Many problems in real life have more than one decision criterion, referred to as multi-objective optimization (MOO) problems, and the objective functions of these problems are conflicting in most cases. Hence, finding non-dominated solutions is very critical for decision making process. Tri-objective mixed-integer linear programs (TOMILP) are an important subclass of MOOs that are applicable to many problems in economics, business, science, technology, and engineering such as sustainable systems that must consider economic, environmental, and social concerns, simultaneously. There is a deficient literature on finding the non-dominated solutions of TOMILPs, and to the best of our knowledge, there are very few existing algorithms which do not guarantee generating all non-dominated solutions of these problems. In this paper, we present a new method, called Slicing with Adaptive Steps Search (SASS), for generating all non-dominated solutions of TOMILPs. At each iteration, our method explores all points in the objective space while the third objective function value is fixed. We call these planes in the objective space with the same third objective function contour, slice. We generate non-dominated solutions while moving from one slice to the next until all non-dominated solutions are found.
Rasmi, S.A.B., Fattahi, A., Turkay, M., “An exact algorithm to find non-dominated facets of Tri-Objective MILPs”, The 12th International Conference on Multiple Objective Programming and Goal Programming (MOPGP); 30-31 October 2017; Metz, France. The Laboratory of Design, Optimization and Modelling of Systems, University of Lorraine; 2017. Abstract number, 14.