Multiobjective optimal control of the linear wave equation

Abstract

In this paper, we propose a method for the solution of a multiobjective optimal control problem (MOOCP) in a linear distributed-parameter system governed by a wave equation. An explicit solution for the wave equation is derived and the control problem of this distributed-parameter system is reduced to an approximate multiobjective programming problem. The fuzzy goals are incorporated for objectives and the equilibrium problem in terms of maximization of the degree of attainment for the aggregated fuzzy goals is considered. The solution of the equilibrium optimization problem is a Pareto optimal solution with the best satisfaction performance which is achieved by using a metaheuristic algorithm such as the simulated annealing (SA) together with the simplex method of linear programming (LP) problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method and the capability of the SA in finding optimal solution compared with two popular metaheurestics.