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The practice of evolutionary algorithms involves a mundane yet inescapable phase, namely, finding parameters that work well. How big should the population be? How many generations should the algorithm run? What is the (tournament selection) tournament size? What probabilities should one assign to crossover and mutation? All these nagging questions need good answers if one is to embrace success. Through an extensive series of experiments over multiple evolutionary algorithm implementations and problems we show that parameter space tends to be rife with viable parameters. We aver that this renders the life of the practitioner that much easier, and cap off our study with an advisory digest for the weary.
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Guest Editors: Nadia Boukhelifa and Evelyne Lutton (both at INRA, Versailles-Grignon, France). Please see the full CFP on the Springer site.
Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multiobjective Algorithms
There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe
Shape optimization techniques are becoming increasingly important in design and engineering. This growing significance reflects the need to exploit advances in digital fabrication technologies, and the desire to create new types of surface designs for various engineering applications. Evolutionary algorithms (EAs) offer several key advantages for shape optimization, but they can also be restricted, especially as design problems scale up in size. A key challenge for evolutionary shape optimization is to overcome these challenges in order to apply EAs to large-scale, “real-world” engineering problems. This paper presents a new evolutionary approach to shape optimization using what we call “surface-mapped compositional pattern producing networks (CPPNs).” Our method outperforms a state-of-the-art gradient-based method on a simple benchmark problem, and scales well as degrees of freedom are added to the design problem. Our results demonstrate that surface-mapped CPPNs offer practical ways of approaching large-scale, real-world engineering problems with EAs, opening up exciting new opportunities for engineering design.
The purposes of this paper are twofold. In the first, we describe an exact polynomial-time algorithm for the pair sequencing problem and show how this method can be used to pack fixed-height trapezoids into a single bin such that interitem wastage is minimized. We then go on to examine how this algorithm can be combined with bespoke evolutionary and local search methods for tackling the multiple-bin version of this problem—one that is closely related to 1-D bin packing. In the course of doing this, a number of ideas surrounding recombination, diversity, and genetic repair are also introduced and analyzed.
In this paper, we investigate movement patterns of a particle in the particle swarm optimization (PSO) algorithm. We characterize movement patterns of the particle by two factors: 1) the correlation between its consecutive positions and 2) its range of movement. We introduce the base frequency of movement as a measure for the correlation between positions and the variance of movement as a measure for the range of movement. We determine the base frequency and the variance of movement theoretically and we show how they change with the values of coefficients. We extract a system of equations that enables practitioners to find coefficients’ values to guarantee achieving a given base frequency and variance of movement, i.e., control the movement pattern of particles. We also show that if the base frequency of movement for a particle is small, mid range, or large then the particle’s position at each iteration is positively correlated (smooth movement), uncorrelated (chaotic movement), or negatively correlated (jumping at each iteration) with its previous positions, respectively. We test the effects of the base frequency and variance of movement on the search ability of particles and we show that small base frequencies (i.e., smooth movement) are more effective when the maximum number of function evaluations is large. We found that the most frequently-used coefficient values in PSO literature impose mid-range base frequencies that correspond with a chaotic movement. We also provide new sets of coefficients that outperform existing ones on a set of benchmark functions.
This paper aims to study how the population size affects the computation time of evolutionary algorithms (EAs) in a rigorous way. The computation time of EAs can be measured by either the number of generations (hitting time) or the number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is introduced to compare the expected hitting time of two algorithms and to estimate lower and upper bounds on the population scalability. Several intuitive beliefs are rigorously analyzed. It is proven that: 1) using a population sometimes increases rather than decreases the expected hitting time; 2) using a population cannot shorten the expected running time of any elitist EA on any unimodal function on the time-fitness landscape, however, this statement is not true in terms of the distance-based fitness landscape; and 3) using a population cannot always reduce the expected running time on deceptive functions, which depends on whether the benchmark algorithm uses elitist selection or random selection.