Optimal Production Scheduling by Integer Form of Population-Based Incremental Learning with Initial Probability Matrix Setting Methods and a Practical Production Simulator

This paper proposes an optimal production scheduling method using a practical production simulator and integer form of population-based incremental learning (IF-PBIL) with two initial probability matrix setting methods. There are three parameters for decision variables in a target factory. It is necessary to optimize these three parameters at the same time in order to evaluate them. Moreover, IF-PBIL is one of the cooperative metaheuristics and determines integer values based on probability values and generates solutions. Initial integer values are determined by equal probability values, and various solutions are generated. Hence, there is a possibility that it is difficult to search high-quality solutions from initial stages of the search. Furthermore, since the production simulator requires long execution time, the execution number of the production simulator should be reduced as much as possible. In order to tackle the challenge, the proposed method applies two initial probability matrix setting methods. It is confirmed that the proposed method can search high-quality solutions from initial stages of the search and can reduce the production costs with the fewer execution number of the production simulator using actual factory data of a polishing process of an assembly processing factory.

I. Introduction

In production scheduling researches, many studies have been conducted based on an ideal mathematical formulation such as job-shop scheduling problems (JSPs) in order to minimize production time [1]. At the 26th session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP26) in 2021, parties were asked to take ambitious actions to meet objectives of reducing global carbon dioxide emissions to net zero around mid-century [2]. Up to now, production scheduling problems considering environmental loads have been proposed by adding minimization of energy consumption and CO₂ emissions to the mathematical formulations of the problems [3]–[8].