Mono-Objective Function Analysis Using an Optimization Approach

Abstract

In this paper we propose an evolutionary technique based in a Lyapunov method for mono-objective optimization, that associate to every ergodic controllable finite Markov Chains a Lyapunov-like mono-objective function. For representing the trajectory dynamics properties local-optimal policies are defined to minimize the one-step decrement of the cost-function. We propose a state-value function that increase and decrease between states of the Markov decision processes. Then, we show that a Lyapunov mono-objective function, which can only decrease over time, can be built for the system. For illustration purposes, we present a simulated experiment that shows the trueness of the suggested method.