2. Multiobjective Control

A multi-objective Pareto front solution is presented in this chapter for a particular type of discrete-time ergodic controllable Markov chains. We offer a technique that, given specific boundaries, chooses the best multi-objective option for the Pareto frontier as a decision support system. We only consider a class of finite, ergodic, and controllable Markov chains while addressing this issue. The regularized penalty method utilizes a projection-gradient strategy to identify the Pareto policies along the Pareto frontier and is based on Tikhonov’s regularization method. The goal is to make the parameters as efficient as possible while still maintaining the original form of the functional. After setting the initial value, we gradually reduce it until each policy closely resembles the Pareto policy. In this sense, we specify the precise direction of the parameter tendencies toward zero and establish the convergence of the gradient regularized penalty algorithm. The matching picture in the objective space receives a Pareto frontier of only Pareto policies thanks to our policy-gradient multi-objective algorithms, which, on the other hand, use a gradient-based strategy. In order to improve security when transporting cash and valuables, we empirically validate the technique by providing a numerical example of a genuine alternative solution to the vehicle routing planning problem. In addition, we describe a portfolio optimization and represent the Pareto frontier. The decision-making techniques investigated in this paper are consistent with the most widely used computational intelligent models in the Artificial Intelligence research field.