(621b) Mixed-Integer Multi-Objective Optimization through Multiparametric Programming

Avraamidou, S. - Presenter, Texas A&M University
Katz, J., Texas A&M University
Burnak, B., Texas A&M University
Pappas, I. S., Texas A&M University
Turkay, M., Koc University
Pistikopoulos, E. N., Texas A&M Energy Institute, Texas A&M University
Optimization problems involving more than one objective function are referred to as Multi-Objective Optimization (MOO) problems. Conflicting objectives can arise in cases where the decision makers are concerned with more than one objective (i.e. economic and environmental) or when multiple stakeholders are involved in decision making. Different approaches have been proposed for the development of the pareto front of continuous MOO problems including the ε-constraint approach [1], the weight sum approach [2] and data driven and evolutionary approaches [3, 4]. The explicit derivation of the pareto front for continuous MOO problems through multi-parametric programming has been presented by [5, 6, 7], although very few approaches have been developed for the exact explicit derivation of the pareto front for mixed-integer MOO problems [8].

In this work we present an algorithm for the exact explicit derivation of the pareto front of mixed-integer linear MOO problems based on multi-parametric programming. The ε-constraint approach is used to transform the MOO problem into a single objective multi-parametric mixed-integer linear problem where the tunable suboptimality variables (resulting from the ε-constraints) are considered as parameters. The reformulated problem can be solved using already developed multi-parametric mixed-integer algorithms through the POP toolbox [9], supplying the decision makers with the explicit form of the pareto front in terms of the tunable variables ε. The proposed approach is illustrated through a set of numerical examples and its capabilities are demonstrated in a computational study.


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