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

A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Multi-Criteria Decision Aid (MCDA) or Multi-Criteria Decision Making (MCDM) methods have received much attention from researchers and practitioners in evaluating, assessing and ranking alternatives across diverse industries. Among numerous MCDA/MCDM methods developed to solve real-world decision problems, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) continues to work satisfactorily across different application areas. In this paper, we conduct a state-of-the-art literature survey to taxonomize the research on TOPSIS applications and methodologies. The classification scheme for this review contains 266 scholarly papers from 103 journals since the year 2000, separated into nine application areas: (1) Supply Chain Management and Logistics, (2) Design, Engineering and Manufacturing Systems, (3) Business and Marketing Management, (4) Health, Safety and Environment Management, (5) Human Resources Management, (6) Energy Management, (7) Chemical Engineering, (8) Water Resources Management and (9) Other topics. Scholarly papers in the TOPSIS discipline are further interpreted based on (1) publication year, (2) publication journal, (3) authors' nationality and (4) other methods combined or compared with TOPSIS. We end our review paper with recommendations for future research in TOPSIS decision-making that is both forward-looking and practically oriented. This paper provides useful insights into the TOPSIS method and suggests a framework for future attempts in this area for academic researchers and practitioners.

Review: A state-of the-art survey of TOPSIS applications

The objective of image segmentation is to extract meaningful objects. A meaningful segmentation selects the proper threshold values to optimize a criterion using entropy. The conventional multilevel thresholding methods are efficient for bi-level thresholding. However, they are computationally expensive when extended to multilevel thresholding since they exhaustively search the optimal thresholds to optimize the objective functions. To overcome this problem, two successful swarm-intelligence-based global optimization algorithms, cuckoo search (CS) algorithm and wind driven optimization (WDO) for multilevel thresholding using Kapur's entropy has been employed. For this purpose, best solution as fitness function is achieved through CS and WDO algorithm using Kapur's entropy for optimal multilevel thresholding. A new approach of CS and WDO algorithm is used for selection of optimal threshold value. This algorithm is used to obtain the best solution or best fitness value from the initial random threshold values, and to evaluate the quality of a solution, correlation function is used. Experimental results have been examined on standard set of satellite images using various numbers of thresholds. The results based on Kapur's entropy reveal that CS, ELR-CS and WDO method can be accurately and efficiently used in multilevel thresholding problem.

Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur's entropy

Some uncertainties, such as the uncertain output power of a plug-in electric vehicle (PEV) due to its stochastic charging and discharging schedule, that of a wind generation unit due to the stochastic wind speed, and that of a solar generating source due to the stochastic illumination intensity, volatile fuel prices, and future uncertain load growth could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distribution system planning. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal siting and sizing of DGs. First, a mathematical model of CCP is developed with the minimization of the DGs' investment cost, operating cost, maintenance cost, network loss cost, as well as the capacity adequacy cost as the objective, security limitations as constraints, and the siting and sizing of DGs as optimization variables. Then, a Monte Carlo simulation-embedded genetic-algorithm-based approach is employed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is used to verify the feasibility and effectiveness of the developed model and method, and the test results have demonstrated that the voltage profile and power-supply reliability for customers can be significantly improved and the network loss substantially reduced.

Optimal Siting and Sizing of Distributed Generators in Distribution Systems Considering Uncertainties

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

In this paper, performance comparison of evolutionary algorithms (EAs) such as real coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), covariance matrix adaptation evolution strategy (CMAES) and differential evolution (DE) on optimal design of multivariable PID controller design is considered. Decoupled multivariable PI and PID controller structure for Binary distillation column plant described by Wood and Berry, having 2 inputs and 2 outputs is taken. EAs simulations are carried with minimization of IAE as objective using two types of stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax along with tolerance of PID parameters and IAE. To compare the performances of various EAs, statistical measures like best, mean, standard deviation of results and average computation time, over 20 independent trials are considered. Results obtained by various EAs are compared with previously reported results using BLT and GA with multi-crossover approach. Results clearly indicate the better performance of CMAES and MPSO designed PI/PID controller on multivariable system. Simulations also reveal that all the four algorithms considered are suitable for off-line tuning of PID controller. However, only CMAES and MPSO algorithms are suitable for on-line tuning of PID due to their better consistency and minimum computation time.

Evolutionary algorithms based design of multivariable PID controller

Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, design of centralized PID controller using Covariance Matrix Adaptation Evolution Strategy (CMAES) is presented. Binary distillation column plant described by Wood and Berry (WB) having two inputs and two outputs and by Ogunnike and Ray (OR) having three inputs and three outputs are considered for the design of multivariable PID controller. Optimal centralized PID controller is designed by minimizing IAE for servo response with unit step change. Simulations are carried out using SIMULINK-MATLAB software. The statistical performances of the designed controllers such as best, mean, standard deviations of IAE and average functional evaluations for 20 independent trials. For the purpose of comparison, recent version of real coded Genetic Algorithm (RGA) with simulated binary crossover (SBX) and conventional BLT method are used. In order to validate the performance of optimal PID controller for robustness against load disturbance rejection, load regulation experiment with step load disturbance is conducted. Also, to determine the performance of optimal PID controller for robustness against model uncertainty, servo and load response with +20% variations in gains and dead times is conducted. Simulation results reveal that for both OR and WB systems, CMAES designed centralized PID controller is better than other methods and also it is more robust against model uncertainty and load disturbance.

M. Willjuice Iruthayarajan

Papers

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

Evolutionary algorithms based design of multivariable PID controller

Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

Covariance matrix adaptation evolution strategy based design of centralized PID controller