Non-standard approaches to evolutionary algorithms in an optimization dilemma

Este artículo pretende ser un ensayo de tipo crítico-reflexivo, que toma como base el conocido problema que se presenta en el Dilema Exploración-Explotación (DEE) cuando se trabaja con Algoritmos Evolutivos (AEs) y se centra en las propuestas, en este aspecto, tanto de los enfoques tradicionales, como de los enfoques recientes que manejan la población de soluciones (individuos) de manera distinta a los AEs estándar, a saber: el Modelo Evolutivo Aprendible (MEVA) y los Algoritmos de Estimación de Distribuciones (AEDs).This article is intended to be a critical-reflexive essay based on a well-known problem: the Exploration-Exploitation Dilemma (DEE, in spanish) when working with Evolutionary Algorithms (AEs, in Spanish) and, in this respect, focuses on the proposals that study both: traditional approaches and recent ones handling the population of solutions (individuals) differently from the AEs standard, which are: the Learnable Evolution Model (MEVA, in spanish) and the Estimation of Distribution Algorithms (AEDs, in spanish

Probabilistic Tools for the Analysis of Randomized Optimization Heuristics

This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like stochastic domination and coupling or Chernoff bounds for geometrically distributed random variables and for negatively correlated random variables. Most of the results presented here have appeared previously, some, however, only in recent conference publications. While the focus is on collecting tools for the analysis of randomized search heuristics, many of these may be useful as well in the analysis of classic randomized algorithms or discrete random structures.Comment: 91 page

Artificial Immune Systems for Combinatorial Optimisation: A Theoretical Investigation

We focus on the clonal selection inspired computational models of the immune system developed for general-purpose optimisation. Our aim is to highlight when these artificial immune systems (AIS) are more efficient than evolutionary algorithms (EAs). Compared to traditional EAs, AIS use considerably higher mutation rates (hypermutations) for variation, give higher selection probabilities to more recent solutions and lower selection probabilities to older ones (ageing). We consider the standard Opt-IA that includes both of the AIS distinguishing features and argue why it is of greater applicability than other popular AIS. Our first result is the proof that the stop at first constructive mutation version of its hypermutation operator is essential. Without it, the hypermutations cannot optimise any function with an arbitrary polynomial number of optima. Afterwards we show that the hypermutations are exponentially faster than the standard bit mutation operator used in traditional EAs at escaping from local optima of standard benchmark function classes and of the NP-hard Partition problem. If the basin of attraction of the local optima is not too large, then ageing allows even greater speed-ups. For the Cliff benchmark function this can make the difference between exponential and quasi-linear expected time. If the basin of attraction is too large, then ageing can implicitly detect the local optimum and escape it by automatically restarting the search process. The described power of hypermutations and ageing allows us to prove that they guarantee (1+epsilon) approximations for Partition in expected polynomial time for any constant epsilon. These features come at the expense of the hypermutations being a linear factor slower than EAs for standard unimodal benchmark functions and of eliminating the power of ageing at escaping local optima in the complete Opt-IA. We show that hypermutating with inversely proportional rates mitigates such drawbacks at the expense of losing the explorative advantages of the standard operator. We conclude the thesis by designing fast hypermutation operators that are provably a linear factor faster than the traditional ones for the unimodal benchmark functions and Partition, while maintaining explorative power and working in harmony together with ageing