DEUM: a framework for an estimation of distribution algorithm based on Markov random fields.

Estimation of Distribution Algorithms (EDAs) belong to the class of population based optimisation algorithms. They are motivated by the idea of discovering and exploiting the interaction between variables in the solution. They estimate a probability distribution from population of solutions, and sample it to generate the next population. Many EDAs use probabilistic graphical modelling techniques for this purpose. In particular, directed graphical models (Bayesian networks) have been widely used in EDA. This thesis proposes an undirected graphical model (Markov Random Field (MRF)) approach to estimate and sample the distribution in EDAs. The interaction between variables in the solution is modelled as an undirected graph and the joint probability of a solution is factorised as a Gibbs distribution. The thesis describes a model of fitness function that approximates the energy in the Gibbs distribution, and shows how this model can be fitted to a population of solutions to estimate the parameters of the MRF. The estimated MRF is then sampled to generate the next population. This approach is applied to estimation of distribution in a general framework of an EDA, called Distribution Estimation using Markov Random Fields (DEUM). The thesis then proposes several variants of DEUM using different sampling techniques and tests their performance on a range of optimisation problems. The results show that, for most of the tested problems, the DEUM algorithms significantly outperform other EDAs, both in terms of number of fitness evaluations and the quality of the solutions found by them. There are two main explanations for the success of DEUM algorithms. Firstly, DEUM builds a model of fitness function to approximate the MRF. This contrasts with other EDAs, which build a model of selected solutions. This allows DEUM to use fitness in variation part of the evolution. Secondly, DEUM exploits the temperature coefficient in the Gibbs distribution to regulate the behaviour of the algorithm. In particular, with higher temperature, the distribution is closer to being uniform and with lower temperature it concentrates near some global optima. This gives DEUM an explicit control over the convergence of the algorithm, resulting in better optimisation

Analysing the effect of demand uncertainty in dynamic pricing with EAs.

Dynamic pricing is a pricing strategy where a firm adjust the price for their products and services as a function of its perceived demand at different times. In this paper, we show how Evolutionary algorithms (EA) can be used to analyse the effect of demand uncertainty in dynamic pricing. The experiments are conducted in a range of dynamic pricing problems considering a number of different stochastic scenarios with a number of different EAs. The results are analysed, which suggest that higher demand fluctuation may not have adverse effect to the profit in comparison to the lower demand fluctuation, and that the reliability of EA for finding accurate policy could be higher when there is higher fluctuation then when there is lower fluctuation

An application of EDA and GA to dynamic pricing.

E-commerce has transformed the way firms develop their pricing strategies, producing shift away from fixed pricing to dynamic pricing. In this paper, we use two different Estimation of distribution algorithms (EDAs), a Genetic Algorithm (GA) and a Simulated Annealing (SA) algorithm for solving two different dynamic pricing models. Promising results were obtained for an EDA confirming its suitability for resource management in the proposed model. Our analysis gives interesting insights into the application of population based optimization techniques for dynamic pricing

The Markov network fitness model

Fitness modelling is an area of research which has recently received much interest among the evolutionary computing community. Fitness models can improve the efficiency of optimisation through direct sampling to generate new solutions, guiding of traditional genetic operators or as surrogates for a noisy or long-running fitness functions. In this chapter we discuss the application of Markov networks to fitness modelling of black-box functions within evolutionary computation, accompanied by discussion on the relationship betweenMarkov networks andWalsh analysis of fitness functions.We review alternative fitness modelling and approximation techniques and draw comparisons with the Markov network approach. We discuss the applicability of Markov networks as fitness surrogates which may be used for constructing guided operators or more general hybrid algorithms.We conclude with some observations and issues which arise from work conducted in this area so far

ABSTRACT An Application of EDA and GA to Dynamic Pricing

E-commerce has transformed the way firms develop their pricing strategies, producing shift away from fixed pricing to dynamic pricing. In this paper, we use two different Estimation of distribution algorithms (EDAs), a Genetic Algorithm (GA) and a Simulated Annealing (SA) algorithm for solving two different dynamic pricing models. Promising results were obtained for an EDA confirming its suitability for resource management in the proposed model. Our analysis gives interesting insights into the application of population based optimization techniques for dynamic pricing. Categories and Subject Descriptor

Markov Networks in Evolutionary Computation

Markov networks and other probabilistic graphical modes have recently received an upsurge in attention from Evolutionary computation community, particularly in the area of Estimation of distribution algorithms (EDAs).  EDAs have arisen as one of the most successful experiences in the application of machine learning methods in optimization, mainly due to their efficiency to solve complex real-world optimization problems and their suitability for theoretical analysis. This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current research trends and future perspectives in the enhancement and applicability of EDAs are also covered.  The contributions included in the book address topics as relevant as the application of probabilistic-based fitness models, the use of belief propagation algorithms in EDAs and the application of Markov network based EDAs to real-world optimization problems. The book should be of interest to researchers and practitioners from areas such as optimization, evolutionary computation, and machine learning

Applications of distribution estimation using markov network modelling (DEUM)

In recent years, Markov Network EDAs have begun to find application to a range of important scientific and industrial problems. In this chapter we focus on several applications of Markov Network EDAs classified under the DEUM framework which estimates the overall distribution of fitness from a bitstring population. In Section 1 we briefly review the main features of the DEUM framework and highlight the principal features that havemotivated the selection of applications. Sections 2 - 5 describe four separate applications: chemotherapy optimisation; dynamic pricing; agricultural biocontrol; and case-based feature selection. In Section 6 we summarise the lessons learned from these applications. These include: comparisons with other techniques such as GA and Bayesian Network EDAs; trade-offs between modelling cost and reduction in search effort; and the use of MN models for surrogate evaluation. We also present guidelines for further applications and future research