Exploring dynamic self-adaptive populations in differential evolution

Although the Differential Evolution (DE) algorithm has been shown to be a simple yet powerful evolutionary algorithm for optimizing continuous functions, users are still faced with the problem of preliminary testing and hand-tuning of the evolutionary parameters prior to commencing the actual optimization process. As a solution, self-adaptation has been found to be highly beneficial in automatically and dynamically adjusting evolutionary parameters such as crossover rates and mutation rates. In this paper, we present a first attempt at self-adapting the population size parameter in addition to self-adapting crossover and mutation rates. Firstly, our main objective is to demonstrate the feasibility of self-adapting the population size parameter in DE. Using De Jong's F1–F5 benchmark test problems, we showed that DE with self-adaptive populations produced highly competitive results compared to a conventional DE algorithm with static populations. In addition to reducing the number of parameters used in DE, the proposed algorithm actually outperformed the conventional DE algorithm for one of the test problems. It was also found that that an absolute encoding methodology for self-adapting population size in DE produced results with greater optimization reliability compared to a relative encoding methodology.     

Evolutionary and population dynamics of 3 parents differential evolution (3PDE) using self-adaptive tuning methodologies

Differential Evolution is known for its simplicity and effectiveness as an evolutionary optimizer. In recent years, many researchers have focused on the exploration of Differential Evolution (DE). The objective of this paper is to show the evolutionary and population dynamics for the empirical testing on 3-Parents Differential Evolution (3PDE) for unconstrained function optimization (Teng et al. 2007). In this paper, 50 repeated evolutionary runs for each of 20 well-known benchmarks were carried out to test the proposed algorithms against the original 4-parents DE algorithm. As a result of the observed evolutionary dynamics, 3PDE-SAF performed the best among the preliminary proposed algorithms that included 3PDE-SACr and 3PDE-SACrF. Subsequently, 3PDE-SAF is chosen for the self-adaptive population size for testing dynamic population sizing methods using the absolute (3PDE-SAF-Abs) and relative (3PDE-SAF-Rel) population size encodings. The final result shows that 3PDE-SAF-Rel produced a better performance and convergence overall compared to all the other proposed algorithms, including the original DE. In terms of population dynamics, the population size in 3PDE-SAF-Abs exhibited disadvantageously high dynamics that caused less efficient results. On the other hand, the population size in 3PDE-SAF-Rel was observed to be approximately constant at ten times the number of variables being optimized, hence giving a better and more stable performance.     

Modified differential evolution approach for optimization of planar parallel manipulators force capabilities

The global optimization problem is not easy to solve and is still an open challenge for researchers since an analytical optimal solution is difficult to obtain even for relatively simple application problems. Conventional deterministic numerical algorithms tend to stop the search in local minimum nearest to the input starting point, mainly when the optimization problem presents nonlinear, non-convex and non-differential functions, multimodal and nonlinear. Nowadays, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. The primary advantage of EAs over other numerical methods is that they just require the objective function values, while properties such as differentiability and continuity are not necessary. In this context, the differential evolution (DE), a paradigm of the evolutionary computation, has been widely used for solving numerical global optimization problems in continuous search space. DE is a powerful population-based stochastic direct search method. DE simulates natural evolution combined with a mechanism to generate multiple search directions based on the distribution of solutions in the current population. Among DE advantages are its simple structure, ease of use, speed, and robustness, which allows its application on several continuous nonlinear optimization problems. However, the performance of DE greatly depends on its control parameters, such as crossover rate, mutation factor, and population size and it often suffers from being trapped in local optima. Conventionally, users have to determine the parameters for problem at hand empirically. Recently, several adaptive variants of DE have been proposed. In this paper, a modified differential evolution (MDE) approach using generation-varying control parameters (mutation factor and crossover rate) is proposed and evaluated. The proposed MDE presents an efficient strategy to improve the search performance in preventing of premature convergence to local minima. The efficiency and feasibility of the proposed MDE approach is demonstrated on a force optimization problem in Robotics, where the force capabilities of a planar 3-RRR parallel manipulator are evaluated considering actuation limits and different assembly modes. Furthermore, some comparison results of MDE approach with classical DE to the mentioned force optimization problem are presented and discussed.     

Cooperative bare-bone particle swarm optimization for data clustering

Cooperative coevolution (CC) was used to improve the performance of evolutionary algorithms (EAs) on complex optimization problems in a divide-and-conquer way. In this paper, we show that the CC framework can be very helpful to improve the performance of particle swarm optimization (PSO) on clustering high-dimensional datasets. Based on CC framework, the original partitional clustering problem is first decomposed to several subproblems, each of which is then evolved by an optimizer independently. We employ a very simple but efficient optimization algorithm, namely bare-bone particle swarm optimization (BPSO), as the optimizer to solve each subproblem cooperatively. In addition, we design a new centroid-based encoding schema for each particle and apply the Chernoff bounds to decide a proper population size. The experimental results on synthetic and real-life datasets illustrate the effectiveness and efficiency of the BPSO and CC framework. The comparisons show the proposed algorithm significantly outperforms five EA-based clustering algorithms, i.e., PSO, SRPSO, ACO, ABC and DE, and K-means on most of the datasets.     

Hybrid adaptive differential evolution for mobile robot localization

This paper introduces a new evolutionary optimization algorithm named hybrid adaptive differential evolution (HADE) and applies it to the mobile robot localization problem. The behaviour of evolutionary algorithms is highly dependent on the parameter selection. This algorithm utilizes an adaptive method to tune the mutation parameter to enhance the rate of convergence and eliminate the need for manual tuning. A hybrid method for mutation is also introduced to give more diversity to the population. This method which constantly switches between two mutation schemes guarantees a sufficient level of diversity to avoid local optima. We use a well-known test set in continuous domain to evaluate HADE’s performance against the standard version of differential evolution (DE) and a self-adaptive version of the algorithm. The results show that HADE outperforms DE and self-adaptive DE in three of four benchmarks. Moreover, we investigate the performance of HADE in the well-known localization problem of mobile robots. Results show that HADE is capable of estimating the robot’s pose accurately with a decreased number of individuals needed for convergence compared with DE and particle swarm optimization methods. Comparative study exposes HADE algorithm as a competitive method for mobile robot localization.     

Alopex-based evolutionary algorithm and its application to reaction kinetic parameter estimation

In this paper, a novel Alopex-based evolutionary algorithm (AEA) is proposed, whose distinguished features are stochastic selection and self-adaptive evolutionary computation. The AEA not only inherits the primary characteristics of basic evolutionary algorithms (EAs), but also possesses the merits of gradient methods and simulated annealing algorithm. It can efficiently maintain the population diversity and improve the capabilities of escaping from local optima. The numerical simulation results of 22 benchmark functions demonstrate that the performance of the proposed AEA is superior to that of the basic EAs. Finally, the new algorithm is applied to estimate the kinetic parameters of 2-chlorophenol oxidation of supercritical water. The promising results illustrate the efficiency of the proposed method and show that it could be used as a reliable tool for engineering applications.     

Opposition-Based Differential Evolution

Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.     

Performance improvement of self-adaptive evolutionary methods with a dynamic lower bound

Recent research on self-adaptive evolutionary programming (EP) methods evidenced the problem of premature convergence. Self-adaptive evolutionary programming methods converge prematurely because their object variables evolve more slowly than do their strategy parameters, which subsequently leads to a stagnation of object variables at a non-optimum value. To address this problem, a dynamic lower bound has been proposed, which is defined here as the differential step lower bound (DSLB) on the strategy parameters. The DSLB on an object variable depends on its absolute distance from the corresponding object variable of the best individual in the population pool. The performance of the self-adaptive EP algorithm with DSLB has been verified over eight different test functions of varied complexities.     

The property analysis of evolutionary algorithms applied to spanning tree problems

The search behavior of an evolutionary algorithm depends on the interactions between the encoding that represents candidate solutions to the target problem and the operators that act on that encoding. In this paper, we focus on analyzing some properties such as locality, heritability, population diversity and searching behavior of various decoder-based evolutionary algorithm (EA) frameworks using different encodings, decoders and genetic operators for spanning tree based optimization problems. Although debate still continues on how and why EAs work well, many researchers have observed that EAs perform well when its encoding and operators exhibit good locality, heritability and diversity properties. We analyze these properties of various EA frameworks with two types of analytical ways on different spanning tree problems; static analysis and dynamic analysis, and then visualize them. We also show through this analysis that EA using the Edge Set encoding (ES) and the Edge Window Decoder encoding (EWD) indicate very good locality and heritability as well as very good diversity property. These are put forward as a potential explanation for the recent finding that they can outperform other recent high-performance encodings on the constrained spanning tree problems.     

Immigrant schemes for evolutionary algorithms in dynamic environments: Adapting the replacement rate

One approach for evolutionary algorithms (EAs) to address dynamic optimization problems (DOPs) is to maintain diversity of the population via introducing immigrants.So far all immigrant schemes developed for EAs have used fixed replacement rates.This paper examines the impact of the replacement rate on the performance of EAs with immigrant schemes in dynamic environments,and proposes a self-adaptive mechanism for EAs with immigrant schemes to address DOPs.Our experimental study showed that the new approach ...