The Collaborative Learning Differential Evolution Algorithm And Its Applied Research For The Shop Scheduling Problem

Green scheduling in manufacturing industry has attracted enormous attention from researchers and practitioners with the increasing focus on energy saving problems in manufacturing system.As a typical scheduling problem,the no-wait flow shop scheduling problem has been extensively studied due to its vastly industrial applications.However,energy consumption is usually ignored in various researches on typical scheduling problems.Due to the inherent complexity of the no-wait flow shop scheduling problem with energy constraints,the traditional exact algorithms are not suitable to solve it.Therefore,intelligent optimization algorithms came into being.Differential evolution algorithm is a typical swarm intelligence optimization algorithm.It has been widely studied and applied because of its few controlled parameters,easy implementation,simple and powerful search framework.Aiming at the energy-saving scheduling problem of a no wait flow shop,a collaborative learning differential evolution algorithm and a two-stage collaborative evolution algorithm are proposed.The main research contents in this study are as follows:(1)A hybrid cooperative differential evolution with the perturbation of CMAES with local search of Limited-Memory Broyden–Fletcher–Goldfarb–Shanno(LBFGS)mechanism,named jSO_CMA-ES_LBFGS,is proposed to solve the complex continuous problems.In the proposed algorithm,jSO,as a variant of Differential Evolution(DE),is used as a global search operator to explore the entire solution space.When the population is falling into stagnation,a relative reliable initial solution for the local search operator is generated by the CMA-ES,which is activated to perturb the optimal candidates in the solution space.The LBFGS utilized as the local search strategy,is embedded in CMA-ES to obtain the potential local optimal solutions.A cooperative co-evolutionary dynamic system is formed by jSO and CMA-ES with local search operator.The proposed jSO_CMA-ES_LBFGS is tested on CEC2017 benchmark test suite and compared with five the state-of-theart algorithms.The experimental results reveal the effectiveness and efficiency of the jSO_CMA-ES_LBFGS.(2)At the problem level,variable grouping method based on interaction is used to detect the interdependence between variables for the CEC2017 benchmark test function.According to the interaction between variables,the variables are grouped.In the differential evolution algorithm,a method of constructing optimal solutions based on variable grouping learning is proposed for variable part separable function.Compared with the parent algorithm,the proposed algorithm has significantly improved search performance.(3)On the basis of studying the operation mechanism of the differential evolution algorithm,a two-stage cooperative evolution algorithm with problemspecific knowledge,which is named TS-CEA,is proposed to address an energyefficient scheduling of the no-wait flow-shop problem(EENWFSP)with the criteria of minimizing both makespan and total energy consumption.In the TS-CEA,two constructive heuristics are used to generate a desirable initial solution after the properties of the problem are analyzed.In the first stage of TS-CEA,an iterative local search strategy(ILS)is employed to search for potential extreme solutions.Moreover,a hybrid neighborhood structure is designed for improving the quality of the solution.In the second stage of TS-CEA,a mutation strategy,which is based on critical path knowledge,is proposed to extend the extreme solutions to the whole Pareto front found.A co-evolutionary closed-loop system is generated with the ILS and mutation strategies in the iteration process.Experimental results demonstrate the effectiveness and efficiency of the TS-CEA in solving the EENWFSP.