Splitting the fitness and penalty factor for temporal diversity increase in practical problem solving

Abstract In this paper, we propose an optimization system based on an evolutionary algorithm developed to solve a real-life optimization problem related to the optimization of the computer networks. In particular, we focus on an NP-hard flow allocation problem in computer networks related to network survivability and addressing various constraints specific to computer networks. The constrained problems are usually handled by evolutionary methods by the introduction of the so-called penalty factor. However, such techniques raise difficulties regardless of their simple working principle. The more oppressive the penalty factor is, the more likely the evolutionary method is to stuck in the local optima with feasible solutions and propose final results of low-quality. On the other hand, a low penalty factor may lead the method to regions of high-rated solutions that violate the constraints and are useless due to their infeasibility. Therefore, we address the issue of penalty handling by proposing Ranking-based Fitness and Penalty Weighting (RFPW). RFPW is inspired by a theory-driven penalty parameter estimation using a bi-objective and weighted sum approach. It separates the objective and penalty functions and removes the necessity of hand-made weighting. RFPW was introduced to the recent proposition of an evolutionary method dedicated to solving hard NP-complete practical problem. The performed experiments related to the flow allocation problem confirm that employing RFPW may lead to a significant improvement in results quality. In our opinion, the proposed RFPW framework of the penalty function handling has the potential to be adapted to a wide range of optimization systems that utilize the idea of penalty function. RFPW allows the optimization method to reduce or increase the strength of a convergence automatically. Therefore, RFPW has the potential of results quality improvement and may replace expensive commonly-used diversity preservation techniques (e.g., island models).

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