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An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
An invasive weed optimization (iwo) approach
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An invasive weed optimization (iwo) approach

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  • 1. INTERNATIONAL JOURNAL and Technology (IJMET), ISSN ENGINEERINGInternational Journal of Mechanical Engineering OF MECHANICAL 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 3, Issue 3, September - December (2012), pp. 627-637 IJMET© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2012): 3.8071 (Calculated by GISI)www.jifactor.com ©IAEME AN INVASIVE WEED OPTIMIZATION (IWO) APPROACH FOR MULTI-OBJECTIVE JOB SHOP SCHEDULING PROBLEMS (JSSPs) Hymavathi Madivada1, C.S.P. Rao21 (Research Scholar, Department of Mechanical Engineering, National Institute of Technology – Warangal, Warangal – 506004, India, hyma.madivada07@gmail.com) 2 (Professor, Department of Mechanical Engineering, National Institute of Technology – Warangal, Warangal – 506004, India, csp_rao@rediffmail.com, csp_rao63@yahoo.com)ABSTRACT In this paper, a new meta-heuristic solution approach for Multi-objective Job ShopScheduling Problems (JSSP) is presented. The proposed algorithm makes use of Mehrabian &Lucas’s heuristic ‘Invasive Weed Optimization’ (IWO) in generating optimal schedules. Forperformance evaluation of solutions in a Multi-objective scenario, a concept called’ Fuzzydominance’ has been employed. The results obtained from our study have shown that theproposed algorithm can be used as a new alternative solution technique for finding goodsolutions to the complex Multi-objective Job Shop Scheduling problems.Keywords:Invasive Weed Optimization, Job Shop scheduling, Metahueristics, Multi-Objective Optimization1. INTRODUCTION1.1. Job Shop Scheduling Scheduling may be viewed as an optimization process where limited resources areallocated over time among both parallel and sequential activities.It comes into picture whencertain activities are to be carried out with limited resources. In a Job-shop SchedulingProblem (JSSP) activities refer to the operations on jobs and resources refer to machinehours. It is a NP-hard problem. In many cases, the combination of goals and resourcesexponentially increases the search space, and thus the generation of good schedule is difficultbecause we have a very large combinatorial search space. Several problems in variousindustrial environments are combinatorial. This is the case for numerous scheduling andplanning problems. Generally, it is extremely difficult to solve this type of problems in theirgeneral form, as it comprises several concurrent goals and several resources which must beallocated to lead to our goals, which are to maximize the utilization of individuals and/or machinesand minimize the time required to complete the entire process being scheduled. Therefore, the exact 627
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEmethods such as the branch and bound method, dynamic programming and constraint logicprogramming need a lot of time to find an optimal solution. So, we expect to find not necessarily anoptimal solution, but a good one to solve the problem. Realistically, we are satisfied by obtaining agood solution near the optimal one. New search techniques such as genetic algorithms, simulatedannealing or tabu search[2] are able to lead to our objective i.e. to find near-optimal solutions for awide range of combinatorial optimization problems. The task of production scheduling consists in the temporal planning of the processing of agiven set of orders. The processing of an order corresponds to the production of a particular product.It is accomplished by the execution of a set of operations in a predefined sequence on certainresources, subject to several constraints. The result of scheduling is a schedule showing the temporalassignment of operations of orders to the resources to be used. Each operation can be performed bysome machines with different processing times. The difficulty is to find a good assignment of anoperation to a machine in order to obtain a schedule which minimizes the total elapsed time (make-span).1.2. Multi-Objective Job Shop Scheduling Problem Multi Objective Job Shop Scheduling Problem deals with sequencing the operations so thatgiven set of objectives are achieved. One cannot identify a single solution that simultaneouslyoptimizes each objective. While searching for solutions, one reaches points such that, whenattempting to improve an objective further, other objectives suffer as a result. A tentative solution iscalled non-dominated, Pareto optimal, or Pareto efficient if it cannot be eliminated from considerationby replacing it with another solution which improves an objective without worsening another one.Finding such non-dominated solutions, and quantifying the trade-offs in satisfying the differentobjectives, is the goal when setting up and solving a multi objective optimization problem.In the present work an attempt has been made to find the solution to Multi Objective Job ShopScheduling the objectives considered being • Minimizing Make-span, make-span being the maximum completion time of all jobs or the time taken to complete the last job on the last machine in the schedule. • Minimizing Tardiness, tardiness being the lateness of the job if it fails to meet its due-date, and zero otherwise. • Minimizing Mean Flow-time which measures the average response of the schedule to individual demands of jobs for service.2. A REVIEW OF INVASIVE WEED OPTIMIZATION (IWO) Invasive weed optimization (lWO), first designed and developed by Mehrabian and Lucas, isa relatively novel numerical stochastic optimization algorithm inspired from colonization of invasiveweeds. The algorithm is simple but has shown to be effective in converging to optimal solution byemploying basic properties, e.g. seeding, growth and competition, in a weed colony. A weed is anyplant growing where it is not wanted; any tree, vine, shrub or herb may qualify as a weed, in anyspecified geographical area, depending on the situation. Weeds have shown a very robust andadaptive nature that renders them undesirable plants in agriculture. In D-dimensional search space, aweed which represents a potential solution of the objective function is represented by W = (w1, w2,·· ,wm) . Firstly, M weeds, called a population of plants, are initialized with random growth position, andthen each weed produces seeds depending on its fitness and the colonys lowest fitness and highestfitness to simulate the natural survival of the fittest process. The number of seeds each plant produceincreases linearly from minimum possible seed production to its maximum. The generated seeds arebeing distribution randomly in the search area by normal distribution with mean equal to zero and avariance parameter decreasing over the number of iteration. By setting the mean equal to zero, theseeds are distributed randomly such that they locate near to the parent plant and by decreasing thevariance over time, the fitter plants are grouped together and inappropriate plants are eliminated overtimes. The whole process is depicted in Fig 1 shown below [1] . The model and simulation of thecolonizing behavior of weeds in order as a novel optimization algorithm, with some basic propertiesof the colonization process is presented in the following steps given below. 628
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME2.1 Initialization A finite number of seeds are being dispread over the D-dimensional problem space withrandom positions (initializing a population) Fig 1: Flowchart for Invasive Weed Optimization Algorithm 629
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME2.2 Reproduction Every seed grows to a flowering plant and produces seeds depending on their fitness(reproduction): a member of the colony of weeds is allowed to produce seeds depending onits own and the lowest and highest fitness values of the colony, where the number of seedseach plant produces increases linearly from a possible minimum to its maximum; in otherwords, a plant will produce seeds based on its fitness and the lowest and highest fitnessvalues of the colony to ensure that the increase is linear. This step adds a significant propertyto the search algorithm. In evolutionary algorithms that are adopted to solve optimizationproblems, intuitively, the infeasible individuals are not allowed to be reproduced, and feasibleindividuals could be thought to be the ones with better fitness values than infeasibleindividuals, although it is possible that some of the infeasible individuals carry more usefulinformation than feasible individuals during the evolution process; in the reproductionmethod, this chance is given to infeasible individuals to survive and reproduce similar to themechanisms that occur in nature2.3 Spatial Dispersion The produced seeds are being randomly dispread over the search area and grow tonew plants (spatial dispersal): the generated seeds are being randomly distributed over the D-dimensional search space by normally distributed random numbers with a mean equal to zerobut with a varying variance of Witer. Thus, seeds will be randomly distributed such that theyabide near the parent plant. The SD of the random function is reduced from a previouslydefined initial value Wini to a final value Wfin in every step (generation). In simulations, anonlinear alteration has shown satisfactory performance. ୧୲ୣ୰ౣ౗౮ ି୧୲ୣ୰ ୬w୧୲ୣ୰ =ቀ ቁ ሺw୧୬୧ െ wϐ୧୬ ሻ+ wϐ୧୬ ………..(1) ୧୲ୣ୰ౣ౗౮Where itermax is the maximum number of iterations, Witer the SD at the present time stepand n the nonlinear modulation index. This alteration ensures that the probability of droppinga seed in a distant area decreases nonlinearly at each time step, which results in groupingfitter plants and the elimination of inappropriate plants2.4 Competitive-Exclusion This process continues until the maximum number of plants is attained by fastreproduction. At this stage, only the plants with higher fitness can survive and produce seeds,whereas others are eliminated (competitive exclusion). In this process, after the maximumnumber of weeds in a colony is reached, each weed is allowed to produce seeds, spread themover the search area, and find their position and rank together with their parents. Next, weedswith lower fitness values are eliminated in order to attain the maximum allowable populationin a colony. The course continues until the maximum iterations are reached and hopefully theplant with the best fitness is the closest to the optimal solution. . It is worth mentioning thatthe IWO has some distinctive properties when compared with the traditional GA and othernumerical search algorithms, such as reproduction, spatial dispersal and competitiveexclusion. In addition, no genetic operators are employed in the proposed algorithm, whichmakes it more dissimilar from the GA. In this way the algorithm mimics the ecological process of weed colonization and hasbeen proved to be a powerful tool for finding out competitive solutions. It is capable ofsolving general multi-dimensional, linear and non-linear optimization problems withappreciable efficiency. It has been shown to be statistically significant than some state of artexisting evolutionary algorithms. 630
  • 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME3. IMPLEMENTATION OF IWOFOR SOLVING MULTI-OBJECTIVE JSSP3.1 Weed representation of JSSP solution The solution to JSSP is a schedule of operation for jobs. In the present work IWO isused to find the optimum schedule[2]. A weed represents feasible schedule in this case .Thisis similar to a chromosome representing feasible schedule in case of genetic algorithm. In thepresent work a direct approach “Operation based representation” is employed. Following isthe brief description of the representation. The schedule is represented in the form of a stringas shown in figure 3.1. The representation encodes a schedule as a sequence of operations,and each character of the string stands for one operation. All operations for a job arerepresented by the same symbol, the job number and they are interpreted according to theorder of their occurrence in the sequence in which they appear in the solution string. In thiscase the string is called weed and the algorithm IWO is used to evolve these weeds todiscover potential schedules. For example, for a three-job-three-machine problem therepresentation would be as shown below. 3 2 1 2 1 3 3 1 23.2 Inputs for the problemFor solving JSSP using IWO, the following inputs are required: • Number of jobs • Number of Machines • Machine order for all the jobs • Processing Times of all the operations • Due dates for all the jobs • Number of iterations to be carried out • Maximum population allowable • Initial and Final standard deviations of seeds from parent weed • Nonlinear modulation index for finding out standard deviation in each iteration.3.3 Step-wise implementation of IWO for JSSP This section gives a detailed explanation of implementation of the algorithm. Theactual algorithm has been slightly modified for enhancing the performance. INVASIVEWEED OPTIMIZATION adopts the colonization process of weeds for finding optimumsolutions efficiently. In this case weed is a potential solution and the algorithm helps theweeds to evolve and generate better population thus giving rise to fitter weeds whichrepresent competitive schedules. In the present work the algorithm has been programmedusing matlab. Several bench mark problems have been tested using make span and tardinessas objectives.3.3.1 Initialization In the original algorithm initialization is random. ‘n’ number of weeds are generatedrandomly. The modification is that initially 10 weeds i.e 10 different schedules are generatedusing dispatching rules which present a significant optimization capacity. Since the choice ofthe initial population has a high impact on the speed of evolution and the quality of finalresults, the solution scenario would be focused on generating initial population using prioritydispatching rules. Priority dispatching rules are actually the most widely used for solvingJSSP where all the operations available to be scheduled are assigned a priority .The operation 631
  • 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEwith the highest priority is chosen to be sequenced. A priority dispatching rule is a simplemathematical formula that, based on some processing parameters , specifies the priority ofoperations to be executed. 10 initial schedules i.e. weeds are generated using 10 commonlyused priority dispatching rules given in the table below. EXPRESSION DESCRIPTION Shortest Processing Time (SPT) The job with shortest time on machines selected. pi≤ pi+1≤ pi+2≤………≤ pn Longest Processing Time(LPT) The job with longest time on machines selected.pi≥ pi+1≥ pi+2≥……≥pn Minimum Slack Time Per Time remaining until the due date – Processing Operation(MINSOP) timeremaining Minimum Due Date(MINDD) The job with earliest due date is processed first Di≤ Di+1≤ Di+2≤…………….≤ Dn Critical Ratio(CR) Remaining due date/Remaining processing time Most work remaining (MWKR) Select the operation associated with the job of the most work remaining to be processed Least work remaining(LWKR) Select the operation associated with the job of the least work remaining to be processed Shortest remaining Minimum Min(processing tine remaining- minimum Processing Time(SRMPT) processing time) Longest remaining Maximum Max(processing tine remaining- maximum Processing Time(LRMPT) processing time) RANDOM(random selection) Select the next job to be processed randomly. Table 1: Priority Dispatching Rules3.3.2 Performance Evaluation The initial population is made to reproduce depending on the fitness of the individual.The present problem is a Multi- Objective optimization , the objectives being minimizingmake-span, minimizing tardiness and minimizing flow-time. So the fitness of the individualhas to be evaluated considering all the three aspects.The individuals are ranked based on theirfitness values(all the three). This ranking is done based on concept called Fuzzy-Pareto-Dominance.[3] The ranking scheme assigns dominance degrees to any set of vectors in ascale-independent, non-symmetric and set-dependent manner. Based on such a rankingscheme, the fitness values of a population can be replaced by the computed ranking valuesrepresenting the ”dominating strength” of an individual against all other individuals in thepopulation. The three scheduling objectives used in this implementation are (1)make-span of thesequence (2) mean-flow time of the jobs, and (3)the mean tardiness of jobs.3.3.2.1. Make-Span Module (Fitness 1) In Scheduling literature, make-span is defined as the maximum completion time of alljobs, or the time taken to complete the last job on the last machine in the schedule-assumingthat the processing of the first job began at time 0. Make-span is denoted by cmax andcomputed as cmax =max {Fj} , where Fj is the flow time for job j(the total time taken byjob j from the instant of its release to the shop to the time its processing by the last machine isover). 632
  • 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME3.3.2.2. Mean Tardiness Module (Fitness 2) The lateness of a job measures the conformity of the schedule to that job’s due date.Lateness is defined as the amount of time by which the completion time of a job exceeds itsdue-date. MathematicallyLj=Cj-djLj: Lateness of job jCj: Completion time of job jdj: Due date of job j.Tardiness of job is the lateness if it is positive else it is zero.Mean tardiness(T) is defined as the average of tardiness of all jobs.T = (sum of tardiness of all jobs) / number of jobs3.3.2.3.Mean Flow Time Module(Fitness 3) The mean flow time measures the average response of the schedule to individualdemands of jobs for service. Mathematically, mean flow time is the average of the flow timesof all jobs.Mean flow time = sum of flow times of all jobs / number of jobs3.3.2.4. Fuzzification Of Pareto Dominance And Ranking In multiobjective optimization, the optimization goal is given by more than oneobjective to be extreme. Formally, given a domain as subset of Rn, there are assigned mfunctions f1(x1, xn) . . . fm(x1. . . xn). Usually, there is not a single optimum but rather theso-called Pareto set of non-dominated solutions. Evolutionary Computation (EC) has been shown to be a powerful technique for multi-objective optimization (EMO - Evolutionary Multi-Objective Optimization). Thisbiologically inspired methodology offers both flexibility in goal specification and goodperformance in multimodal, nonlinear search spaces. If we want to solve a highly complexmulti-objective optimization problem, we might select one of the best ranked evolutionaryapproaches reviewed in the literature, like NSGA-II and hopefully start reaching good resultsquickly.[11] However, all these algorithms need dominated individuals in the population, toperform the corresponding genetic operators. For a higher number of objectives, this mightbecome a problem, since the probability of having a dominated individual in the populationwill rapidly go to zero. The need for a revision of the Pareto dominance relation for also handling a largernumber of objectives was already pointed out in a few studies, esp. given by Farina andAmato. There, we also find the suggestion to use fuzzy-membership degrees for the degree ofa point belonging to the Pareto set (so called fuzzy optimality). Authors design their reviseddominance measure in a way that the approach to the Pareto front can be registered moreearly in the search. The approach was shown to work successfully in the domain of more thantwo objectives. It came out that the use of fuzzy concepts is fruitful in this regardThe fuzzification of Pareto dominance relation can be written then as follows:It is said that vector a dominates vector b by degree µa with: ୮୰୭ୢ୳ୡ୲ ୭୤ ୫୧୬ሺୟ୧,ୠ୧ሻ µa (a,b) = , ୮୰୭ୢ୳ୡ୲ ୭୤ ୟ୧It is said that the vector a is dominated by vector b by degree µp with: ୮୰୭ୢ୳ୡ୲ ୭୤ ୫୧୬ሺୟ୧,ୠ୧ሻ µp (a,b) = ୮୰୭ୢ୳ୡ୲ ୭୤ ୠ୧ 633
  • 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEHere i denote the dimension of vector, in the present case ‘i’ is 3 as we have considered 3objectives.The definitions differ in denominator and thus are not symmetric. “Dominating bydegree µ” and being dominated by degree µ have different fuzzy values.For a Pareto dominating b, µa (a,b) = 1 and µp (b,a) = 1 but µp (a,b) < 1 and µa (b,a) < 1We use these dominance degrees to rank a set M of multi-variate data(vectors).The vectors inthis case are that sets of three fitness values of the schedules in the population.The vectorhere is (fitness1 ,fitness2 ,fitness3). Consider two weeds or schedules a and b µp(a,b) = s/p.Where s = min (fitness1a, fitness1b) ×min (fitness2a, fitness2b) ×min (fitness3a, fitness3b) p = fitness1b×fitness2b× fitness3b Each element of M(set of schedules) is assigned the maximum degree of beingdominated by any other element in M, and the elements of M are sorted in increasing order ofthe value of dominance degree. After sorting the population is ranked sequentally. So theindividuals having good rank(lower) are fitter members in the population. With the help ofranking scheme performance evaluation is carried out.3.3.3 Reproduction The number of seeds generated by the parent weed depends upon the parent’s fitness,the maximum fitness of the population and the minimum fitness. For all the weeds generatedin the first phase number of seeds for each weed is found out using the following formula.N=maxሺw െ iሻ⁄ሺw െ bሻMax=max no of seeds a weed can havew =worst rankb =best rank, i =fitness of the weed consideredThe seed has similarities with the parent. The seed differs from the parent weed by a standarddeviation the value of which reduces from Sin to Sfin as iterations progress thus ensuringconvergence. At each iteration the value of standard deviation(s) is calculated as followsSf =ሺሺiter െ iሻ୬ ሻ⁄iter ୬Sin =1 (assumption)Sfin=0.001 (assumption)f = ( Sin - Sfin)×SfS = f + Sfiniter = maximum number of iterations for each runn = non-linear index (in this case it is assumed to be 3)i = the iteration for which the standard deviation is being calculatedInitially a 10×o (o is no of operations) matrix of random numbers is generated. Each row ofthe matrix corresponds to a weed (schedule) generated in the first step. Let ‘x’ be the matrixof random numbers and ‘p’ be the matrix of corresponding schedules(each row of the matrixis a schedule coded in operation-based mode) generated using priority dispatching rules.From the initial set of schedules seeds are generated,the number of seeds depending on therank of the parent weed. 634
  • 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME3.3.4 Competitive Exclusion This process continues until the maximum number of plants is attained by fastreproduction. At this stage, only the plants with higher fitness can survive and produce seeds,whereas others are eliminated (competitive exclusion). In this process, after the maximumnumber of weeds in a colony is reached, each weed is allowed to produce seeds, spread themover the search area, and find their position and rank together with their parents. Next, weedswith lower fitness values are eliminated in order to attain the maximum allowable populationin a colony. The course continues until the maximum iterations are reached and hopefully theplant with the best fitness is the closest to the optimal solution. . It is worth mentioning thatthe IWO has some distinctive properties when compared with the traditional GA and othernumerical search algorithms, such as reproduction, spatial dispersal and competitiveexclusion. In addition, no genetic operators are employed in the proposed algorithm, whichmakes it more dissimilar from the GA. The initial weeds generated and their seeds are together compared for their fitness.All aresorted in descending order of their fitness. Only the first ‘m’ solutions are considered and areallowed to proceed to the next generation, ‘m’ being the maximum allowable populationwhich is an assumption depending upon the problem complexity.Maximum allowable population = 20×no of operations (assumption in this case)3.3.5 Stopping CriteriaThe stopping criteria is one of the following • Maximum number of iterations • The population’s worst and best fitness becomes equalThe cycle of steps explained is carried out until one of the stopping criteria is met4. RESULTS AND DISCUSSIONS In this section, the execution of the program is presented by using an exampleproblem. The problem is a 5 machine and 10 job problems [2]. The input to the program is asfollowsS.No Due date Machine Order Matrix Processing Time MatrixJob1 37 1 5 4 2 3 13 16 19 7 14Job2 74 4 5 2 1 3 19 7 13 17 19Job3 111 3 2 5 4 1 19 18 16 18 19Job4 148 1 4 5 2 3 14 15 10 13 17Job5 185 1 2 5 4 3 8 8 19 7 9Job6 222 3 2 5 4 1 16 15 20 18 10Job7 259 2 4 3 1 5 14 17 18 5 20Job8 296 1 2 4 5 3 8 6 9 20 7Job9 333 5 4 3 2 1 16 13 9 16 12Job10 370 2 1 3 5 4 12 19 9 6 7 Table 2: Input data for the problem1-Best Make-span2-Best Mean Flow Time 635
  • 10. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME S.NO IWO NSGA-II 1 165 184 169 190 198 193 2 143 128 136 153.2 140.9 142.4 Table 3: Results obtained for the above problem using IWO Comparison of results of IWO and NSGA 160 Mean Flow Time 150 140 130 MOIWO 120 NSGA 160 170 180 190 200 Make Span Fig2: Comparision of results of IWO and NSGA In view of the results obtained by implementing IWO to solve JSSP (MOIWO), itappears that IWO is efficient. Fuzzy dominance applied for decision making in Multi-objective scenario yielded promising results. The algorithm has been improved by changingits solution coding method and hybridizing with priority dispatching rules leading to fastconvergence. The algorithm’s performance has been compared to that of standard Non-dominated- Search- Genetic- Algorithm (NSGA-2) with the help of some bench-markproblems and has been found to be superior to the latter.5. CONCLUSION In the present work the algorithm has been programmed for JSSP using mat-lab.Bench mark problems have been tested using make span and tardiness as objectives usingIWO algorithm and the results are compared with the best known ones. It is concluded thatthe application of IWO to Multi Objective JSSP is a new area to be explored for competitivesolutionsREFERENCESJournal Papers[1] Siddharth Pal, Anniruddha Basak and Swagatam Das “Linear Antenna Array Synthesis with Invasive Weed Optimization”,International Conference of Soft Computing and Pattern recognition, 2009[2] Edurado Fernandez, Edy Lopez, Segio Bernal “Evolutionary multi-objective optimization using a Fuzzy-based Dominance Concept”[3] Prithwish Chakraborty, Gaurab Ghosh Roy “On Population Variance and Explorative Power of Invasive Weed Optimization ” World congress on nature and biologicaaly inspired computing, 2009 636
  • 11. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME[4] Ritwik Giri ,Aritra Chowdhury, Arnob Ghosh “A Modified Invasive Weed Optimization for training of feed forward neural networks”[5] M.Ramezani Ghalenoei, H.Hajmirsadeghi, C.Lucas “Discrete Invasive Weed Optimization and its application to Co-operative multi-task assignment of UAVs” Comin prac. 48th IEEE conference on Decision and Control, Dec 2009,in Press[6] Rafal Zdonek, Tomasz Ignor “UMTS base station location planning with Invasive Weed Optimization”[7] Takeshi Yamada and Ryohei Nakano “ Genetic Algorithn for Job-shop scheduling problem”Proceedings of Modern Hueristic for Decision support, pp.March 1997, Pages 67-81[8] Takeshi Yamada and Ryohei Nakano “ Job shop scheduling ”Job Shop Scheduling, pp.IEEE Control engineering Services 55,pages 134-160[9] S.Q. Liu, H.L. Ong, K.M. Ng “Applying Tabu search to Job Shop Scheduling Problem ” Annals of Operations research 41, 1993, Pages 231-252Books[10] Tapan P. Bagehi “Multi-objective Scheduling By genetic Algorithms”Chapters in Books[11] Khald Mesghouni, Pierre Borne “Evolutionary Algorith For Job shop scheduling” Int.j.appl.Math.Comput.Sci.vol.14,2004,Pages 91-103[12] Hossein Hajimirsadeghi, Amin Ghazanfari “Co-operative co-evolutionary Invasive Weed Optimization and its application to Nash Equilibrium search in Electricity Markets” 637

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