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...

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...

This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Follo...

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.

The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conflicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions t...

Static and dynamic multiobjective topology optimization of trusses with interval parameters is investigated. The uncertain parameters of the trusses are described by an interval model. The multiobjective topology optimization model of trusses with interval parameters is constructed. On the basis of Taylor expansion and natural interval extension, the stress and displacement response intervals u...

Ridesharing is considered as one of the promising solutions for dropping the consumption of fuel and reducing the congestion in urban cities, hence reducing the environmental pollution. Route planning is a key component for the success of ridesharing systems in which multiple objectives can be optimized. The multiobjective route planning problem in multi-hop ridesharing is categorized as NP–com...