms to find their optimal solution with a given
tolerance 10−5. The three algorithms are genetic algorithm (GA), particle swarm optimiza-tion
(PSO) and the new flower pollination algorithm (FPA). For each algorithm, we have
carried out 100 independent runs using a population size n = 25 and p = 0.8 for FPA,
crossover probability 0.95 and mutation probability 0.05 for GA, and learning parameters
2 for PSO. The results are summarized in Table 1. In the table, the results are provided
as mean ± standard deviation (success rate). For example, 3341 ± 649(100%) means that
mean number iterations is 3341 with one standard deviation of 649 and a success rate of
100%. The total number of function evaluations is n times the mean number of iterations.
For example, the number of iterations is 3341 in the table, so the total number of function
evaluations is 3341n = 3341 × 25 = 83525.
4.2 Design Optimization
Pressure vessels are literally everywhere such as champagne bottles and gas tanks. For a
given volume and working pressure, the basic aim of designing a cylindrical vessel is to
minimize the total cost. Typically, the design variables are the thickness d1 of the head,
the thickness d2 of the body, the inner radius r, and the length L of the cylindrical section
[2]. This is a well-known test problem for optimization and it can be written as
minimize f(x) = 0.6224d1rL + 1.7781d2r2 + 3.1661d2
1L + 19.84d2
1r, (16)
subject to the following constraints
g1(x) = −d1 + 0.0193r ≤ 0
g2(x) = −d2 + 0.00954r ≤ 0
g3(x) = −πr2L − 4
3 r3 + 1296000 ≤ 0
g4(x) = L − 240 ≤ 0.
(17)
The simple bounds are
0.0625 ≤ d1, d2 ≤ 99 × 0.0625, (18)
and
10.0 ≤ r, L ≤ 200.0. (19)
Recently, Cagnina et al (2008) used an efficient particle swarm optimiser to solve this
problem and they found the best solution
f ≈ 6059.714, (20)
at
x ≈ (0.8125, 0.4375, 42.0984, 176.6366). (21)
This means the lowest price is about $6059.71.
Using the proposed flower pollination algorithm, we have easily found the same as the
solution f ≈ 6059.714 obtained by Cagnina et al [2, 6].
The current best solution can be stored during iterations. Then, we can calculate the
errors D in terms of the difference between the current solution to the best mean solution
8. 102
10−2
10−4
10−6
10−8
0 200 400 600 800 1000
100
iterations
D
GA
PSO
FPA
Figure 2: Error variations and comparison of GA, PSO and FPA.
after 40 independent runs. Figure 2 shows the typical variations of D during iterations.
We can also see that the proposed algorithm approaches the optimal solution exponentially
(see Fig. 2).
Among the three methods, the proposed FPA obtained the best result and converged
most quickly.
5 Discussions
Flowering plants have evolved some interesting features of flower pollination, and we have
successfully developed a new flower algorithm to mimic these characteristics. Our simulation
results have shown that the the proposed flower pollination algorithm is very efficient and
can outperform both genetic algorithm and particle swarm optimization. The convergence
rate is essentially exponential as we have seen from the convergence comparison in the
previous section.
The reasons that FPA is efficient can be twofold: long-distance pollinators and flower
consistency. Pollinators such as insects can travel long distance, and thus they introduce
the ability (into the algorithm) that they can escape any local landscape and subsequently
explore larger search space. This acts as exploration moves. On the other hand, flower
consistency ensure that the same species of the flowers (thus similar solutions) are chosen
more frequently and thus guarantee the convergence more quickly. This step is essentially an
exploitation step. The interplay and interaction of these key components and the selection
of the best solution g ensure that the algorithm is very efficient.
6 Conclusions
In the present algorithm, for simplicity, we have assumed that each flower only produce one
pollen gamete, this simplifies the implementation greatly. However, to assign each flower
with multiple pollen gametes and each plant with multiple flowers can have some advantages
for some applications such as image compression, multiobjective optimization, and graph
colouring. This can form a topic for further research.
9. Another possible extension is to use design other schemes for flower constancy. At
present, this constancy is realized by a simple formula. Other more exotic form may be
useful to certain type of problem, though the exact improvement may need some extensive
simulations.
Furthermore, it is possible to extend the flower algorithm to a discrete version so that it
can solve combinatorial optimization problems. All these extensions will be very useful. We
hope that this paper will inspire more active research in metaheuristics in the near future.
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