Evolution Strategies in Dynamic Environments

Abstract

Summary. Numerical parameter optimization is an often needed task. In many times, it is not necessary to find the exact optimum but a good solution in an appropriate time. Especially in dynamic environments the main task is not to find one nearly optimal solution but to track the moving optimum as narrow as possible. For this type of problems it is necessary for an optimization algorithm to own mechanisms for adaptation to the problem at hand. Evolutionary algorithms with self-adaptive features are state-of-the-art and known as good problem solvers for this type of optimization tasks. In this chapter, we present a detailed description of one main variant of this class of problem solvers, namely evolution strategies. IntroductionEvolutionary algorithms (EA) are a class of nature inspired problem solvers. They use mechanisms known from natural evolution and have in common the transfer of their biological background into optimization. EA have proven their potentials in many real world applications. It is known that in static environments evolutionary algorithms find good or nearly optimal solutions even for difficult problems in a short time. In addition, they own a high robustness against changes of the problem instance over a certain range. Moreover, state-of-the-art EA like evolution strategies (ES) can adapt to different situations during the run. Such a feature makes them interesting for application in dynamic environments . These types of problems seem to be the more interesting ones since most real world problems are of non-stationary type.In dynamic optimization we can divide two distinct phases. At first, the algorithm needs some time to search for the optimum. The period needed for this task is called the searching phase. Once the algorithm has found the optimum within a certain accuracy the algorithm must follow the moving optimum with a distance as small as possible. This phase is called the tracking phase and lasts potentially eternally.Dynamic optimization problems are harder to optimize than static problems. The more difficulty of optimization in non-stationary environments is L. Schönemann: Evolution Strategies in Dynamic Environments, Studies in Computational Intelligence (SCI) 51, 51-77 (2007) www.springerlink.com

Optimization in dynamic environments: a survey on problems, methods and measures

“…-Stability: In the context of dynamic optimization, an adaptive algorithm is called stable if changes in the environment do not affect the optimization accuracy Average best function value (ABFV) (Abbass et al 2004;Eberhart and Shi 2001;Montemanni et al 2003;Schönemann 2004Schönemann , 2007 Average error (Bui et al 2005a, b;Kramer and Gallagher 2003) Current best (Aydin and Ö ztemel 2000;Bosman 2005Bosman , 2007Dam et al 2007;Eriksson and Olsson 2002;Esquivel and Coello Coello 2004;Hanshar and Ombuki-Berman 2007;Laredo et al 2008;Mattfeld and Bierwirth 2004;Michalewicz et al 2007;Neri and Mäkinen 2007;Olivetti de França et al 2005;Shi and Eberhart 2001;Tenne and Armfield 2007;Tumer and Agogino 2007;Venayagamoorthy 2004) Current best evolution (Dam et al 2007;Eberhart and Shi 2001;Fernandes et al 2007;Jin and Sendhoff 2004;Mori et al 2000a, b;Riolo 2005, 2006;Stanhope and Daida 1999;Tinos and Yang 1823) Current best-of-generation evolution (Morrison 2003(Morrison , 2004Quintão et al 2007;Richter 2005;Saleem and Reynolds 2000;Schönemann 2007;Simões and Costa 2003;Tinós and Yang 2007a, b;Wineberg and Oppacher 2000;…”

“…In this sense, interesting benchmarks are obtained when the ''peak'' function from (Eriksson and Olsson 2002;Esquivel andCoello Coello 2004, 2006;Morrison 2004;Peng and Reynolds 2004;Saleem and Reynolds 2000) Dynamic Ackley function (Schönemann 2004(Schönemann , 2007 Dynamic bit-matching (Jin and Branke 2005;Mori and Kita 2000a, b;Stanhope and Daida 1999) Dynamic deceptive functions (Tinós and Yang 2007b;Wang et al 2009a, b;Yang 2003Yang , 2006bYang , 2007Yang and Tinós 2007a, b;Yao 2005, 2008) Dynamic knapsack problem (Branke et al 2006a, b;Jin and Branke 2005;Karaman et al 2005;Rohlfshagen and Yao 2009a, b;Simões and Costa 2003;Wang et al 2009b;Yang 2008;Yang and Tinós 2007a, b;Yang and Yao 2005) Dynamic Onemax function (Droste 2003;Fernandes et al 2008;Wang et al 2009a;Yang 2003Yang , 2005Yang , 2007Yang , 2008Yang and Tinós 2007a, b;Yang and Yao 2008) Dynamic plateau functions (Wang et al 2009a;Yang 2006bYang , 2008 Dynamic problem generator (Jin and Sendhoff 2004;Li and Yang 2008a;Morrison and De Jong 1999;…”

“…Ackley function (Schönemann 2004(Schönemann , 2007 Optimization in dynamic environments 1439 Table 6 continued Problem Methods (abbreviations are taken from (Tinós and Yang 2007a, b;Wang et al 2009a, b;Yang 2003Yang , 2005Yang , 2006aYang , b, 2007Yang and Yao 2008) Dyn. knapsack problem (Branke et al 2006a, b (Wang et al 2009a, b;Yang 2003Yang , 2005Yang , 2007Yang , 2008Yang and Tinós 2007a, b;Yang and Yao 2008) Dyn.…”

A Benchmark for Virtual Camera Control

“…The first measure describes how close the current best camera configuration found by the algorithm is to the best existing camera configuration at any given moment. To measure such aspect, we employ the average best function value measure suggested by Schönemann [20] to evaluate dynamic optimisation algorithms. The second measure, reliability, describes how often the algorithm succeeds to provide an acceptable solution during the optimisation.…”

Evolution Strategies with q-Gaussian Mutation for Dynamic Optimization Problems

“…Similar to other evolutionary algorithms (EAs), new candidate solutions are generated in ESs by using a stochastic mutation operator. The parameters of the mutation operator can be modified by self-adaptation during the evolutionary process, which provides an intrinsic mechanism for adaptation to eventual changes in the problem and makes the use of ESs interesting for dynamic optimization problems (DOPs) [1], [7], [12].…”