Improved Heuristic Kalman Algorithm for Solving Multi-Objective Flexible Job Shop Scheduling Problem

Abstract

The Flexible Job Shop Scheduling Problem (FJSSP), as a typical NP-hard optimization problem, has a significant value in manufacturing environment. This paper presents an improved estimation method of Multi-Objective Heuristic Kalman Algorithm (MOHKA) for solving Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSSP). The optimization results of improved MOHKA for the MOFJSSP were implemented in the five Kacem and ten Brendimarte benchmarks. First, an improved mathematical model of MOHKA was proposed and implemented in MATLAB. Then we applied MOHKA to solve MOFJSSP with an improved real number encoding system, optimized for three benchmark optimization parameters, the maximum completion time of on all jobs (makespan), the total workload on all machine, the workload of the critical machine (the maximum workload among the machines). The results presented in the paper show that the improved method of MOHKA for solving MOFJSSP can optimize multi-objective parameters especially for some of these selected cases in which our algorithm gives us high-quality results.