Memetic Differential Evolution Research Articles

Heterogeneous Cooperative Co-Evolution Memetic Differential Evolution Algorithm for Big Data Optimization Problems

Evolutionary algorithms (EAs) have recently been suggested as a candidate for solving big data optimization problems that involve a very large number of variables and need to be analyzed in a short period of time. However, EAs face a scalability issue when dealing with big data problems. Moreover, the performance of EAs critically hinges on the utilized parameter values and operator types, thus it is impossible to design a single EA that can outperform all others in every problem instance. To address these challenges, we propose a heterogeneous framework that integrates a cooperative co-evolution method with various types of memetic algorithms. We use the cooperative co-evolution method to split the big problem into subproblems in order to increase the efficiency of the solving process. The subproblems are then solved using various heterogeneous memetic algorithms. The proposed heterogeneous framework adaptively assigns, for each solution, different operators, parameter values and a local search algorithm to efficiently explore and exploit the search space of the given problem instance. The performance of the proposed algorithm is assessed using the Big Data 2015 competition benchmark problems that contain data with and without noise. Experimental results demonstrate that the proposed algorithm, with the cooperative co-evolution method, performs better than without the cooperative co-evolution method. Furthermore, it obtained very competitive results for all tested instances, if not better, when compared to other algorithms using lower computational times.

Computational investigation of simple memetic approaches for continuous global optimization

In Locatelli et al. (2014) [20] a memetic approach, called MDE (Memetic Differential Evolution), for the solution of continuous global optimization problems, has been introduced and proved to be quite efficient in spite of its simplicity. In this paper we computationally investigate some variants of MDE. The investigation reveals that the best tested variant of MDE outperforms the original MDE itself, but also that the best variant depends on some properties of the function to be optimized. In particular, a greedy variant of MDE turns out to perform very well over functions with a single-funnel landscape, while another variant, based on a diversity measure applied to the members of the population, works better over functions with a multi-funnel landscape. A hybrid approach is also proposed which combines both the previous variants in order to obtain an overall performance which is good over all functions.

A multi-fidelity surrogate-model-assisted evolutionary algorithm for computationally expensive optimization problems

Integrating data-driven surrogate models and simulation models of different accuracies (or fidelities) in a single algorithm to address computationally expensive global optimization problems has recently attracted considerable attention. However, handling discrepancies between simulation models with multiple fidelities in global optimization is a major challenge. To address it, the two major contributions of this paper include: (1) development of a new multi-fidelity surrogate-model-based optimization framework, which substantially improves reliability and efficiency of optimization compared to many existing methods, and (2) development of a data mining method to address the discrepancy between the low- and high-fidelity simulation models. A new efficient global optimization method is then proposed, referred to as multi-fidelity Gaussian process and radial basis function-model-assisted memetic differential evolution. Its advantages are verified by mathematical benchmark problems and a real-world antenna design automation problem.

A Memetic Differential Evolution Algorithm Based on Dynamic Preference for Constrained Optimization Problems

The constrained optimization problem (COP) is converted into a biobjective optimization problem first, and then a new memetic differential evolution algorithm with dynamic preference is proposed for solving the converted problem. In the memetic algorithm, the global search, which uses differential evolution (DE) as the search scheme, is guided by a novel fitness function based on achievement scalarizing function (ASF). The novel fitness function constructed by a reference point and a weighting vector adjusts preference dynamically towards different objectives during evolution, in which the reference point and weighting vector are determined adapting to the current population. In the local search procedure, simplex crossover (SPX) is used as the search engine, which concentrates on the neighborhood embraced by both the best feasible and infeasible individuals and guides the search approaching the optimal solution from both sides of the boundary of the feasible region. As a result, the search can efficiently explore and exploit the search space. Numerical experiments on 22 well-known benchmark functions are executed, and comparisons with five state-of-the-art algorithms are made. The results illustrate that the proposed algorithm is competitive with and in some cases superior to the compared ones in terms of the quality, efficiency, and the robustness of the obtained results.

A Multi-Objective Approach to Subarrayed Linear Antenna Arrays Design Based on Memetic Differential Evolution

In this paper we present a multi-objective optimization approach to subarrayed linear antenna arrays design. We define this problem as a bi-objective one. We consider two objective functions for directivity maximization and sidelobe level minimization. Memetic algorithms (MAs) are hybrid algorithms that combine the benefits of a global search Evolutionary Algorithm (EA) with a local search method. In this paper, we introduce a new memetic multi-objective evolutionary algorithm namely the memetic generalized differential evolution (MGDE3). This algorithm is a memetic extension of the popular generalized differential evolution (GDE3) algorithm. Another popular MOEA is the nondominated sorting genetic algorithm-II (NSGA-II). MGDE3, GDE3 and NSGA-II are applied to the synthesis of uniform and nonuniform subarrayed linear arrays, providing an extensive set of solutions for each design case. Depending on the desired array characteristics, the designer can select the most suitable solution. The results of the proposed method are compared with those reported in the literature, indicating the advantages and applicability of the multi-objective approach.

Adaptive Memetic Differential Evolution with Global and Local neighborhood-based mutation operators

Differential Evolution (DE) is one of the most popular optimization methods for real-valued problems and a large number of its variants have been proposed so far. However, bringing together different ideas that already led to successful DE versions is rare in the literature. In the present paper a novel DE algorithm is proposed, in which three among the most efficient concepts already applied separately within DE framework are gathered together, namely: (1) the adaptation of algorithm control parameters and probabilities of using different mutation strategies; (2) the use of Nelder–Mead algorithm as a local search method hybridized with DE; and (3) the splitting mutation into Global and Local models, when Local mutation model is based on the concept of neighborhood of individuals organized on a ring topology. The performance of the novel algorithm, called Adaptive Memetic DE with Global and Local neighborhood-based mutation operators is compared with 13 different DE variants on a set of 25 popular problems which include rotated, shifted and hybrid composition functions. It is found that, although none DE algorithm outperforms all the others for the majority of problems, on average the proposed approach perform better than all 13 DE algorithms selected for comparison.The proposed algorithm is another heuristic approach developed to solve optimization problems. The question may arise, whether proposing novel methods is useful as No Free Lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal. In the last section of the paper the limitations and implications of No Free Lunch theorems are discussed based on rich, but unfortunately frequently neglected literature. A very simple continuous and differentiable minimization problem is proposed, for which it is empirically verified that each among considered 14 DE algorithms perform poorer than random sampling. It is also empirically shown that when all considered DE algorithms search for the maximum of the proposed problem, they found lower minimum than DE algorithms searching for the minimum. Such result is not unexpected according to No Free Lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods.

A memetic differential evolution algorithm for the inverse kinematics problem of robot manipulators

The inverse kinematics (IK) of robot manipulators defines the problem of finding the joint configuration that places the end-effector in an arbitrary position and orientation. This problem can be formulated in the configuration space as a constrained optimisation model to avoid the numerical instability of Jacobian-based IK methods. Previous works have shown that differential evolution (DE) is effective in finding accurate solutions to the IK optimisation problem, but exhibits low convergence speed rates. In this paper we propose a memetic differential evolution (dDE) to improve the convergence behaviour of the standard DE scheme. Both algorithms are tested and compared in a simulation environment as kinematic inversion methods for two non-redundant robot manipulators. Results revealed that dDE outperforms the original DE algorithm in accuracy and convergence speed.

Distributed memetic differential evolution with the synergy of Lamarckian and Baldwinian learning

As a population-based optimizer, the differential evolution (DE) algorithm has a very good reputation for its competence in global search and numerical robustness. In view of the fact that each member of the population is evaluated individually, DE can be easily parallelized in a distributed way. This paper proposes a novel distributed memetic differential evolution algorithm which integrates Lamarckian learning and Baldwinian learning. In the proposed algorithm, the whole population is divided into several subpopulations according to the von Neumann topology. In order to achieve a better tradeoff between exploration and exploitation, the differential evolution as an evolutionary frame is assisted by the Hooke–Jeeves algorithm which has powerful local search ability. We incorporate the Lamarckian learning and Baldwinian learning by analyzing their characteristics in the process of migration among subpopulations as well as in the hybridization of DE and Hooke–Jeeves local search. The proposed algorithm was run on a set of classic benchmark functions and compared with several state-of-the-art distributed DE schemes. Numerical results show that the proposed algorithm has excellent performance in terms of solution quality and convergence speed for all test problems given in this study.

An effective memetic differential evolution algorithm based on chaotic local search

This paper proposes an effective memetic differential evolution (DE) algorithm, or DECLS, that utilizes a chaotic local search (CLS) with a ‘shrinking’ strategy. The CLS helps to improve the optimizing performance of the canonical DE by exploring a huge search space in the early run phase to avoid premature convergence, and exploiting a small region in the later run phase to refine the final solutions. Moreover, the parameter settings of the DECLS are controlled in an adaptive manner to further enhance the search ability. To evaluate the effectiveness and efficiency of the proposed DECLS algorithm, we compared it with four state-of-the-art DE variants and the IPOP-CMA-ES algorithm on a set of 20 selected benchmark functions. Results show that the DECLS is significantly better than, or at least comparable to, the other optimizers in terms of convergence performance and solution accuracy. Besides, the DECLS has also shown certain advantages in solving high dimensional problems.

Nonlinear system identification using memetic differential evolution trained neural networks

Several gradient-based approaches such as back propagation (BP) and Levenberg Marquardt (LM) methods have been developed for training the neural network (NN) based systems. But, for multimodal cost functions these procedures may lead to local minima, therefore, the evolutionary algorithms (EAs) based procedures are considered as promising alternatives. In this paper we focus on a memetic algorithm based approach for training the multilayer perceptron NN applied to nonlinear system identification. The proposed memetic algorithm is an alternative to gradient search methods, such as back-propagation and back-propagation with momentum which has inherent limitations of many local optima. Here we have proposed the identification of a nonlinear system using memetic differential evolution (DE) algorithm and compared the results with other six algorithms such as Back-propagation (BP), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm Back-propagation (GABP), Particle Swarm Optimization combined with Back-propagation (PSOBP). In the proposed system identification scheme, we have exploited DE to be hybridized with the back propagation algorithm, i.e. differential evolution back-propagation (DEBP) where the local search BP algorithm is used as an operator to DE. These algorithms have been tested on a standard benchmark problem for nonlinear system identification to prove their efficacy. First examples shows the comparison of different algorithms which proves that the proposed DEBP is having better identification capability in comparison to other. In example 2 good behavior of the identification method is tested on an one degree of freedom ( 1DOF) experimental aerodynamic test rig, a twin rotor multi-input–multi-output system ( TRMS), finally it is applied to Box and Jenkins Gas furnace benchmark identification problem and its efficacy has been tested through correlation analysis.

Memetic Differential Evolution Assisted Minimum Bit Error Rate Detector for Multi-user MIMO System

Differential Evolution (DE) is a novel but powerful optimizer. It has been proved that the DE is superior to Genetic Algorithm (GA) in many real life applications. This paper proposed a memetic Differential Evolution assisted Minimum Bit Error Rate (MBER) linear detector for Multiple-input and multiple-output (MIMO) multi-user system. Compared with GA based MBER and other linear MIMO detectors such as minimum mean square error (MMSE) and zero forcing(ZF)detectors, the proposed scheme shows a better performance in terms of the bit error rate.

A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test

Continuous optimization is one of the areas with more activity in the field of heuristic optimization. Many algorithms have been proposed and compared on several benchmarks of functions, with different performance depending on the problems. For this reason, the combination of different search strategies seems desirable to obtain the best performance of each of these approaches. This contribution explores the use of a hybrid memetic algorithm based on the multiple offspring framework. The proposed algorithm combines the explorative/exploitative strength of two heuristic search methods that separately obtain very competitive results. This algorithm has been tested with the benchmark problems and conditions defined for the special issue of the Soft Computing Journal on Scalability of Evolutionary Algorithms and other Metaheuristics for Large Scale Continuous Optimization Problems. The proposed algorithm obtained the best results compared with both its composing algorithms and a set of reference algorithms that were proposed for the special issue.

A memetic Differential Evolution approach in noisy optimization

This paper proposes a memetic approach for solving complex optimization problems characterized by a noisy fitness function. The proposed approach aims at solving highly multivariate and multi-modal landscapes which are also affected by a pernicious noise. The proposed algorithm employs a Differential Evolution framework and combines within this three additional algorithmic components. A controlled randomization of scale factor and crossover rate are employed which should better handle uncertainties of the problem and generally enhance performance of the Differential Evolution. Two combined local search algorithms applied to the scale factor, during offspring generation, should enhance performance of the Differential Evolution framework in the case of multi-modal and high dimensional problems. An on-line statistical test aims at assuring that only strictly necessary samples are taken and that all pairwise selections are properly performed. The proposed algorithm has been tested on a various set of test problems and its behavior has been studied, dependent on the dimensionality and noise level. A comparative analysis with a standard Differential Evolution, a modern version of Differential Evolution employing randomization of the control parameters and four metaheuristics tailored to optimization in a noisy environment has been carried out. One of these metaheuristics is a classical algorithm for noisy optimization while the other three are modern Differential Evolution based algorithms for noisy optimization which well represent the state-of-the-art in the field. Numerical results show that the proposed memetic approach is an efficient and robust alternative for various and complex multivariate noisy problems and can be exported to real-world problems affected by a noise whose distribution can be approximated by a Gaussian distribution.

An Enhanced Memetic Differential Evolution in Filter Design for Defect Detection in Paper Production

This article proposes an Enhanced Memetic Differential Evolution (EMDE) for designing digital filters which aim at detecting defects of the paper produced during an industrial process. Defect detection is handled by means of two Gabor filters and their design is performed by the EMDE. The EMDE is a novel adaptive evolutionary algorithm which combines the powerful explorative features of Differential Evolution with the exploitative features of three local search algorithms employing different pivot rules and neighborhood generating functions. These local search algorithms are the Hooke Jeeves Algorithm, a Stochastic Local Search, and Simulated Annealing. The local search algorithms are adaptively coordinated by means of a control parameter that measures fitness distribution among individuals of the population and a novel probabilistic scheme. Numerical results confirm that Differential Evolution is an efficient evolutionary framework for the image processing problem under investigation and show that the EMDE performs well. As a matter of fact, the application of the EMDE leads to a design of an efficiently tailored filter. A comparison with various popular metaheuristics proves the effectiveness of the EMDE in terms of convergence speed, stagnation prevention, and capability in detecting solutions having high performance.

Super-fit control adaptation in memetic differential evolution frameworks

This paper proposes the super-fit memetic differential evolution (SFMDE). This algorithm employs a differential evolution (DE) framework hybridized with three meta-heuristics, each having different roles and features. Particle Swarm Optimization assists the DE in the beginning of the optimization process by helping to generate a super-fit individual. The two other meta-heuristics are local searchers adaptively coordinated by means of an index measuring quality of the super-fit individual with respect to the rest of the population. The choice of the local searcher and its application is then executed by means of a probabilistic scheme which makes use of the generalized beta distribution. These two local searchers are the Nelder mead algorithm and the Rosenbrock Algorithm. The SFMDE has been tested on two engineering problems; the first application is the optimal control drive design for a direct current (DC) motor, the second is the design of a digital filter for image processing purposes. Numerical results show that the SFMDE is a flexible and promising approach which has a high performance standard in terms of both final solutions detected and convergence speed.

An effective parameter extraction method based on memetic differential evolution algorithm

This paper provides an effective method for parameter extraction of microelectronic devices and elements. A novel method, memetic differential evolution (MDE) algorithm, is proposed in this paper. By combining differential evolution (DE) algorithm, mutations in immune algorithm (IA), and special operators for parameter extraction, MDE possesses characteristics of high accuracy, stability, generality, and efficiency. The effectiveness of the method has been shown by two typical examples, including small-signal equivalent circuit models for an AlGaN/GaN HEMT device up to 40GHz, as well as an equivalent circuit model for on-chip differential spiral inductors. In both cases, the initial values and parameter ranges of the elements in the equivalent circuits are hard to determine in optimization. The results and comparisons with Levenberg–Marquardt (LM) algorithm, genetic algorithm (GA), particle swarm optimization (PSO) algorithm and canonical DE algorithm, demonstrate the superiority of MDE in terms of accuracy and generality.