Generating equidistant representations in biobjective programming

Abstract

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective optimization problems. This paper presents two methods for generating discrete representations with equidistant points for biobjective problems with solution sets determined by convex, polyhedral cones. The Constraint Controlled-Spacing method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. The Bilevel Controlled-Spacing method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing, and is extended to multiobjective problems. Both methods are proven to produce (weakly) nondominated points and are demonstrated on a variety of test problems.

Discrete representation of non-dominated sets in multi-objective linear programming

“…Another recent paper dedicated to generating equidistant representations in bi-objective optimisation proposed by Faulkenberg and Wiecek (2012) is based on the ǫ-constraint method.…”

Equidistant representations: Connecting coverage and uniformity in discrete biobjective optimization

“…In this paper we focus on the latter case. For the former case, some recent works include Faulkenberg and Wiecek (2012), Hancock and Mattson (2013), Shao and Ehrgott (2016), Lin et al (2017) and Kirlik and Sayın (2017). As far as we are aware, for the latter case only four papers propose insertion methods specifically designed for the representation problem in discrete optimization, namely the works by Hamacher et al (2007), Sylva and Crema (2007), Masin and Bukchin (2008) and Eusébio et al (2014).…”

“…This problem is not new, and has been considered at least as early as 1980, for example by Steuer and Harris (1980). Since then it has received considerable attention in various areas of multiobjective optimization, including nonlinear optimization (Faulkenberg and Wiecek, 2012;Hancock and Mattson, 2013), linear programming (Shao and Ehrgott, 2016), (mixed) integer (non)linear programming (Sylva and Crema, 2007;Masin and Bukchin, 2008;Eusébio et al, 2014), and discrete optimization in general (Hamacher et al, 2007;Vaz et al, 2015).…”

Navigation in multiobjective optimization methods

“…Subsequent to the work of Sayın (), the most commonly considered criteria are cardinality (the size of R should not be too large), coverage (every area of the Pareto front should be represented), and uniformity (the representative points should be uniformly distributed across the Pareto front). Because a survey of methods for the computation of representative sets is beyond the scope of this paper, we refer to Faulkenberg and Wiecek (); () and references therein.…”