In this paper we provide a duality theory for multiobjective optimization problems with convex objective functions and finitely many D.C. constraints. In order to do this, we study first the duality for a scalar convex optimization problem with inequality constraints defined by extended real-valued convex functions. For a family of multiobjective problems associated to the initial one we determ...

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...

Consolidation carriers transport shipments that are small relative to trailer capacity. To be cost-effective, the carrier must consolidate shipments, which requires coordinating their paths in both space and time, i.e., the carrier must solve a Service Network Design problem. Most service network design models rely on discretization of time, i.e., instead of determining the exact time at which ...

Very large-scale neighborhood search (VLSNS) is a technique intensively used in single-objective optimization. However, there is almost no study of VLSNS for multiobjective optimization. We show in this paper that this technique is very efficient for the resolution of multiobjective combinatorial optimization problems. Two problems are considered: the multiobjective multidimensional knapsack pr...

In this work we present a quantum algorithm for multiobjective combinatorial optimization. We show that the adiabatic algorithm of Farhi et al. [arXiv:quant-ph/0001106] can be used by mapping a multiobjective combinatorial optimization problem onto a Hamiltonian using a convex combination among objectives. We present mathematical properties of the eigenspectrum of the associated Hamiltonian and...

Understanding the search dynamics of multiobjective evolutionary algorithms (MOEAs) is still an open problem. This paper extends a recent network-based tool, trajectory networks (STNs), to model behavior MOEAs. Our approach uses idea decomposition, where problem transformed into several single-objective problems. We show that STNs can be used and distinguish two popular algorithms, MOEA/D NSGA-...

A mixed-integer optimal control framework for analyzing the interaction of process synthesis, design, and control is presented in this paper. The approach integrates the economic design and dynamic controllability into a multiobjective Mixed-Integer Optimal Control Problem (MIOCP). The problem formulation includes dynamic models and incorporates both discrete and continuous decisions. An algori...

In this paper, a new multiobjective genetic algorithm is employed to support the design of a hydraulic actuation system. First, the proposed method is tested using benchmarks problems gathered from the literature. The method performs well and it is capable of identifying multiple Pareto frontiers in multimodal function spaces. Secondly, the method is applied to a mixed variable design problem w...

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

This paper deals with a nonlinear multiobjective semi-infinite programming problem involving generalized (C,α, ρ, d)-convex functions. We obtain sufficient optimality conditions and formulate the Mond-Weirtype dual model for the nonlinear multiobjective semi-infinite programming problem. We also establish weak, strong and strict converse duality theorems relating the problem and the dual problem.