Research On Multi-objective Optimization Algorithm And Its Application For The Distributed Flexible Job Shop Scheduling Problems

Most of the problems belong to multi-objective optimization problems essentially in the real world,the objectives of these problems are conflicted with each other and need to be optimized simultaneously,and a set of compromise solutions are used to represent the optimal solutions.The evolutionary algorithms,which do not need other prior information of problems,could obtain a set of optimal solutions in a single run.Therefore,it has been accepted as an effective way to address the multi-objective optimization problems.The goal of multi-objective optimization algorithm will achive twofold: 1)the obtained solutions converged to the Pareto front(convergence);2)the solutions evenly distributed along the Pareto front(diversity).In the past two dacades,although numerous multi-objective optimization algorithms have been proposed,there are still difficulties in balancing diversity and convergence of population for multiobjective optimization problems.Especially for the complex engineering problems,the number of objectives and variables will become larger,which brings great challenges for algorithms to solve.For example,in the high-dimensional space,the poor selection pressure makes it difficult for solution to converge to the Pareto front,and it is also difficult to maintain the diversity of the final population.Therefore,this content focuses on designing effective multi-objective algorithms and evolution strategy by making full use of the characteristics of problems and mining the characteristics of problems.The main work of this content are summarized as follows.(1)Aiming at the multi-objective problems with complex Pareto front,a two-stage evolution strategy based MOEA/D is proposed.For the problems with complex Pareto front,it is difficult for existing methods to converge and uniformly distributed.To address this issue,a novel algorithm named MOEA/D-TS is proposed to efficiently address MOPs.The MOEA/D-TS adopts a two-stage evolution strategy,the first stage focuses on pushing the solutions into the Pareto front regions and accelerates its convergence ability,while the second stage concentrates on the diversity of the solutions and makes the solution evenly distributed in the Pareto front.In the first stage,MOEA/D-TS mainly adopts the framework of MOEA/D algorithm,and an improved weight vector generation mechanism is adopted to solve the complex Pareto front.In the second stage,a local search strategy is designed to adjust the distribution of the solutions.The performance of MOEA/D-TS is verified on ZDT,DTLZ and IMOP benchmark problems,the experimental results show that the MOEA/D-TS exhibits a competitive performance on most of test problems than other compared algorithms.(2)Aiming at the many-objective optimization problems,an angle-based manyobjective evolutionary algorithm is proposed.Due to the curse of dimensionality,the solutions in the searching space will become non-dominance,the existing evolutionary algorithms have difficulties in balancing convergence and diversity in many-objective problems.To address this shortcoming,an efficient many-objective optimizer named Ma OEA-ASS is designed.In the Ma OEA-ASS,the angle-based selection strategy is used to obtain solutions with good diversity from the population.In addition,the combination of the shift-based density estimation and the sum of objectives,which uses the iteration information and emphasis the distribution of solutions,is employed to obtain the high-quality solutions approximating the optimal solutions.The proposed Ma OEA-ASS is compared with eight state-of-the-art many-objective optimization algorithms on the DTLZ and WFG test suites.The experimental results demonstrate that the proposed Ma OEA-ASS has a superior performance over the peer competitors on all considered many-objective problems.(3)Aiming at the constrained multi-objective optimization problems(CMOPs),a constrained multi-objective optimization algorithm with two cooperative populations is proposed.The CMOPs are difficulty to be solved because they not only need to balance convergence and diversity,but also consider the feasibility of solutions.The existing constrained multi-objective optimization algorithms(CMOEAs)exhibit poor performance when solving CMOPs with complex feasible regions.To address this issue,a novel algorithm named CMOEA-TCP is designed.CMOEA-TCP maintains two populations which work cooperatively to push the solutions approximate constrained Pareto front.Specifically,one population is evolved by Pareto-based method and aims to strength its convergence ability.Meanwhile another population is maintained by decomposition-based method and devotes to improve its diversity.Two populations work cooperatively in the whole evolution process with the constraint-handling technique.Three set of test suites are employed to verify the performance of CMOEATCP.Experiment results demonstrate that CMOEA-TCP has competitive performance compared to other six state-of-the-art CMOEAs on the most of problems.(4)Aiming at the constrained many-objective optimization problems,a constrained many-objective evolutionary algorithm with dynamic reference vector is proposed.The constrined many-objective optimization problems are difficult to solve because of many objectives and various constraints.In order to address this issure,a dynaminc-based reference vector guided evolutionary algorithm(CMa OEA-DR)for constrained many-objective optimization is desinged.In the CMa OEA-DR,the reference vector changes dynamically with the iteration information during the evolution process,so it can be well adapted to various complex problems.In addition,in order to adjust the weight vector effectivelly,an external archive is constructed to save the promising solutions generated in the evolution process.The CMa OEA-DR is verified on three sets of test suites.Compared with other six state-of-the-art constrained many-objective optimization algorithms,the CMa OEA-DR has obvious advantages in solving constrained many-objective optimization problems.(5)Aiming at the application of the multi-objective evolutionary algorithm in practical problems,the MOEA/D-TS is adopted to solve the multi-objective distributed flexible job shop scheduling for minimizing the maximum completion time and total energy consumption.In the evolution process,the job sequences,machine sequences and factory sequences are generated by using crossover and mutation.Furthermore,in order to reduce the total energy consumption,a local search strategy is designed to reduce the idle time in the working process.Two sets of test suites are utilized to demonstrate the performance of MOEA/D-TS on distributed flexible job shop problem,the experimental results show that the MOEA/D-TS can effectively solve the distributed flexible job shop scheduling than other peer algorithms.