Abstract
Surfing in rough waters is not always as fun as wave riding the “big one”. Similarly, in optimization problems, fitness landscapes with a huge number of local optima make the search for the global optimum a hard and generally annoying game. Computational Intelligence optimization metaheuristics use a set of individuals that “surf” across the fitness landscape, sharing and exploiting pieces of information about local fitness values in a joint effort to find out the global optimum. In this context, we designed surF, a novel surrogate modeling technique that leverages the discrete Fourier transform to generate a smoother, and possibly easier to explore, fitness landscape. The rationale behind this idea is that filtering out the high frequencies of the fitness function and keeping only its partial information (i.e., the low frequencies) can actually be beneficial in the optimization process. We prove our theory by combining surF with a settings free variant of Particle Swarm Optimization (PSO) based on Fuzzy Logic, called Fuzzy Self-Tuning PSO. Specifically, we introduce a new algorithm, named F3ST-PSO, which performs a preliminary exploration on the surrogate model followed by a second optimization using the actual fitness function. We show that F3ST-PSO can lead to improved performances, notably using the same budget of fitness evaluations.
Highlights
Most optimization problems, related to real-life applications, are characterized by the existence of a large number of local optima, which might induce a premature convergence of optimization methods and prevent the identification of the global optimum
The aim of the tests presented is twofold: first, we assess the actual capability of Surrogate Modeling with Fourier Filtering (surF) in creating surrogate models that are easier to explore, while preserving the specific features of the fitness landscape; second, we investigate the entire process to evaluate whether our methodology could be beneficial to solve the optimization problem
From similar surrogate modeling approaches—which are generally adopted to mitigate the computational effort of fitness evaluations—surF allows the user to select the level of “ruggedness” of the search space by setting a specific hyperparameter γ, which gives control over the number of low-frequency harmonics used for the inverse Fourier transform
Summary
Most optimization problems, related to real-life applications, are characterized by the existence of a large number of local optima, which might induce a premature convergence of optimization methods and prevent the identification of the global optimum. If we consider this issue from the perspective of a search on the fitness landscape, we are forced to face the exploration of a rugged multidimensional surface, which makes the search for the global optimum pretty hard and time consuming. In this work we aim at simplifying the optimization task by smoothing the fitness landscape, i.e., getting rid of (a number of) local optima thanks to the generation of a surrogate fitness surface. In the field of optimization, surrogate modeling consists in the definition of an approximated fitness function, whose evaluation is typically less expensive than its original counterpart [1].
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