Statistical framework for terminating evolutionary algorithms at their steady state

Student thesis: Doctoral thesis


The goal of this Thesis is assessing the quality of existing stopping conditions for terminating Evolutionary Algorithms at its steady state. An Evolutionary Algorithm (EA) is an iterative population based technique based on natural evolution rules principles to find (or explore) in a given search space the set of point that best fits a given real situation according to a cost function. When a problem is presented in practically all situations, an exploration of a set of possible solutions is needed and for each possible solution its goodness is valuable. EAs can be viewed as an optimization technique if a function is given. As any iterative technique, a stop criterion for terminating EA numeric implementation is mandatory. In the case of optimization methods, the algorithm should stop at the time it has reached a steady state so it can not improve results anymore. Assessing the reliability of termination conditions for evolutionary algorithms is of prime importance. A wrong or weak stop criterion can negatively affect both the computational effort and the final result. In this Thesis, we introduce a statistical framework for assessing whether a termination condition is able to stop EA at its steady state. In one hand a numeric approximation to steady states to detect the point in which EA population has lost its diversity has been presented for EA termination. This approximation has been applied to different EA paradigms based on diversity and a selection of functions covering the properties most relevant for EA convergence. Experiments show that our condition works regardless of the search space dimension and function landscape and Differential Evolution (DE) arises as the best EA paradigm. On the other hand, we use a regression model in order to determine the requirements ensuring that a measure derived from EA evolving population is related to the distance to the optimum in x-space. Our theoretical framework is analyzed across several benchmark test functions and two standard termination criteria based on function improvement in function space and EA population x-space distribution for the DE paradigm. Results validate our statistical framework as a powerful tool for determining the capability of a measure for terminating EA and select the x-space distribution as the best-suited for accurately stopping DE in real-world applications.
Date of Award24 Jul 2015
Original languageEnglish
SupervisorDebora Gil Resina (Director) & Jesus Giraldo Arjonilla (Director)

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