Compact Optimization Algorithms with Re-sampled Inheritance

The file attached to this record is the author's final peer reviewed version.Compact optimization algorithms are a class of Estimation of Distribution Algorithms (EDAs) characterized by extremely limited memory requirements (hence they are called \compact"). As all EDAs, compact algorithms build and update a probabilistic model of the distribution of solutions within the search space, as opposed to population-based algorithms that instead make use of an explicit population of solutions. In addition to that, to keep their memory consumption low, compact algorithms purposely employ simple probabilistic models that can be described with a small number of parameters. Despite their simplicity, compact algorithms have shown good performances on a broad range of benchmark functions and real-world problems. However, compact algorithms also come with some drawbacks, i.e. they tend to premature convergence and show poorer performance on non-separable problems. To overcome these limitations, here we investigate a possible algorithmic scheme obtained by combining compact algorithms with a non-disruptive restart mechanism taken from the literature, named Re-Sampled Inheritance (RI). The resulting compact algorithms with RI are tested on the CEC 2014 benchmark functions. The numerical results show on the one hand that the use of RI consistently enhances the performances of compact algorithms, still keeping a limited usage of memory. On the other hand, our experiments show that among the tested algorithms, the best performance is obtained by compact Differential Evolution with RI

A Differential Evolution Framework with Ensemble of Parameters and Strategies and Pool of Local Search Algorithms

The file attached to this record is the author's final peer reviewed version. The publisher's final version can be found by following the DOI link.The ensemble structure is a computational intelligence supervised strategy consisting of a pool of multiple operators that compete among each other for being selected, and an adaptation mechanism that tends to reward the most successful operators. In this paper we extend the idea of the ensemble to multiple local search logics. In a memetic fashion, the search structure of an ensemble framework cooperatively/competitively optimizes the problem jointly with a pool of diverse local search algorithms. In this way, the algorithm progressively adapts to a given problem and selects those search logics that appear to be the most appropriate to quickly detect high quality solutions. The resulting algorithm, namely Ensemble of Parameters and Strategies Differential Evolution empowered by Local Search (EPSDE-LS), is evaluated on multiple testbeds and dimensionality values. Numerical results show that the proposed EPSDE-LS robustly displays a very good performance in comparison with some of the state-of-the-art algorithms

Can compact optimisation algorithms be structurally biased?

In the field of stochastic optimisation, the so-called structural bias constitutes an undesired behaviour of an algorithm that is unable to explore the search space to a uniform extent. In this paper, we investigate whether algorithms from a subclass of estimation of distribution algorithms, the compact algorithms, exhibit structural bias. Our approach, justified in our earlier publications, is based on conducting experiments on a test function whose values are uniformly distributed in its domain. For the experiment, 81 combinations of compact algorithms and strategies of dealing with infeasible solutions have been selected as test cases. We have applied two approaches for determining the presence and severity of structural bias, namely an (existing) visual and an (updated) statistical (Anderson-Darling) test. Our results suggest that compact algorithms are more immune to structural bias than their counterparts maintaining explicit populations. Both tests indicate that strong structural bias is found only in the cBFO algorithm, regardless of the choice of strategy of dealing with infeasible solutions, and cPSO with mirror strategy. For other test cases, statistical and visual tests disagree on some cases classified as having mild or strong structural bias: the former one tends to make harsher decisions, thus needing further investigation

Large Scale Problems in Practice: The effect of dimensionality on the interaction among variables

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This article performs a study on correlation between pairs of variables in dependence on the problem dimensionality. Two tests, based on Pearson and Spearman coefficients, have been designed and used in this work. In total, $86$ test problems ranging between 10 and 1000 variables have been studied. If the most commonly used experimental conditions are used, the correlation between pairs of variables appears, from the perspective of the search algorithm, to consistently decrease. This effect is not due to the fact that the dimensionality modifies the nature of the problem but is a consequence of the experimental conditions: the computational feasibility of the experiments imposes an extremely shallow search in case of high dimensions. An exponential increase of budget and population with the dimensionality is still practically impossible. Nonetheless, since real-world application may require that large scale problems are tackled despite of the limited budget, an algorithm can quickly improve upon initial guesses if it integrates the knowledge that an apparent weak correlation between pairs of variables occurs, regardless the nature of the problem

On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments

Sampling has been often employed by evolutionary algorithms to cope with noise when solving noisy real-world optimization problems. It can improve the estimation accuracy by averaging over a number of samples, while also increasing the computation cost. Many studies focused on designing efficient sampling methods, and conflicting empirical results have been reported. In this paper, we investigate the effectiveness of sampling in terms of rigorous running time, and find that sampling can be ineffective. We provide a general sufficient condition under which sampling is useless (i.e., sampling increases the running time for finding an optimal solution), and apply it to analyzing the running time performance of (1+1)-EA for optimizing OneMax and Trap problems in the presence of additive Gaussian noise. Our theoretical analysis indicates that sampling in the above examples is not helpful, which is further confirmed by empirical simulation results

Memetic viability evolution for constrained optimization

The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while covariance matrix adaptation evolution strategy (CMA-ES) is one of the most efficient algorithms for unconstrained optimization problems, it cannot be readily applied to constrained ones. Here, we used concepts from memetic computing, i.e., the harmonious combination of multiple units of algorithmic information, and viability evolution, an alternative abstraction of artificial evolution, to devise a novel approach for solving optimization problems with inequality constraints. Viability evolution emphasizes the elimination of solutions that do not satisfy viability criteria, which are defined as boundaries on objectives and constraints. These boundaries are adapted during the search to drive a population of local search units, based on CMAES, toward feasible regions. These units can be recombined by means of differential evolution operators. Of crucial importance for the performance of our method, an adaptive scheduler toggles between exploitation and exploration by selecting to advance one of the local search units and/or recombine them. The proposed algorithm can outperform several state-of-the-art methods on a diverse set of benchmark and engineering problems, both for quality of solutions and computational resources needed

A Genetic Approach to the Ethical Knob

4nonenoneIacca G; Lagioia F; Loreggia A; Sartor GIacca, G; Lagioia, F; Loreggia, A; Sartor,