## Abstract

In this paper we propose a two-stage multi-population genetic algorithm (MPGA) to solve parallel machine scheduling problems with multiple objectives. In the first stage, multiple objectives are combined via the multiplication of the relative measure of each objective. Solutions of the first stage are arranged into several sub-populations, which become the initial populations of the second stage. Each sub-population then evolves separately while an elitist strategy preserves the best individuals of each objective and the best individual of the combined objective. This approach is applied in parallel machine scheduling problems with two objectives: makespan and total weighted tardiness (TWT). The MPGA is compared with a benchmark method, the multi-objective genetic algorithm (MOGA), and shows better results for all of the objectives over a wide range of problems. The MPGA is extended to scheduling problems with three objectives: makespan, TWT, and total weighted completion times (TWC), and also performs better than MOGA. Scheduling and sequencing are important factors to survive in the marketplace. Since scheduling began to be studied at the beginning of this century, numerous papers have been published. Almost all optimize a single objective. Many industries such as aircraft, electronics, semiconductors manufacturing, etc., have tradeoffs in their scheduling problems where multiple objectives need to be considered in order to optimize the overall performance of the system. Optimizing a single objective generally leads to deterioration of another objective. For example, increasing the input rate of product into a system generally leads to higher throughput, but also to increased work-in-process (WIP). Parallel machine scheduling is a Polynomial (NP)-hard problem even for the least complex single objective problem solved. No method is able to generate optimal solutions for the multi-objective case in polynomial time. This limits the quality of design and analysis that can be accomplished in a fixed amount of time. For multi-objective problems, determining a good set of Pareto Front solutions provides maximum information about the optimization. Consider a set of solutions for a problem with multiple objectives. By comparing each solution to every other solution, those solutions dominated by any other for all objectives are flagged as inferior. The set of non-inferior individuals is then the Pareto Front solution set. In this paper, an extremely computationally efficient method for determining a good set of Pareto Front solutions in multi-objective parallel machine scheduling problems is presented.

Original language | English (US) |
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Pages (from-to) | 1087-1102 |

Number of pages | 16 |

Journal | Computers and Operations Research |

Volume | 30 |

Issue number | 7 |

DOIs | |

State | Published - Jun 2003 |

## Keywords

- Genetic algorithms
- Multiple objectives
- Parallel machine scheduling

## ASJC Scopus subject areas

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research