We present a new variant of the full (p − 1)-split algorithm, the Quadrant Shrinking Method, for finding all nondominated points of a triobjective integer program. The algorithm is easy to implement and solves at most 3|YN |+1 single-objective integer programs, where YN is the set of all nondominated points, when computing the entire nondominated frontier. A computational study demonstrates the...

Given a finite set N of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point of N , i.e. the part of the objective space which may contain further nondominated points. In this paper, we consider a representation of the search region by a set of tight local u...

The vector evaluated particle swarm optimisation (VEPSO) algorithm was previously improved by incorporating nondominated solutions for solving multiobjective optimisation problems. However, the obtained solutions did not converge close to the Pareto front and also did not distribute evenly over the Pareto front. Therefore, in this study, the concept of multiple nondominated leaders is incorpora...

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...

Because of non-convexities in the model, computing much of anything along the nondominated frontier of a large-scale (1000 to 3000 securities) portfolio selection problem with semi-continuous variables is a task that has not previously been achieved. But (a) given the speed at which the nondominated frontier of a classical portfolio problem can now be computed and (b) the possibility that there...

In this paper, we review the development of studies on multiobjective noncooperative games, and particularly we focus on nondominated equilibrium solutions in multiobjective two-person nonzero-sum games in normal and extensive forms. After outlining studies related to multiobjective noncooperative games, we treat multiobjective two-person nonzero-sum games in normal form, and a mathematical pro...

The -indicator subset selection selects a subset of a nondominated point set that is as close as possible to a reference point set with respect to the -indicator. This selection procedure is used by population-based heuristic approaches for multiobjective optimization problems. Given that this procedure is called very often during the run of the heuristic approach, efficient ways of computing t...

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i....