A discrete particle swarm optimization algorithm with adaptive inertia weight (DPSO-AIW) is proposed to solve the multiobjective Flexible Job-shop Scheduling Problem. The algorithm uses a two-layer coding structure to encode the chromosomes, namely operation sequence (OS) and machine assignment (MA). The initial population combined random selection of OS and the global selection based on operation (GSO) of MA. In order to obtain the Pareto optimal solution, non-dominated fronts are obtained by rapid non-dominated sorting. In the evolution process, the discrete particle swarm optimization algorithm is used to directly solve the values of the next generation chromosomes in the discrete domain, and the population diversity is enhanced by adaptively adjusting the variation of the inertia weight ω, and the Pareto optimal solution obtained in the process is stored in the Pareto optimal solution set (POS). Finally, numerical simulation based on two sets of international standard instances and comparisons with some existing algorithms are carried out. The comparative results demonstrate the effectiveness and practicability of the proposed DPSO-AIW in solving the multiobjective Flexible Job-shop Scheduling Problem. INDEX TERMS Discrete particle swarm optimization, global selection based on operation, multiobjective FJSP, Pareto optimality.

For solving the complex flexible job-shop scheduling problem, an improved genetic algorithm with adaptive variable neighborhood search (IGA-AVNS) is proposed. The improved genetic algorithm first uses a hybrid method combining operation sequence (OS) random selection with machine assignment (MA) hybrid method selection to generate the initial population, and it then groups the population. Each group uses an improved genetic operation for global search, then the better solutions from each group are stored in the elite library, and finally, the adaptive local neighborhood search is used in the elite library for detailed local searches. The simulation experiments are carried out by three sets of international standard examples. The experimental results show that the IGA-AVNS algorithm is an effective algorithm for solving flexible job-shop scheduling problems.

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Regarding the complicated flexible job-shop scheduling problem, it is not only required to get optimal solution of the problem but also required to ensure low-carbon and environmental protection. Based on the NSGA-II algorithm, this article proposes an improved adaptive non-dominated sorting genetic algorithm with elite strategy (IA-NSGA-ES). Firstly, the constructive heuristic algorithm is introduced in the initial population phase, and the weight aggregation method is used to restrain the multi-objective mathematical model which takes total completion time, carbon emission and maximum machine tools load as objectives; secondly, elite strategy is improved, simulated annealing method is used to replace parent generation by child generation to enhance the replaced population quality. The improved algorithm obtains the Pareto optimal solution set faster. Using standard computation example and practical workshop problem for simulation, the results of simulation prove that the algorithm is effective and feasible.INDEX TERMS non-dominated sorting, genetic algorithm, adaptive, job-shop scheduling

This paper proposes a hybrid artificial bee colony (HABC) to solve the multiobjective lowcarbon flexible job-shop scheduling problem (MLFJSP). HABC algorithm uses a two-layer coding method to establish the initial population as the nectar source for the employed bees. In the optimization process, the employed bee phase and the onlooker bee phase adopt improved crossover mutation strategies and adaptive neighborhood search strategies to generate new nectar sources, and the greedy method is used to retain better solutions. The scout bee update mechanism prevents the algorithm from falling into a local optimum and enhances the convergence of the algorithm. In order to prevent the loss of the optimal solution, the optimization results of each phase are saved in the Pareto archive (PA). Finally, two sets of international standard instances are used to carry out simulation experiments. After analyzing the simulation results, it is concluded that HABC is an effective algorithm to solve the multiobjective low-carbon flexible job shop scheduling problem.INDEX TERMS artificial bee colony, multiobjective flexible job-shop problem, low-carbon, adaptive variable neighborhood search