Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems

• Published in: Engineering optimization Vol. 54; no. 8; pp. 1413 - 1425
• Main Authors: Burachik, Regina S., Kaya, C. Yalçın, Rizvi, Mohammed Mustafa
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03-08-2022; Taylor & Francis Ltd
• Subjects: Algorithms; Integer programming; Mixed integer; mixed-integer programming; Multi-objective optimization; numerical methods; Pareto front; scalarization
• ISSN: 0305-215X; 1029-0273
• DOI: 10.1080/0305215X.2021.1939695

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present article shows that certain algorithms that were originally devised for continuous problems can be successfully adapted to approximate the Pareto front for integer, and mixed-integer, multi-objective problems. Relationships amongst various scalarization techniques are established to motivate the choice of a particular scalarization in these algorithms. The proposed algorithms are tested by means of two-, three- and four-objective integer and mixed-integer problems, and comparisons are made. In particular, a new four-objective algorithm is used to solve a rocket injector design problem with a discrete variable, which is a challenging mixed-integer programming problem.