This paper deals with the computation of d-dimensional multicriteria shortest paths. In a weighted graph with arc weights represented by vectors, the cost of a path is the vector sum of the weights of its arcs. For a given pair consisting of a source s and a destination t, a path P dominates a path Q if and only if P 's cost is component-wise small...
Published in Computational Mathematics and Mathematical Physics
AbstractA universal computational procedure is used to construct numerical methods for Pareto set approximation. The numerical methods are developed relying on the assumptions necessary for proving the convergence of the universal procedure to the Pareto set.
When considering techniques for producing the Pareto front of a Multi-Objective Optimization Problem (MOOP), there exists a trade-off between the effectiveness of the method in obtaining the Pareto front and the computational cost required to achieve that. For a method to be effective, the generated solutions must result in a true representation of...
Water resources systems are often characterized by multiple objectives. Typically, there is no single optimal solution which can simultaneously satisfy all the objectives but rather a set of technologically efficient non-inferior or Pareto optimal solutions exists. Another point regarding multi-objective optimization is that interdependence and con...
Published in Polymers
In this paper, the synthesis of a chitosan–montmorillonite nanocomposite material grafted with acrylic acid is presented based on its function in a case study analysis. Fuzzy optimization is used for a multi-criteria decision analysis to determine the best desirable swelling capacity ( Y Q ) of the material synthesis at its lowest possible variable...
In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional.We then propose a novel set of convex-quadratic test problems, describe...
Published in Journal of Heuristics
In this paper we address the problem of computing suitable representations of the set of approximate solutions of a given multi-objective optimization problem via stochastic search algorithms. For this, we will propose different archiving strategies for the selection of the candidate solutions maintained by the generation process of the stochastic ...
Published in Journal of Global Optimization
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more ob...
This paper presents a novel trade-off chart to support the design of multilayer acoustic packages. In this multi-objective problem, a designer has to specify a combination of layers from a set of available acoustic materials and thicknesses. Material types may include porous, mass-weighted, facing, among others. The combination must meet requiremen...
Published in Journal of Mathematical Chemistry
The main purpose of the study is to introduce the multi-objective optimization using Pareto approximations to problems of chemical kinetics. We report the setting up and solution of the multi-objective optimization problem for conditions of a chemical reaction on the basis of a kinetic model. The study addresses the reaction of alcohols with dimeth...
