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4251. An interactive multi-objective algorithm using preference cones

Invited abstract in session WD-37: Multiobjective Mixed-Integer Linear Optimization, stream Multiobjective Optimization.

Wednesday, 14:30-16:00
Room: 33 (building: 306)

Authors (first author is the speaker)

1. Mariana Mesquita-Cunha
Departamento de Engenharia e Gestão, Instituto Superior Técnico, Universidade de Lisboa
2. José Rui Figueira
CEG-IST, Instituto Superior Técnico, Universidade de Lisboa
3. Ana Barbosa-Povoa
Departamento de Engenharia e Gestão, Instituto Superior Técnico, Universidade de Lisboa

Abstract

Multi-objective problems are common real-world problems. However, computing the whole Pareto front and analyzing it to make a decision is often impractical. Therefore, we propose an interactive algorithm to help the decision-maker (DM) reach the most preferred solution. The interactive algorithm alternates between generation stages, using a representation method based on the epsilon-constraint algorithm, and analysis stages, in which pairwise comparisons are required. Convex preference cones are used to adapt the search region based on the pairwise comparison. To that end, the H-representation of the 3-pointed convex cone is developed so that those types of preference cones can be included as inequality constraints in the generation phase. Moreover, two boosting strategies are put forward to increase the algorithm's convergence. The algorithm is tested on different sets of multi-objective problems, namely binary and integer problems with multiple constraints. The DM’s preferences are simulated through linear and Chebyshev value functions with different weight vectors. The algorithm has proven effective, converging to the most preferred point in the Pareto front, and the boosting strategies improved the efficiency of the algorithm. Furthermore, the advantage of increasing the size of the solution subset shown to the DM in each iteration is made clear in those instances in terms of iterations and computational time.

Keywords

Status: accepted

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