Solution approaches to multiple objective linear programming

Abstract

Multiple Objective Linear Programming (MOLP) has become an important optimization framework for solving decision-making problems involving multiple and often conflicting objectives. Over the years, several algorithms have been developed to generate efficient or nondominated solutions to MOLP problems, each exhibiting distinct computational characteristics and solution capabilities. This study reviews and evaluates four widely used MOLP solution approaches: the Evans–Steuer Multiobjective Simplex Algorithm (MSA), the Parametric Simplex Algorithm (PSA), the Affine Scaling Interior MOLP Algorithm (ASIMOLP), and Benson’s Outer Approximation Algorithm (BOA). The algorithms are compared using ten benchmark and randomly generated MOLP test problems ranging from small to medium dimensions. Computational performance is assessed using CPU execution times, while solution quality is evaluated based on the nondominated solutions generated by each method. The results indicate that ASIMOLP consistently achieves the shortest computation times and is therefore the most computationally efficient among the algorithms considered. The PSA also demonstrates competitive computational performance, whereas the MSA becomes increasingly inefficient as problem size grows. In contrast, BOA provides the highest-quality solutions by generating a more complete representation of the nondominated frontier, although at a higher computational cost than ASIMOLP. The findings highlight the trade-off between computational efficiency and solution quality and provide guidance for selecting appropriate MOLP solution methods based on problem characteristics and decision-making requirements.