Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.

Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization

A comparative study of Artificial Bee Colony algorithm

We describe an efficient technique for adapting control parameter settings associated with differential evolution (DE). The DE algorithm has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters, which are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE. We present an algorithm-a new version of the DE algorithm-for obtaining self-adaptive control parameter settings that show good performance on numerical benchmark problems. The results show that our algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained

Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems

A new differential evolution (DE) algorithm, JADE, is proposed to improve optimization performance by implementing a new mutation strategy ldquoDE/current-to-p bestrdquo with optional external archive and updating control parameters in an adaptive manner. The DE/current-to-pbest is a generalization of the classic ldquoDE/current-to-best,rdquo while the optional archive operation utilizes historical data to provide information of progress direction. Both operations diversify the population and improve the convergence performance. The parameter adaptation automatically updates the control parameters to appropriate values and avoids a user's prior knowledge of the relationship between the parameter settings and the characteristics of optimization problems. It is thus helpful to improve the robustness of the algorithm. Simulation results show that JADE is better than, or at least comparable to, other classic or adaptive DE algorithms, the canonical particle swarm optimization, and other evolutionary algorithms from the literature in terms of convergence performance for a set of 20 benchmark problems. JADE with an external archive shows promising results for relatively high dimensional problems. In addition, it clearly shows that there is no fixed control parameter setting suitable for various problems or even at different optimization stages of a single problem.

JADE: Adaptive Differential Evolution With Optional External Archive

In this article we introduce a molecular docking algorithm called MolDock. MolDock is based on a new heuristic search algorithm that combines differential evolution with a cavity prediction algorithm. The docking scoring function of MolDock is an extension of the piecewise linear potential (PLP) including new hydrogen bonding and electrostatic terms. To further improve docking accuracy, a re-ranking scoring function is introduced, which identifies the most promising docking solution from the solutions obtained by the docking algorithm. The docking accuracy of MolDock has been evaluated by docking flexible ligands to 77 protein targets. MolDock was able to identify the correct binding mode of 87% of the complexes. In comparison, the accuracy of Glide and Surflex is 82% and 75%, respectively. FlexX obtained 58% and GOLD 78% on subsets containing 76 and 55 cases, respectively.

MolDock: a new technique for high-accuracy molecular docking.

Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance in several real-world applications. In this paper, we evaluate the performance of DE, PSO, and EAs regarding their general applicability as numerical optimization techniques. The comparison is performed on a suite of 34 widely used benchmark problems. The results from our study show that DE generally outperforms the other algorithms. However, on two noisy functions, both DE and PSO were outperformed by the EA.

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A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems

Multimodal optimization is an important area of active research within the evolutionary computation community. The ability of algorithms to discover and maintain multiple optima is of great importance - in particular when several global optima exist or when other high-quality solutions might be of interest. The differential evolution algorithm (DE) is extended with a crowding scheme making it capable of tracking and maintaining multiple optima. The introduced CrowdingDE algorithm is compared with a DE using the well-known sharing scheme that penalizes similar candidate solutions. In conclusion, the introduced CrowdingDE outperformed the sharing-based DE algorithm on fourteen commonly used benchmark problems.

Multimodal optimization using crowding-based differential evolution

Structure and reactivity of synthetic CaO-Al2O3-SiO2 glasses

A novel approach to incorporate water molecules in protein−ligand docking is proposed. In this method, the water molecules display the same flexibility during the docking simulation as the ligand. The method solvates the ligand with the maximum number of water molecules, and these are then retained or displaced depending on energy contributions during the docking simulation. Instead of being a static part of the receptor, each water molecule is a flexible on/off part of the ligand and is treated with the same flexibility as the ligand itself. To favor exclusion of the water molecules, a constant entropy penalty is added for each included water molecule. The method was evaluated using 12 structurally diverse protein−ligand complexes from the PDB, where several water molecules bridge the ligand and the protein. A considerable improvement in successful docking simulations was found when including flexible water molecules solvating hydrogen bonding groups of the ligand. The method has been implemented in the ...

René Thomsen

Papers

MolDock: a new technique for high-accuracy molecular docking.

A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems

Multimodal optimization using crowding-based differential evolution

Structure and reactivity of synthetic CaO-Al2O3-SiO2 glasses

Molecular docking with ligand attached water molecules.