Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early  

作　　者：Karrar Alshaikhli Aws Alshaikhli Karrar Alshaikhli;Aws Alshaikhli(Department of Engineering and Mathematics, St. Philip’s College, San Antonio, USA;Department of Biology, Northeastern Illinois University, Chicago, USA)

机构地区：[1]Department of Engineering and Mathematics, St. Philip’s College, San Antonio, USA [2]Department of Biology, Northeastern Illinois University, Chicago, USA

出　　处：《Journal of Applied Mathematics and Physics》2024年第2期661-682,共22页应用数学与应用物理（英文）

摘　　要：This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V_max), maximum tardy job, denoted by (T_max), and maximum earliness (E_max). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (V_max, T_max, E_max) and 1//(V_max + T_max + E_max). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V_max), maximum tardy job, denoted by (T_max), and maximum earliness (E_max). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (V_max, T_max, E_max) and 1//(V_max + T_max + E_max). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.

关 键 词：Scheduling Single Machine Hierarchical Simultaneous Minimization ALGORITHMS Branch and Bound Local Search Heuristic Methods 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]