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The importance of operator-based metrics to characterize Evolutionary Algorithms is nowadays a clear and widely accepted fact. Defining a distance measure, or a measure of similarity, that is, in some sense “consistent” with (or “bound” to, or “based” on) the genetic operator(s) informally means that if two individuals are close to each other, or similar, one can be transformed into the other in a few applications of the operator(s). We propose a new crossover-based distance measure for GAs that quantifies the minimum number of crossover operations that have to be applied to transform an individual into another. For doing this, we need to consider all the possible next populations, which is a difficult task. We propose a solution to overcome this difficulty using schema theory. In particular, we show how it is possible to define a lattice structure over some sets of schemata represented in a GA population, and, exploiting some well known properties of lattices and of discrete dynamic systems, we define a distance between populations. We finally define a family of distances between GA individuals using the distance between populations defined beforehand.

The Sharpened No Free Lunch theorem states that all optimization algorithms have the same performance on sets of functions that are closed under permutation, independently of the considered performance measure. However, not all performance measures are informative on how fast or how accurately an algorithm can solve a given problem. In this paper we focus on a particular performance measure, called optimization speed, that quanti fies how fast a search algorithm is able to find an optimal solution, and we try to characterize the set of functions on which all possible search algorithms have the same optimization speed. We call fair these sets, and we prove some results about their structure, the number of such sets and the computational complexity of checking fairness.

The classification of cancer patients into risk classes is a very active field of research, with direct clinical applications. We have recently compared several machine learning methods on the well known 70-genes signature dataset. In that study, genetic programming showed promising results, given that it outperformed all the other techniques. Nevertheless, the study was preliminary, mainly because the validation dataset was preprocessed and all its features binarized in order to use logical operators for the genetic programming functional nodes. If this choice allowed simple interpretation of the solutions from the biological viewpoint, on the other hand the binarization of data was limiting, since it amounts to a sizable loss of information. The goal of this paper is to overcome this limitation, using the 70-genes signature dataset with real-valued expression data. The results we present show that genetic programming using the number of incorrectly classified instances as fitness function is not able to outperform the other machine learning methods. However, when a weighted average between false positives and false negatives is used to calculate fitness values, genetic programming obtains performances that are comparable with the other methods in the minimization of incorrectly classified instances and outperforms all the other methods in the minimization of false negatives, which is one of the main goals in breast cancer clinical applications. Also in this case, the solutions returned by genetic programming are simple, easy to understand, and they use a rather limited subset of the available features.

The goal of this paper is to present four new parallel and distributed particle swarm optimization methods and to experimentally compare their performances. These methods include a genetic algorithm whose individuals are co-evolving swarms, a different multiswarm system and their respective variants enriched by adding a repulsive component to the particles. We have tried to carry out this comparison using the benchmark test suite that has been defined for the CEC-2005 numerical optimization competition and we have remarked that it is hard to have a clear picture of the experimental results on that benchmark suite. We believe that this is due to the fact that the CEC-2005 benchmark suite is only composed by either very easy or very hard test functions. For this reason, we introduce two new sets of test functions whose difficulty can be tuned by simply modifying the values of few real-valued parameters. We propose to integrate the CEC-2005 benchmark suite by adding these sets of test functions to it. Experimental results on these two sets of test functions clearly show that the proposed repulsive multi-swarm system outperforms all the other presented methods.

The goal of this paper is to present four new parallel and distributed particle swarm optimization methods and to experimentally compare their performances on a wide set of benchmark functions. These methods include a genetic algorithm whose individuals are co-evolving swarms, an "island model"-based multi-swarm system, where swarms are independent and they interact by means of particle migrations at regular time steps, and their respective variants enriched by adding a repulsive component to the particles. The benchmark functions used in our experimental study are two new sets of test functions (whose difficulty can be tuned by simply modifying the values of few real-valued parameters), the well known Rastrigin test functions, and the test functions proposed in the CEC 2005 numerical optimization competition. We show that the proposed repulsive multi-swarm system outperforms all the other presented methods. Copyright 2010 ACM.

The crossover bias theory for bloat [18] is a recent result which predicts that bloat is caused by the sampling of short, unfit programs. This theory is clear and simple, but it has some weaknesses: (1) it implicitly assumes that the population is large enough to allow sampling of all relevant program sizes (although it does explain what to expect in the many practical cases where this is not true, e.g., because the population is small); (2) it does not explain what is meant by its assumption that short programs are unfit. In this paper we discuss these weaknesses and propose a refined version of the crossover bias theory that clarifies the relationship between bloat and finite populations, and explains what features of the fitness landscape cause bloat to occur. The theory, in particular, predicts that smaller populations will bloat more slowly than larger ones. Additionally, the theory predicts that bloat will only be observed in problems where short programs are less fit than longer ones when looking at samples created by fitness-based importance sampling, i.e. samplings of the search space in which fitter programs have a higher probability of being sampled (e.g., the Metropolis-Hastings method). Experiments with two classical GP benchmarks fully corroborate the theory. Copyright 2008 ACM.

Elitism is commonly used in generational GP to ensure that the best individuals discovered in a generation are not lost, and are made available for possible further improvements to new generations. Using two GP systems and four problems, we show how elitism reduces the growth of mean program size.

Cooperative coevolution has proven to be a promising technique for solving complex combinatorial optimization problems. In this paper, we present four different strategies which involve cooperative coevolution of a genetic program and of a population of constants evolved by a genetic algorithm. The genetic program evolves expressions that solve a problem, while the genetic algorithm provides “good” values for the numeric terminal symbols used by those expressions. Experiments have been performed on three symbolic regression problems and on a “real-world” biomedical application. Results are encouraging and confirm that our coevolutionary algorithms can be used effectively in different domains

Neutrality of some boolean parity fitness landscapes is investigated in this paper. Compared with some well known contributions on the same issue, we define some new measures that help characterizing neutral landscapes, we use a new sampling methodology, which captures some features that are disregarded by uniform random sampling, and we introduce new genetic operators to define the neighborhood of tree structures. We compare the fitness landscape induced by two different sets of functional operators ({nand} and {xor ; not}). The different characteristics of the neutral networks seem to justify the different difficulties of these landscapes for genetic programming