This paper is concerned with the numerical solution of multiobjective control problems associated with linear (resp., nonlinear) partial differential equations. More precisely, for such problems, we look for Nash equilibria, which are solutions to noncooperative games. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the...

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

Nowadays, manufacturing enterprises face the challenge of just-in-time (JIT) production and energy saving. Therefore, study of JIT production and energy consumption is necessary and important in manufacturing sectors. Moreover, energy saving can be attained by the operational method and turn off/on idle machine method, which also increases the complexity of problem solving. Thus, most researche...

An eecient numerical solution scheme entitled adaptive diierential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the \optimal" weighting coeecients for various performance indices are time-varying as the system evolves along any noninferior tr...

We introduce multiobjective disk cover problems and study their approximability. We construct a polynomial-time approximation scheme (PTAS) for the multiobjective problem where k types of points (customers) in the plane have to be covered by disks (base stations) such that the number of disks is minimized and for each type of points, the number of covered points is maximized. Our approximation ...

The Genetic Immune Strategy for Multiple Objective Optimization (GISMOO) is a hybrid algorithm for solving multiobjective problems. The performance of this approach has been assessed using a classical combinatorial multiobjective optimization benchmark: the multiobjective 0/1 knapsack problem (MOKP) [1] and two-dimensional unconstrained multiobjective problems (ZDT) [2]. This paper shows that t...