Solving multi-objective dynamic optimization problems with fuzzy satisfying method

This article proposes a novel algorithm integrating iterative dynamic programming and fuzzy aggregation to solve multi-objective optimal control problems. First, the optimal control policies involving these objectives are sequentially determined. A payoff table is then established by applying each optimal policy in series to evaluate these multiple objectives. Considering the imprecise nature of decision-maker's judgment, these multiple objectives are viewed as fuzzy variables. Simple monotonic increasing or decreasing membership functions are then defined for degrees of satisfaction for these linguistic objective functions. The optimal control policy is finally searched by maximizing the aggregated fuzzy decision values. The proposed method is rather easy to implement. Two chemical processes, Nylon 6 batch polymerization and Penicillin G fed-batch fermentation, are used to demonstrate that the method has a significant potential to solve real industrial problems.