Mimicking biological evolution and harnessing its power for adaptation are problems that have intrigued computer scientists for at least four decades. Genetic algorithms (GAs), invented by John Holland in the 1960s, are the most widely used approaches to computational evolution. In his book Adaptation in Natural and Artificial Systems (Holland, 1992, also reviewed in this issue), Holland presented GAs in a general theoretical framework for adaptation in nature. Holland’s motivation was largely scientific — he was attempting to understand and link diverse types of natural phenomena—but he also proposed potential engineering applications of GAs. Since the publication of Holland’s book, the field of GAs has grown into a significant sub-area of artificial intelligence and machine learning. Nowadays one can find several international conferences each year as well as a number of journals devoted to GAs and other “evolutionary computation ” approaches. Research on GAs has spread from computer science to engineering and, more recently, to fields such as molecular biology, immunology, economics, and physics. One result of this growth in interest has been a division of the field of GAs into several subspecies. One major division is between research on GAs as engineering tools and research

A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori “head-to-head” minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems’ enforcing of a type of uniformity over all algorithms.

Abstract: This paper introduces stacked generalization, a scheme for minimizing the generalization error rate of one or more generalizers. Stacked generalization works by deducing the biases of the generalizer(s) with respect to a provided learning set. This deduction proceeds by generalizing in a second space whose inputs are (for example) the guesses of the original generalizers when taught with part of the learning set and trying to guess the rest of it, and whose output is (for example) the correct guess. When used with multiple generalizers, stacked generalization can be seen as a more sophisticated version of cross-validation, exploiting a strategy more sophisticated than cross-vali-dation’s crude winner-takes-all for combining the individual generalizers. When used with a single generalizer, stacked generalization is a scheme for estimating (and then correcting for) the error of a generalizer which has been trained on a particular learning set and then asked a particular ques-tion. After introducing stacked generalization and justifying its use, this paper presents two numer-ical experiments. The first demonstrates how stacked generalization improves upon a set of sepa-rate generalizers for the NETtalk task of translating text to phonemes. The second demonstrates how stacked generalization improves the performance of a single surface-fitter. With the other ex-perimental evidence in the literature, the usual arguments supporting cross-validation, and the ab-stract justifications presented in this paper, the conclusion is that for almost any real-world gener-alization problem one should use some version of stacked generalization to minimize the general-ization error rate. This paper ends by discussing some of the variations of stacked generalization, and how it touches on other fields like chaos theory. Key Words: generalization and induction, combining generalizers, learning set pre-processing, cross-validation, error estimation and correction.

This paper reports work done over the past three years using rank-based allocation of reproductive trials. New evidence and arguments are presented which suggest that allocating reproductive trials according to rank is superior to fitness proportionate reproduction. Ranking can not only be used to slow search speed, but also to increase search speed when appropriate. Furthermore, the use of ranking provides a degree of control over selective pressure that is not possible with fitness proportionate reproduction. The use of rank-based allocation of reproductive trials is discussed in the context of 1) Holland's schema theorem, 2) DeJong's standard test suite, and 3) a set of neural net optimization problems that are larger than the problems in the standard test suite. The GENITOR algorithm is also discussed; this algorithm is specifically designed to allocate reproductive trials according to rank.

Genetic algorithms (GAs) are biologically motivated adaptive systems which have been used, with varying degrees of success, for function optimization. In this study, an abstraction of the basic genetic algorithm, the Equilibrium Genetic Algorithm (EGA), and the GA in turn, are reconsidered within the framework of competitive learning. This new perspective reveals a number of different possibilities for performance improvements. This paper explores population-based incremental learning (PBIL), a method of combining the mechanisms of a generational genetic algorithm with simple competitive learning. The combination of these two methods reveals a tool which is far simpler than a GA, and which out-performs a GA on large set of optimization problems in terms of both speed and accuracy. This paper presents an empirical analysis of where the proposed technique will outperform genetic algorithms, and describes a class of problems in which a genetic algorithm may be able to perform better. Extensions to this algorithm are discussed and analyzed. PBIL and extensions are compared with a standard GA on twelve problems, including standard numerical optimization functions, traditional GA test suite problems, and NP-Complete problems.

This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies’ foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the ACO metaheuristic are defined. In the second part of the article a number of applications of ACO algorithms to combinatorial optimization and routing in communications networks are described. We conclude with a discussion of related work and of some of the most important aspects of the ACO metaheuristic.

We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its information-theoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm 's performance. We also investigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and time-varying cost functions. We conclude with some discussion of the justifiability of biologically-inspired search methods.

Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to nd pro table actions while taking the empirically best action as often as possible. A popular measure of a policy's success in addressing this dilemma is the regret, that is the loss due to the fact that the globally optimal policy is not followed all the times. One of the simplest examples of the exploration/exploitation dilemma is the multi-armed bandit problem.

This paper presents a model for predicting the convergence quality of genetic algorithms. The model incorporates previous knowledge about decision making in genetic algorithms and the initial supply of building blocks in a novel way. The result is an equation that accurately predicts the quality of the solution found by a GA using a given population size. Adjustments for different selection intensities are considered and computational experiments demonstrate the effectiveness of the model. I. Introduction The size of the population in a genetic algorithm (GA) is a major factor in determining the quality of convergence. The question of how to choose an adequate population size for a particular domain is difficult and has puzzled GA practitioners for a long time. Hard questions are better approached using a divide-and-conquer strategy and the population sizing issue is no exception. In this case, we can identify two factors that influence convergence quality: the initial supply of build...

Similar to Genetic Algorithms, Evolution Strategies (ESs) are algorithms which imitate the principles of natural evolution as a method to solve parameter optimization problems. The development of Evolution Strategies from the first mutation--selection scheme to the refined (¯,)--ES including the general concept of self--adaptation of the strategy parameters for the mutation variances as well as their covariances are described. 1 Introduction The idea to use principles of organic evolution processes as rules for optimum seeking procedures emerged independently on both sides of the Atlantic ocean more than two decades ago. Both approaches rely upon imitating the collective learning paradigm of natural populations, based upon Darwin's observations and the modern synthetic theory of evolution. In the USA Holland introduced Genetic Algorithms in the 60ies, embedded into the general framework of adaptation [Hol75]. He also mentioned the applicability to parameter optimization which was fir...