A Knowledge-Based Two-Population Optimization Algorithm for Distributed Energy-Efficient Parallel Machines Scheduling

In recent years, both distributed scheduling problem and energy-efficient scheduling have attracted much attention. As the integration of these two problems, the distributed energy-efficient scheduling problem is of great realistic significance. To the best of our knowledge, the distributed energy-efficient parallel machines scheduling problem (DEPMSP) has not been studied yet. This article aims to solve DEPMSP by integrating factory assignment and machine assignment into an extended machine assignment to handle the coupled relations of subproblems. A knowledge-based two-population optimization (KTPO) algorithm is proposed to minimize total energy consumption and total tardiness simultaneously. Five properties are derived by analyzing the characteristics of DEPMSP. The population is initialized by using two heuristics based on problem-specific knowledge and a random heuristic. The nondominated sorting genetic algorithm-II and differential evolution perform cooperatively on the population in parallel. Moreover, two knowledge-based local search operators are proposed to enhance the exploitation. Extensive simulation experiments are conducted by comparing KTPO with four algorithms from the literature. The comparative results and statistical analysis demonstrate the effectiveness and advantages of KTPO in solving DEPMSP.