A study of the effects of dimensionality on stochastic hill climbers and estimation of distribution algorithms Laurent Grosset 1,2 , Rodolphe Le Riche 2 , and Raphael T. Haftka 1 1 Mechanical and Aerospace Engineering Department, University of Florida, USA 2 CNRS URA 1884 / SMS, ´ Ecole des Mines de Saint ´ Etienne, France Abstract. One of the most important features of an optimization me- thod is its response to an increase in the number of variables, n. Random stochastic hill climber (SHC) and univariate marginal distribution algo- rithms (UMDA) are two fundamentally different stochastic optimizers. SHC proceeds with local perturbations while UMDA infers and uses a global probability density. The response to dimensionality of the two methods is compared both numerically and theoretically on unimodal functions. SHC response is O(n ln n), while UMDA response ranges from O(  (n) ln(n)) to O(n ln(n)). On two test problems whose sizes go up to 7 200 , SHC is faster than UMDA. 1 Introduction Random stochastic hill climber (SHC) and univariate marginal distribution al- gorithms (UMDA, M¨ uhlenbein and Paaß, 1996) are two fundamentally different stochastic optimizers. SHC proceeds with local perturbations while UMDA in- fers and uses a global probability density. It is important to understand how these two different search processes scale with the number of variables n. Previous contributions have analyzed stochastic hill climbers and population- based evolutionary algorithms on specific objective functions. Garnier et al. (1999) computed the expected first hitting time and its variance for two variants of stochastic hill-climbers. Droste et al. (2002) extended the estimation of the running time of O(n ln n) for a (1+1)-evolution strategy (ES) to general linear functions. Several studies have investigated the benefits of a population. For ex- ample, SHC and genetic algorithms have been compared in Mitchell et al. (1994) on the Royal Road function. Jansen and Wegener (2001) presented a family of functions for which it can be proven that populations accelerate convergence to the optimum even without crossover. He and Yao (2002) used a Markov chain analysis to estimate the time complexity of evolutionary algorithms (EA) for various problems and showed that a population is beneficial for some multi- modal problems. Comparisons between single point and population-based evo- lution strategies on Long-Path problems are given in Garnier and Kallel (2000). There has been little work on the time complexity of estimation of distribution algorithms. The convergence of estimation of distribution algorithms has been