An Adapting Quantum Field Surrogate for Evolution Strategies
Black-box optimization largely suffers from the absence of analytical objective forms. Thus, no derivatives or other structure information can be harnessed for guiding optimization algorithms. But, even with analytic form, high-dimensionality and multi-mo
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Abstract Black-box optimization largely suffers from the absence of analytical objective forms. Thus, no derivatives or other structure information can be harnessed for guiding optimization algorithms. But, even with analytic form, highdimensionality and multi-modality often hinder the search for a global optimum. Heuristics based on populations or evolution strategies are a proven and effective means to, at least partly, overcome these problems. Evolution strategies have thus been successfully applied to optimization problems with rugged, multi-modal fitness landscapes from numerous applications, to nonlinear problems, and to derivative free optimization. One obstacle in heuristics in general is the occurrence of premature convergence, meaning a solution population converges too early and gets stuck in a local optimum. In this paper, we present an approach that harnesses the adapting quantum potential field determined by the spatial distribution of elitist solutions as guidance for the next generation. The potential field evolves to a smoother surface leveling local optima but keeping the global structure what in turn allows for a faster convergence of the solution set. On the other hand, the likelihood of premature convergence decreases. We demonstrate the applicability and the competitiveness of our approach compared with particle swarm optimization and the well-established evolution strategy CMA-ES. Keywords Evolution strategies · Global optimization · Surrogate optimization · Premature convergence · Quantum potential
J. Bremer (B) · S. Lehnhoff University of Oldenburg, 26129 Oldenburg, Germany e-mail: [email protected] S. Lehnhoff e-mail: [email protected] © Springer Nature Switzerland AG 2019 J. J. Merelo et al. (eds.), Computational Intelligence, Studies in Computational Intelligence 792, https://doi.org/10.1007/978-3-319-99283-9_1
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J. Bremer and S. Lehnhoff
1 Introduction Global optimization comprises many problems in practice as well as in the scientific community. These problems are often hallmarked by presence of a rugged fitness landscape with many local optima and non-linearity. Thus optimization algorithms are likely to become stuck in local optima and guaranteeing the exact optimum is often intractable. Evolution Strategies [1] have shown excellent performance in global optimization especially when it comes to complex multi-modal, high dimensional, real valued problems [2, 3]. A major drawback of population based algorithms is the large number of objective function evaluations. Real world problems often face computational efforts for fitness evaluations; e. g.in Smart Grid load planning scenarios, fitness evaluation involves simulating a large number of energy resources and their behaviour [4]. Another problem is known as premature convergence [5–7], when a heuristics converges too early towards a sub-optimal solution and then gets stuck in this local optimum. This might for instance happen if an adaption strategy decreases the mutation range and thus the range o
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