A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Combining model-based EAs for Mixed-Integer problems

A key characteristic of Mixed-Integer (MI) problems is the presence of both continuous and discrete problem variables. These variables can interact in various ways, resulting in challenging optimization problems. In this paper, we study the design of an algorithm that combines the strengths of LTGA and iAMaLGaM: state-of-the-art model-building EAs designed for discrete and continuous search spaces, respectively. We examine and discuss issues which emerge when trying to integrate those two algorithms into the MI setting. Our considerations lead to a design of a new algorithm for solving MI problems, which we motivate and compare with alternative approaches

Using landscape topology to compare continuous metaheuristics: a framework and case study on EDAs and ridge structure

In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behavior of continuous metaheuristic optimization algorithms. In particular, we generate twodimensional landscapes with parameterized, linear ridge structure, and perform pairwise comparisons of algorithms to gain insight into what kind of problems are easy and difficult for one algorithm instance relative to another.We apply thismethodology to investigate the specific issue of explicit dependency modeling in simple continuous estimation of distribution algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modeling is useful, harmful, or has little impact on mean algorithm performance. Heat maps are used to compare algorithm performance over a large number of landscape instances and algorithm trials. Finally, we perform ameta-search in the landscape parameter space to find landscapes which maximize the performance between algorithms. The results are related to some previous intuition about the behavior of these algorithms, but at the same time lead to new insights into the relationship between dependency modeling in EDAs and the structure of the problem landscape. The landscape generator and overall methodology are quite general and extendable and can be used to examine specific features of other algorithms

Combining Model-based EAs for Mixed-Integer Problems

A key characteristic of Mixed-Integer (MI) problems is the presence of both continuous and discrete problem variables. These variables can interact in various ways, resulting in challenging optimization problems. In this paper, we study the design of an algorithm that combines the strengths of LTGA and iAMaLGaM: state-of-the-art model-building EAs designed for discrete and continuous search spaces, respectively. We examine and discuss issues which emerge when trying to integrate those two algorithms into the MI setting. Our considerations lead to a design of a new algorithm for solving MI problems, which we motivate and compare with alternative approaches

MATEDA: A suite of EDA programs in Matlab

This paper describes MATEDA-2.0, a suite of programs in Matlab for estimation of distribution algorithms. The package allows the optimization of single and multi-objective problems with estimation of distribution algorithms (EDAs) based on undirected graphical models and Bayesian networks. The implementation is conceived for allowing the incorporation by the user of different combinations of selection, learning, sampling, and local search procedures. Other included methods allow the analysis of the structures learned by the probabilistic models, the visualization of particular features of these structures and the use of the probabilistic models as fitness modeling tools

A Clustering-Based Model-Building EA for Optimization Problems with Binary and Real-Valued Variables

We propose a novel clustering-based model-building evolutionary algorithm to tackle optimization problems that have both binary and real-valued variables. The search space is clustered every generation using a distance metric that considers binary and real-valued variables jointly in order to capture and exploit dependencies between variables of different types. After clustering, linkage learning takes place within each cluster to capture and exploit dependencies between variables of the same type. We compare this with a model-building approach that only considers dependencies between variables of the same type. Additionally, since many real-world problems have constraints, we examine the use of different well-known approaches to handling constraints: constraint domination, dynamic penalty and global competitive ranking. We experimentally analyze the performance of the proposed algorithms on various unconstrained problems as well as a selection of well-known MINLP benchmark problems that all have constraints, and compare our results with the Mixed-Integer Evolution Strategy (MIES). We find that our approach to clustering that is aimed at the processing of dependencies between binary and real-valued variables can significantly improve performance in terms of required population size and function evaluations when solving problems that exhibit properties such as multiple optima, strong mixed dependencies and constraints

Derivative-Free Optimization

Abstract. In many engineering applications it is common to find optimization problems where the cost function and/or constraints require complex simulations. Though it is often, but not always, theoretically possible in these cases to extract derivative information efficiently, the associated implementation procedures are typically non-trivial and time-consuming (e.g., adjoint-based methodologies). Derivative-free (non-invasive, black-box) optimization has lately received considerable attention within the optimization community, including the establishment of solid mathematical foundations for many of the methods considered in practice. In this chapter we will describe some of the most conspicuous derivative-free optimization techniques. Our depiction will concentrate first on local optimization such as pattern search techniques, and other methods based on interpolation/approximation. Then, we will survey a number of global search methodologies, and finally give guidelines on constraint handling approaches