A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

• We present an algorithm based on ε-constraint method for multiobjective programming.
• It proposes a novel way of partitioning the search space in terms of rectangles.
• Two stage epsilon-constraint formulation is used to generate nondominated points.
• Theoretical results establish the validity of the algorithm.
• Computational results indicate superior performance compared to existing methods.

Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p − 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known ε-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved.