Use of a goal-constraint-based approach for finding the region of interest in multi-objective problems

This paper presents a hybrid approach that combines an evolutionary algorithm with a classical multi-objective optimization technique to incorporate the preferences of the decision maker into the search process. The preferences are given as a vector of goals, which represent the desirable values for each objective. The proposed approach enhances the goal-constraint technique in such a way that, instead of use the provided $$\varepsilon $$ ε values to compute the upper bounds of the restated problem, it uses only the information of the vector of goals to generate the constraints. The bounds of the region of interest are obtained using an efficient constrained evolutionary optimization algorithm. Then, an interpolation method is placed in charge of populating such a region. It is worth noting that although goal-constraint is able to obtain the bounds of problems regardless of their number objectives, the interpolation method adopted in this paper is restricted to bi-objective problems. The proposed approach was validated using problems from the ZDT, DTLZ, and WFG benchmarks. In addition, it was compared with two well-known algorithms that use the g-dominance approach to incorporate the preferences of the decision maker. The results corroborate that the incorporation of a priori preferences into the proposed approach is useful to direct the search efforts towards the decision’s maker region of interest.