Optimization over the efficient set using an active constraint approach

Abstract

Abstract:In this work the problem of maximizing a nonlinear objective over the set of efficient solutions of a multicriteria linear program is considered. This is a nonlinear program with nonconvex constraints. The approach is to develop an active constraint algorithm which utilizes the fact that the efficient structure in decision space can be associated in a natural way with hyperplanes in the space of objective values. Examples and numerical experience are included.

A face search heuristic algorithm for optimizing over the efficient set

“…Each of the test problems was constructed to belong to one of three categories, where a category is defined by the values of p , k , and n. We chose the values (4,8,12), ( 5 , 12, 16), and (5,16,16) for ( p , k , n ) to define categories 1, 2, and 3, respectively. In each category, 10 test problems were generated.…”

“…Two of these, given in (91, essentially simply suggest initiating one of the search procedures [17] for globally solving problem P, but terminating it prematurely with a locally optimal solution. Another suggestion [8] also attempts to find a local optimum. It involves sequentially searching adjacent efficient faces of X using an active constraint approach.…”

Multicriteria Optimization In Engineering: A Tutorial And Survey

“…Dauer 59 recently considered maximizing a nonlinear decision function over the set of efficient solutions utilizing an active constraint approach, as in nonlinear programming. This approach is motivated by the fact that decision makers usually have nonlinear utility preferences.…”

A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs

“…It is worth mentioning there exist many studies about solving the problem of optimizing a linear function over the efficient set of multi-objective linear programs, see for instance Benson (1984), Benson (1991), Benson (1992), Benson (1993), Dauer (1991), Ecker and Song (1994), Sayin (2000) and Yamamoto (2002). Moreover, there are a few studies on optimizing a linear function over the set of efficient solutions of multi-objective pure integer linear programs, see for instance Abbas and Chaabane (2006), Jorge (2009), Djamal and Marc (2010), Chaabane et al (2012) and Boland et al (2016b).…”