This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for ...

There are currently three different game strategies to solve multi-criteria design problems: 1) Cooperative Games (Pareto Front), 2) Competitive Games (Nash Game) and 3) Hierarchical Games (Stackelberg Game). Nowadays EAs and Pareto front concept are more and more in solving practical design problems in industry, but this process is time consuming. Here, deterministic optimization method and Pa...

To meet the increasing computational demands, geographically distributed resources need to be logically coupled to make them work as a unified resource. In analyzing the performance of such distributed heterogeneous computing systems scheduling a set of tasks to the available set of resources for execution is highly important. Task scheduling being an NP-complete problem, use of metaheuristics ...

One of the most common approaches for multiobjective optimization is to generate the whole or partial efficient frontier and then decide about the preferred solution in a higher-level decision-making process. In this paper, a new method for generating the efficient frontier for multiobjective problems is developed, called the diversity maximization approach (DMA). This approach is capable of so...

In the design of many mechanical systems, the human designer knows its topology and shape. The goal for computational design thus results in finding a parameter set that optimizes multiple design goals. This paper presents a novel optimization method for such parametric design, the process of which is based on the human design process, but the search algorithm of which is gradient-based for eff...

We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set...

We consider the notion of Pareto optimality under the assumption that only the pairwise majority relation is known and show that the set of necessarily Pareto optimal alternatives coincides with the McKelvey uncovered set. As a consequence, the McKelvey uncovered set constitutes the coarsest Pareto optimal majoritarian social choice function. Moreover, every majority relation is induced by a pr...

The hypervolume indicator is an increasingly popular set measure to compare the quality of two Pareto sets. The basic ingredient of most hypervolume indicator based optimization algorithms is the calculation of the hypervolume contribution of single solutions regarding a Pareto set. We show that exact calculation of the hypervolume contribution is #P-hard while its approximation is NP-hard. The...

This paper presents a new class of operators for multiobjective evolutionary algorithms that are inspired on feedback-control techniques. The proposed operators, the archive-set reduction and the surface-filling crossover, have the purpose of enhancing the quality of the description of the Pareto-set in multiobjective optimization problems. They act on the Pareto-estimate sample set, performing...