Traditional Differential Evolution Research Articles

Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

Optimal trajectory searching based differential evolution

A well-designed best solution selection scheme is usually beneficial to enhance the effectiveness and efficiency of evolutionary algorithms. Optimal trajectory searching, a new best solution selection mechanism in the search behaviour of the traditional differential evolution DE, is presented and analysed. Then an improved algorithm based on traditional DE and optimal trajectory searching mechanism is presented for enhancing the performance of DE. Performance compared with other four DE variants indicates that our algorithm outperforms them in terms of convergence speed and solution accuracy.

A Thermodynamical Selection-Based Discrete Differential Evolution for the 0-1 Knapsack Problem

Many problems in business and engineering can be modeled as 0-1 knapsack problems. However, the 0-1 knapsack problem is one of the classical NP-hard problems. Therefore, it is valuable to develop effective and efficient algorithms for solving 0-1 knapsack problems. Aiming at the drawbacks of the selection operator in the traditional differential evolution (DE), we present a novel discrete differential evolution (TDDE) for solving 0-1 knapsack problem. In TDDE, an enhanced selection operator inspired by the principle of the minimal free energy in thermodynamics is employed, trying to balance the conflict between the selective pressure and the diversity of population to some degree. An experimental study is conducted on twenty 0-1 knapsack test instances. The comparison results show that TDDE can gain competitive performance on the majority of the test instances.

A novel differential evolution based clustering algorithm for wireless sensor networks

Clustering is an efficient topology control method which balances the traffic load of the sensor nodes and improves the overall scalability and the life time of the wireless sensor networks (WSNs). However, in a cluster based WSN, the cluster heads (CHs) consume more energy due to extra work load of receiving the sensed data, data aggregation and transmission of aggregated data to the base station. Moreover, improper formation of clusters can make some CHs overloaded with high number of sensor nodes. This overload may lead to quick death of the CHs and thus partitions the network and thereby degrade the overall performance of the WSN. It is worthwhile to note that the computational complexity of finding optimum cluster for a large scale WSN is very high by a brute force approach. In this paper, we propose a novel differential evolution (DE) based clustering algorithm for WSNs to prolong lifetime of the network by preventing faster death of the highly loaded CHs. We incorporate a local improvement phase to the traditional DE for faster convergence and better performance of our proposed algorithm. We perform extensive simulation of the proposed algorithm. The experimental results demonstrate the efficiency of the proposed algorithm.

Uncertainty Management in Differential Evolution Induced Multiobjective Optimization in Presence of Measurement Noise

This paper aims to design new strategies to extend traditional multiobjective optimization algorithms to efficiently obtain Pareto-optimal solutions in presence of noise on the objective surfaces. The first strategy, referred to as adaptive selection of sample size, is employed to balance the tradeoff between quality measure of fitness and run-time complexity. The second strategy is concerned with determining statistical expectation, instead of conventional averaging, of fitness samples as the measure of fitness of the trial solutions. The third strategy attempts to extend Goldberg's method to compare slightly worse trial solutions with its competitor by a more statistically viable comparator to examine possible placement of the former solution in the Pareto optimal front. The traditional differential evolution for multiobjective optimization algorithm has been modified by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the extended algorithm reveal that the extended algorithm outperforms its competitors with respect to three performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions. The extended algorithm has been applied on the well known box-pushing problem, where the forces and torques required to shift the box by two robots are evaluated to jointly satisfy the conflicting objectives on task-execution time and energy consumption in presence of noise on range estimates from the sidewalls of the workspace. The application justifies the importance of the proposed noise-handling strategies in practical systems.

Self-adaptive learning based discrete differential evolution algorithm for solving CJWTA problem

Cooperative jamming weapon-target assignment (CJWTA) problem is a key issue in electronic countermeasures (ECM). Some symbols which relevant to the CJWTA are defined firstly. Then, a formulation of jamming fitness is presented. Finally, a model of the CJWTA problem is constructed. In order to solve the CJWTA problem efficiently, a self-adaptive learning based discrete differential evolution (SLDDE) algorithm is proposed by introducing a self-adaptive learning mechanism into the traditional discrete differential evolution algorithm. The SLDDE algorithm steers four candidate solution generation strategies simultaneously in the framework of the self-adaptive learning mechanism. Computational simulations are conducted on ten test instances of CJWTA problem. The experimental results demonstrate that the proposed SLDDE algorithm not only can generate better results than only one strategy based discrete differential algorithms, but also outperforms two algorithms which are proposed recently for the weapon-target assignment problems.

A Novel Adaptive Elite-Based Particle Swarm Optimization Applied to VAR Optimization in Electric Power Systems

Particle swarm optimization (PSO) has been successfully applied to solve many practical engineering problems. However, more efficient strategies are needed to coordinate global and local searches in the solution space when the studied problem is extremely nonlinear and highly dimensional. This work proposes a novel adaptive elite-based PSO approach. The adaptive elite strategies involve the following two tasks: (1) appending the mean search to the original approach and (2) pruning/cloning particles. The mean search, leading to stable convergence, helps the iterative process coordinate between the global and local searches. The mean of the particles and standard deviation of the distances between pairs of particles are utilized to prune distant particles. The best particle is cloned and it replaces the pruned distant particles in the elite strategy. To evaluate the performance and generality of the proposed method, four benchmark functions were tested by traditional PSO, chaotic PSO, differential evolution, and genetic algorithm. Finally, a realistic loss minimization problem in an electric power system is studied to show the robustness of the proposed method.

Geometric Differential Evolution for Combinatorial and Programs Spaces

Geometric differential evolution (GDE) is a recently introduced formal generalization of traditional differential evolution (DE) that can be used to derive specific differential evolution algorithms for both continuous and combinatorial spaces retaining the same geometric interpretation of the dynamics of the DE search across representations. In this article, we first review the theory behind the GDE algorithm, then, we use this framework to formally derive specific GDE for search spaces associated with binary strings, permutations, vectors of permutations and genetic programs. The resulting algorithms are representation-specific differential evolution algorithms searching the target spaces by acting directly on their underlying representations. We present experimental results for each of the new algorithms on a number of well-known problems comprising NK-landscapes, TSP, and Sudoku, for binary strings, permutations, and vectors of permutations. We also present results for the regression, artificial ant, parity, and multiplexer problems within the genetic programming domain. Experiments show that overall the new DE algorithms are competitive with well-tuned standard search algorithms.

Ensemble of differential evolution algorithms for electromagnetic target recognition problem

In this study, an ensemble of differential evolution (DE) algorithms is presented to classify electromagnetic targets in resonance scattering region. The algorithm aims to synthesize a special incident signal for each target, which is defined as the main discrimination feature in the given target recognition method. In the proposed algorithm, the amplitudes of basis functions and the duration of this incident signal are optimised to give minimum late-time scattered signal's energy, which is the main fitness function of the algorithm. The proposed DE algorithm is applied to a target set consisting of lossless dielectric spheres and correct recognition rates for both noiseless and noisy signals are obtained. The results for both developed DE algorithm and other DE variants of traditional DE, adaptive differential evolution with optional external archive (JADE), jDE are also given to compare the algorithms and show the effectiveness of the proposed one.

Constrained Multi-Objective Differential Evolution for Security Constrained Economic/Environmental Dispatch

A newly constrained multi-objective differential evolution optimization technique (CMODE) for security constrained economic/environmental dispatch (EED) was proposed. The proposed CMODE evolved a constrained multi-objective version of differential evolution (DE) by employing the traditional multi-objective differential evolution (DEMO) and constrain handle technique to balance the search between feasible region and infeasible region. The proposed CMODE method had been applied to solve the security constrained EED problem. Experiments had been carried on a standard test system. The results demonstrate the high efficiency of the proposed method to solve security constrained EED problem, and the necessary of taking security constrains into consideration.

Production Scheduling of Batch Processes Based on Adaptive DE Algorithm

Production scheduling problems and traditional differential evolution(DE) are analyzed in this paper. Taking the minimum of total completion time as the objective function of production scheduling, a production scheduling model is established for batch processes in process industry.Considering that the performance of the traditional DE algorithm is sensitive to the parameter settings,an adaptive control evolution strategy is used to control the parameter scale factor F and crossover probability CR to solve the problem of parameter settings. Taking a practical production problem as a scheduling example,the established model and adaptive DE algorithm are applied to implement the production scheduling simulation. The simulation results show that compared with the ant colony system(ACS) algorithm,the adaptive DE algorithm is effective and feasible.

Unconventional initialization methods for differential evolution

The crucial role played by the initial population in a population-based heuristic optimization cannot be neglected. It not only affects the search for several iterations but often also has an influence on the final solution. If the initial population itself has some knowledge about the potential regions of the search domain then it is quite likely to accelerate the rate of convergence of the optimization algorithm. In the present study we propose two schemes for generating the initial population of differential evolution (DE) algorithm. These schemes are based on quadratic interpolation (QI) and nonlinear simplex method (NSM) in conjugation with computer generated random numbers. The idea is to construct a population that is biased towards the optimum solution right from the very beginning of the algorithm. The corresponding algorithms named as QIDE (using quadratic interpolation) and NSDE (using non linear simplex method), are tested on a set of 20 traditional benchmark problems with box constraints and 7 shifted (non-traditional) functions taken from literature. Comparison of numerical results with traditional DE and opposition based DE (ODE) show that the proposed schemes considered by us for generating the random numbers significantly improves the performance of DE in terms of convergence rate and average CPU time.

Model and algorithm of fuzzy joint replenishment problem under credibility measure on fuzzy goal

The joint replenishment problem (JRP) has received considerable attention and all of the work on JRP is under explicit environment. In fact, the decision makers often have to face vague operational conditions. In this paper, a novel JRP model with fuzzy minor replenishment cost and fuzzy inventory holding cost is developed. More concisely, this model is a fuzzy dependent-chance programming (DCP) model. Subsequently, the technique of the traditional fuzzy simulation (FS) approach and differential evolution algorithm (DE) are integrated to design a hybrid intelligent algorithm named FSDE-I to solve this practical fuzzy JRP. Thirdly, another intelligent algorithm named FSDE-II using an improved FS approach is proposed to estimate the credibility more precisely. Finally, FSDE-I and FSDE-II are illustrated with numerical examples and the results show the effectiveness of FSDE-II.

Remote Sensing Image Subpixel Mapping Based on Adaptive Differential Evolution

In this paper, a novel subpixel mapping algorithm based on an adaptive differential evolution (DE) algorithm, namely, adaptive-DE subpixel mapping (ADESM), is developed to perform the subpixel mapping task for remote sensing images. Subpixel mapping may provide a fine-resolution map of class labels from coarser spectral unmixing fraction images, with the assumption of spatial dependence. In ADESM, to utilize DE, the subpixel mapping problem is transformed into an optimization problem by maximizing the spatial dependence index. The traditional DE algorithm is an efficient and powerful population-based stochastic global optimizer in continuous optimization problems, but it cannot be applied to the subpixel mapping problem in a discrete search space. In addition, it is not an easy task to properly set control parameters in DE. To avoid these problems, this paper utilizes an adaptive strategy without user-defined parameters, and a reversible-conversion strategy between continuous space and discrete space, to improve the classical DE algorithm. During the process of evolution, they are further improved by enhanced evolution operators, e.g., mutation, crossover, repair, exchange, insertion, and an effective local search to generate new candidate solutions. Experimental results using different types of remote images show that the ADESM algorithm consistently outperforms the previous subpixel mapping algorithms in all the experiments. Based on sensitivity analysis, ADESM, with its self-adaptive control parameter setting, is better than, or at least comparable to, the standard DE algorithm, when considering the accuracy of subpixel mapping, and hence provides an effective new approach to subpixel mapping for remote sensing imagery.

Self-Adaptive Differential Evolution Algorithm Applied to Water Distribution System Optimization

Differential evolution (DE) is a relatively new technique that has recently been used to optimize the design for water distribution systems (WDSs). Several parameters need to be determined in the use of DE, including population size, N; mutation weighting factor, F; crossover rate, CR, and a particular mutation strategy. It has been demonstrated that the search behavior of DE is especially sensitive to the F and CR values. These parameters need to be fine-tuned for different optimization problems because they are generally problem-dependent. A self-adaptive differential evolution (SADE) algorithm is proposed to optimize the design of WDSs. Three new contributions are included in the proposed SADE algorithm: (1) instead of pre-specification, the control parameters of F and CR are encoded into the chromosome of the SADE algorithm, and hence are adapted by means of evolution; (2) F and CR values of the SADE algorithm apply at the individual level rather than the generational level normally used by the traditional DE algorithm; and (3) a new convergence criterion is proposed for the SADE algorithm as the termination condition, thereby avoiding pre-specifying a fixed number of generations or computational budget to terminate the evolution. Four WDS case studies have been used to demonstrate the effectiveness of the proposed SADE algorithm. The results show that the proposed algorithm exhibits good performance in terms of solution quality and efficiency. The advantage of the proposed SADE algorithm is that it reduces the effort required to fine-tune algorithm parameter values.

Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration

Recently an interesting evolutionary mechanism, sensibility, inherited from a concept model of Free Search (FS) was introduced and used for solving network problems. Unfortunately, the original FS is not easy to implement because it requires key knowledge that is not clearly defined in the existing literature to determine the neighborhood space that profoundly affects the performance of the original FS. This paper thus designs a new implementation for the concept model of FS, and proposes a new algorithm, called Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration (ADEQFS) to address this issue. In ADEQFS, we focus on designing a new mutation strategy by employing adaptive differential evolution techniques as well as concepts and principles from real-coded quantum-inspired evolutionary algorithm. In addition, we use the crossover operation from the traditional Differential Evolution scheme to alleviate the premature convergence for the proposed algorithm. Furthermore, we employ the greedy mechanism to preserve the best solutions found at each generation. The convergence analysis of the proposed algorithm is also presented in this paper. We give the proof of convergence by using the Markov chain model. Thirty-four optimization test functions with different mathematical characteristics are employed as benchmark set to test the performance of ADEQFS. The numerical results highlight the improved convergence rate and computation reliability.

A multi-population cultural algorithm with adaptive diversity preservation and its application in ammonia synthesis process

A multi-population cultural differential evolution (MCDE) algorithm is proposed. Each of the populations is managed by its private cultural differential evolution algorithm, in which a center individual is introduced into the belief space and selection function follows a new method to select the offspring for the next generation. To accelerate the convergence speed, the populations exchange their knowledge with each other every given generations. An adaptive mechanism of population diversity preservation is put forward to prevent the populations from being trapped in local optima. In the adaptive mechanism, the idea of culture fusion between populations is used to know the convergence status, so that the diversity of populations is kept along the evolutionary process. The performance evaluation on MCDE using eleven constrained optimization problems shows that MCDE is a competitive approach. MCDE is further applied to a practical optimization problem in an ammonia synthesis system with the objective to maximize the net value of ammonia. The results achieved by MCDE are compared with those by two traditional differential evolution algorithms, which indicate that MCDE has more excellent performance and better effectiveness.

Hybrid Taguchi‐Differential Evolution Algorithm for Parameter Estimation of Differential Equation Models with Application to HIV Dynamics

This work emphasizes solving the problem of parameter estimation for a human immunodeficiency virus (HIV) dynamical model by using an improved differential evolution, which is called the hybrid Taguchi‐differential evolution (HTDE). The HTDE, used to estimate parameters of an HIV dynamical model, can provide robust optimal solutions. In this work, the HTDE approach is effectively applied to solve the problem of parameter estimation for an HIV dynamical model and is also compared with the traditional differential evolution (DE) approach and the numerical methods presented in the literature. An illustrative example shows that the proposed HTDE gives an effective and robust way for obtaining optimal solution, and can get better results than the traditional DE approach and the numerical methods presented in the literature for an HIV dynamical model.

An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.

Discrete Differential Evolutionの提案(機械要素,潤滑,設計,生産加工,生産システムなど)

The Differential Evolution (DE), which is the population-based optimization technique, is one of the global optimizers for the continuous design variables such as the Particle Swarm Optimization (PSO). In the traditional DE, due to the mutation in the algorithm, the rounding-off and truncating are often employed to handle the discrete and integer variables. In this paper, the Discrete Differential Evolution (DDE) to handle the discrete or integer design variables is proposed. In the proposed DDE, the mutation is considered as the exchange possibility between two particles. By considering the mutation as the exchange possibility, it is easy and possible to handle the discrete and integer variables. In addition, the initialization of the population are also introduced in the proposed DE. It is possible to escape from local minimum by introducing the initialization of the population. The algorithm of the proposed DDE is very simple, and can be easily extend to the Mixed-Discrete Nonlinear Problems (MDNLPs). The proposed DDE can be applied to a variety of discrete and integer optimization problems. The validity is examined through typical benchmark problems.