OPTIMIZATION, vol.72, pp.1-23, 2022 (SCI-Expanded)
A new game theoretical approach is proposed to build near-optimal solutions of the social planner in the context of economics. In this regard, one target two-player pursuit-evasion game is designed under complete information where each player's strategy is determined by the dynamics of the optimization problem. The game starts with the move of the evader who aims to follow the optimal policy of the social planner and he is chased by the pursuer whose purpose is to capture his opponent within his target region after a finite number of moves. A novel meta-heuristic approach is developed to design a discrete control model which determines each player's course of action by means of a finite set. Capturing scenarios of the pursuer are provided by designing his finite sets according to the given target range. Numerical experiments are performed in the simple case where the proposed model is compared with grey wolf optimizer through numerical simulations. Here, it is seen that the new model is more effective and accurate which requires less computation and fewer iterations to construct near-optimal solutions. Moreover, the proposed method becomes more powerful for converging to the optimal cost of the problem when the optimal solution is finite.