Single- versus Multiobjective Optimization for Evolution of Neural Controllers in Ms. Pac-Man

The objective of this study is to focus on the automatic generation of game artificial intelligence (AI) controllers for Ms. Pac-Man agent by using artificial neural network (ANN) and multiobjective artificial evolution. The Pareto Archived Evolution Strategy (PAES) is used to generate a Pareto optimal set of ANNs that optimize the conflicting objectives of maximizing Ms. Pac-Man scores (screen-capture mode) and minimizing neural network complexity. This proposed algorithm is called Pareto Archived Evolution Strategy Neural Network or PAESNet. Three different architectures of PAESNet were investigated, namely, PAESNet with fixed number of hidden neurons (PAESNet_F), PAESNet with varied number of hidden neurons (PAESNet_V), and the PAESNet with multiobjective techniques (PAESNet_M). A comparison between the single- versus multiobjective optimization is conducted in both training and testing processes. In general, therefore, it seems that PAESNet_F yielded better results in training phase. But the PAESNet_M successfully reduces the runtime operation and complexity of ANN by minimizing the number of hidden neurons needed in hidden layer and also it provides better generalization capability for controlling the game agent in a nondeterministic and dynamic environment. 1. Introduction A number of optimization solution techniques have been introduced for solving Multi-Objective Problems (MOPs) [1]. An MOP has a set of conflicting objective functions subject to certain constraints which are to be minimized or maximized [2]. Among these techniques, Evolutionary Algorithms (EAs) are particularly suited for handling MOPs [3, 4] because of its population approach that can help in finding a set of trade-off solutions in single simulation run, instead of having to perform a series of separate runs such as in the case of traditional optimization techniques. Moreover, EAs have been successfully used in solving complex problems such as discontinuities, multimodality, disjoint feasible spaces, and noisy function evaluations [5]. A large range of practical applications of Multi-Objective Evolutionary Algorithms (MOEAs) to real-life problems across a host of different disciplines can be found in the reference texts by Deb [6] and Coello et al. [3]. There are several types of effective MOEAs such as Pareto Archived Evolution Strategy (PAES) [7], Strength Pareto Evolutionary Algorithm 2 [8], Nondominated Sorting Genetic Algorithm II [9], and Pareto-frontier Differential Evolution [10]. Generally, MOEAs are able to solve separate distinct varied dimensional optimization