Differential Evolution: A review of more than two decades of research

Differential evolution is a very popular optimization algorithm and considerable research has been devoted to the development of efficient search operators. Motivated by the different manner in which various search operators behave, we propose a novel framework based on the proximity characteristics among the individual solutions as they evolve. Our framework incorporates information of neighboring individuals, in an attempt to efficiently guide the evolution of the population toward the global optimum, without sacrificing the search capabilities of the algorithm. More specifically, the random selection of parents during mutation is modified, by assigning to each individual a probability of selection that is inversely proportional to its distance from the mutated individual. The proposed framework can be applied to any mutation strategy with minimal changes. In this paper, we incorporate this framework in the original differential evolution algorithm, as well as other recently proposed differential evolution variants. Through an extensive experimental study, we show that the proposed framework results in enhanced performance for the majority of the benchmark problems studied.

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Enhancing Differential Evolution Utilizing Proximity-Based Mutation Operators

Self regulating particle swarm optimization algorithm

Evolutionary computation (EC) is a kind of optimization methodology inspired by the mechanisms of biological evolution and behaviors of living organisms. In the literature, the terminology evolutionary algorithms is frequently treated the same as EC. This article focuses on making a survey of researches based on using ML techniques to enhance EC algorithms. In the framework of an ML-technique enhanced-EC algorithm (MLEC), the main idea is that the EC algorithm has stored ample data about the search space, problem features, and population information during the iterative search process, thus the ML technique is helpful in analyzing these data for enhancing the search performance. The paper presents a survey of five categories: ML for population initialization, ML for fitness evaluation and selection, ML for population reproduction and variation, ML for algorithm adaptation, and ML for local search.

Evolutionary Computation Meets Machine Learning: A Survey

Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints. The conventional optimization methods are not able to solve such problems as due to local optimum solution convergence. Meta-heuristic optimization techniques especially particle swarm optimization (PSO) has gained an incredible recognition as the solution algorithm for such type of ED problems in last decade. The application of PSO in ED problem, which is considered as one of the most complex optimization problem has been summarized in present paper.

Economic dispatch using particle swarm optimization: A review

In this paper we have proposed three variations of the Basic Particle Swarm Optimization (BPSO), called GWPSO+ED, GWPSO+GD and GWPSO+UD The novelty of the approach is the combination a newly developed inertia weight with different probability distributions The numerical results of the modified versions are compared with the BPSO Simulations show that the proposed versions are comparable with BPSO and in most of the cases give superior performance

Particle Swarm Optimization Using Gaussian Inertia Weight

In this paper, we present a new mutation operator called the systematic mutation (SM) operator for enhancing the performance of basic particle swarm optimization (BPSO) algorithm. The SM operator unlike most of its contemporary mutation operators do not use the random probability distribution for perturbing the swarm population, but uses a quasi random Sobol sequence to find new solution vectors in the search domain. The comparison of SM-PSO is made with BPSO and some other variants of PSO. The empirical results show that SM operator significantly improves the performance of PSO.

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Particle Swarm Optimization Using Sobol Mutation

Differential evolution (DE) has emerged as a powerful tool for solving optimization problems in the last few years. However, the convergence rate of DE still does not meet all the requirements, and attempts to speed up differential evolution are considered necessary. In order to improve the performance of DE, we propose a modified DE algorithm called DEPCX which uses parent centric approach to manipulate the solution vectors. The performance of DEPCX is evaluated on a test bed of five functions. Numerical results are compared with original differential evolution (DE) and with TDE, another recently modified version of DE. Empirical results indicate that this modification enables the algorithm to get a better transaction between the convergence rate and robustness.

Differential Evolution with Parent Centric Crossover

The performance of population based search techniques like Differential Evolution (DE) depends largely on the selection of initial population. A good initialization scheme not only helps in giving a better final solution but also helps in improving the convergence rate of the algorithm. In the present study we propose a novel initialization scheme which uses the concept of quadratic interpolation to generate the initial population. The proposed DE is validated on a test bed of 10 benchmark problems with varying dimensions and the results are compared with the classical DE using random initialization, DE using opposition based learning for generating the initial population. The numerical results show that the proposed algorithm using quadratic interpolation for generating the initial population accelerates the convergence speed quite considerably.

Differential Evolution using Quadratic Interpolation for Initializing the Population

Self-similar solutions arise naturally as special solutions of system of partial differential equations (PDEs) from dimensional analysis and, more generally, from the invariance of system of PDEs under scaling of variables. Usually, such solutions do not globally satisfy imposed boundary conditions. However, through delicate analysis, one can often show that a self-similar solution holds asymptotically in certain identified domains. In the present paper, it is shown that self-similar phenomena can be studied through use of many ideas arising in the study of dynamical systems. In particular, there is a discussion of the role of symmetries in the context of self-similar dynamics. We use the method of Lie group invariance to determine the class of self-similar solutions to a problem involving plane and radially symmetric flows of a relaxing non-ideal gas involving strong shocks. The ambient gas ahead of the shock is considered to be homogeneous. The method yields a general form of the relaxation rate for which the self-similar solutions are admitted. The arbitrary constants, occurring in the expressions for the generators of the local Lie group of transformations, give rise to different cases of possible solutions with a power law, exponential or logarithmic shock paths. In contrast to situations without relaxation, the inclusion of relaxation effects imply constraint conditions. A particular case of the collapse of an imploding shock is worked out in detail for radially symmetric flows. Numerical calculations have been performed to determine the values of the self-similarity exponent and the profile of the flow variables behind the shock. All computations are performed using the computation package Mathematica.

V. P. Singh

Papers

Particle Swarm Optimization Using Gaussian Inertia Weight

Particle Swarm Optimization Using Sobol Mutation

Differential Evolution with Parent Centric Crossover

Differential Evolution using Quadratic Interpolation for Initializing the Population

Similarity method for imploding strong shocks in a non-ideal relaxing gas