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Dynamic characteristics of a continuous optimization method based on fictitious play theory

JOURNAL OF THE KOREAN PHYSICAL SOCIETY 2017年第9期70卷 880-890页

作者： Lee, Chang-Yong Kongju Natl Univ Dept Ind & Syst Engn Cheonan 31080 South Korea

In this paper, we propose a continuous optimization algorithm based on fictitious play theory and investigate the dynamic characteristics of the proposed algorithm. Fictitious play is a model for a learning rule in evolutionary game theory, and it can be used as an optimization method when all players have an identical utility function. In order to apply fictitious play to a continuous optimization algorithm, we consider two methods, equal width and equal frequency, of discretizing continuous values into a finite set of a player's strategies. The equal-frequency method turns out to outperform the equal-width method in terms of minimizing inseparable functions. To understand the mechanism of the equal-frequency method, we investigate two important quantities, the mixed strategy and the best response, in the algorithm from the statistical physics viewpoint. We find that the dynamics of the mixed strategies can be described as a 1/f noise. In addition, we adopt the set of best responses as the probability measure and find that the probability distribution of the set can be best characterized by a multifractal;moreover, the support of the measure has a fractal dimension. The dynamics of the proposed algorithm with equal-frequency discretization contains a complex and rich structure that can be related to the optimization mechanism.

关键词： continuous optimization algorithm Fictitious play theory Bayesian estimate 1/f noise Multifractal

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continuous optimization algorithms for tuning real and integer parameters of swarm intelligence algorithms

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SWARM INTELLIGENCE 2012年第1期6卷 49-75页

作者： Yuan, Zhi de Oca, Marco A. Montes Birattari, Mauro Stuetzle, Thomas Univ Libre Bruxelles CoDE IRIDIA Brussels Belgium

The performance of optimization algorithms, including those based on swarm intelligence, depends on the values assigned to their parameters. To obtain high performance, these parameters must be fine-tuned. Since many parameters can take real values or integer values from a large domain, it is often possible to treat the tuning problem as a continuous optimization problem. In this article, we study the performance of a number of prominent continuous optimization algorithms for parameter tuning using various case studies from the swarm intelligence literature. The continuous optimization algorithms that we study are enhanced to handle the stochastic nature of the tuning problem. In particular, we introduce a new post-selection mechanism that uses F-Race in the final phase of the tuning process to select the best among elite parameter configurations. We also examine the parameter space of the swarm intelligence algorithms that we consider in our study, and we show that by fine-tuning their parameters one can obtain substantial improvements over default configurations.

关键词： Automated algorithm configuration Parameter tuning continuous optimization algorithm Swarm intelligence F-Race

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