A solution to the crucial problem of population degeneration in high-dimensional evolutionary optimization

Three popular evolutionary optimization algorithms are tested on high-dimensional benchmark functions. An important phenomenon responsible for many failures - population degeneration - is discovered. That is, through evolution, the population of searching particles degenerates into a subspace of the search space, and the global optimum is exclusive from the subspace. Subsequently, the search will tend to be confined to this subspace and eventually miss the global optimum. Principal components analysis (PCA) is introduced to discover population degeneration and to remedy its adverse effects. The experiment results reveal that an algorithm's efficacy and efficiency are closely related to the population degeneration phenomenon. Guidelines for improving evolutionary algorithms for high-dimensional global optimization are addressed. An application to highly nonlinear hydrological models demonstrates the efficacy of improved evolutionary algorithms in solving complex practical problems. © 2011 IEEE

Do not be afraid of local minima: affine shaker and particle swarm

Stochastic local search techniques are powerful and flexible methods to optimize difficult functions. While each method is characterized by search trajectories produced through a randomized selection of the next step, a notable difference is caused by the interaction of different searchers, as exemplified by the Particle Swarm methods. In this paper we evaluate two extreme approaches, Particle Swarm Optimization, with interaction between the individual "cognitive" component and the "social" knowledge, and Repeated Affine Shaker, without any interaction between searchers but with an aggressive capability of scouting out local minima. The results, unexpected to the authors, show that Affine Shaker provides remarkably efficient and effective results when compared with PSO, while the advantage of Particle Swarm is visible only for functions with a very regular structure of the local minima leading to the global optimum and only for specific experimental conditions

A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses

In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc

Adaptive particle swarm optimization

An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity

Cuckoo Search Inspired Hybridization of the Nelder-Mead Simplex Algorithm Applied to Optimization of Photovoltaic Cells

A new hybridization of the Cuckoo Search (CS) is developed and applied to optimize multi-cell solar systems; namely multi-junction and split spectrum cells. The new approach consists of combining the CS with the Nelder-Mead method. More precisely, instead of using single solutions as nests for the CS, we use the concept of a simplex which is used in the Nelder-Mead algorithm. This makes it possible to use the flip operation introduces in the Nelder-Mead algorithm instead of the Levy flight which is a standard part of the CS. In this way, the hybridized algorithm becomes more robust and less sensitive to parameter tuning which exists in CS. The goal of our work was to optimize the performance of multi-cell solar systems. Although the underlying problem consists of the minimization of a function of a relatively small number of parameters, the difficulty comes from the fact that the evaluation of the function is complex and only a small number of evaluations is possible. In our test, we show that the new method has a better performance when compared to similar but more compex hybridizations of Nelder-Mead algorithm using genetic algorithms or particle swarm optimization on standard benchmark functions. Finally, we show that the new method outperforms some standard meta-heuristics for the problem of interest