Differential Evolution Approach Research Articles

Simultaneous scheduling of machines and vehicles in an FMS environment with alternative routing

Scheduling of flexible manufacturing systems is a well-known NP-hard problem which is very complex, due to additional considerations like material handling, alternative routing, and alternative machines. Improvement in the performance of a flexible manufacturing system can be expected by efficient utilization of its resources, by proper integration and synchronization of their scheduling. Differential evolution is a powerful tool which proved itself as a better alternative for solving optimization problems like scheduling. In this paper, the authors addressed simultaneous scheduling of both machines and material handling system with alternative machines for the makespan minimization objective. The authors proposed a machine selection heuristic and a vehicle assignment heuristic which are incorporated in the differential evolution approach to assign the tasks, to appropriate machine and vehicle, and to minimize cycle time.

A Fast Restoration Strategy in Distribution Systems Using an Enhanced Differential Evolution Approach

This paper proposes a fast restoration strategy of distribution systems using an enhanced differential evolution (EDE) approach. Service restoration of distribution systems is an emergent task that must be performed rapidly by the system operators. Basically, it is a complicated combinatorial optimization problem, often having many candidate solutions to be evaluated by the operators. To improve the efficiency of restoration and reduce the burden on the operators, this paper proposes an EDE method combining variable scaling differential evolution (VSDE) algorithm and ant system (AS) to solve the combinatorial optimization problem. To verify the effectiveness of the proposed method, a typical distribution system of the Taiwan Power Company (TPC) was tested and compared with the existing methods. The results show the proposed method was superior to the existing methods in terms of convergence time and the obtained restoration plan.

River suspended sediment concentration modeling using a neural differential evolution approach

Summary In this study, neural differential evolution (NDE) models are proposed to estimate suspended sediment concentration. NDE models are improved by combining two methods, neural networks and differential evolution. The accuracy of NDE models were compared with those of the adaptive neuro-fuzzy (NF), neural networks (NN) and rating curve (RC) models. The daily streamflow and suspended sediment data from two stations, Rio Valenciano Station and Quebrada Blanca Station, operated by the US Geological Survey (USGS) were used as case studies. The models’ accuracies were evaluated using mean square error (MSE) and determination coefficient ( R 2 ) statistics. A comparison of results indicated that the NDE models give better estimates than NF, NN and RC techniques. For the Rio Valenciano Station and Quebrada Blanca Station, it was found that the NDE models with MSE = 2549 mg 2 l −2 , R 2 = 0.884 and MSE = 240 mg 2 l −2 , R 2 = 0.942 in the test stage were superior in estimating suspended sediment concentration to the optimal neuro-fuzzy models with MSE = 0.2704 mg 2 l −2 , R 2 = 0.876 and MSE = 320 mg 2 l −2 , R 2 = 0.929, respectively.

Optimization of lipase production using differential evolution

Differential Evolution (DE) coupled with Response Surface Methodology (RSM) has been used for the optimization of extracellular lipolytic enzyme production by Rhizopus oryzae NRRL 3562 through sold state fermentation. The input space of the experimentally validated RSM-model was optimized using a novel Differential Evolution approach (DE), which works based on the natural selection and survival of the fittest concepts of the biological world. The maximum lipase activity of 96.52 U/gds was observed with the DE stated optimum values of 35.59°C, 1.50, 5.28, and 4.83 days for temperature, liquid to solid ratio, pH, and incubation time respectively. The optimal levels of control parameters namely number of population, generations, crossover operator, and mutation constant were equal to 20, 50, 0.6, and 0.20, respectively. The developed model and its optimization are generic in nature and thus appear to be useful for the design and scale-up of the extracellular lipase production by R. oryzae NRRL 3562 through solid state fermentation.

Optimal image colour extraction by differential evolution

Differential evolution is an optimisation technique that has been successfully employed in various applications. In this paper, we apply differential evolution to the problem of extracting the optimal colours of a colour map for quantised images. The choice of entries in the colour map is crucial for the resulting image quality as it forms a look-up table that is used for all pixels in the image. We show that differential evolution can be effectively employed as a method for deriving the entries in the map. In order to optimise the image quality, our differential evolution approach is combined with a local search method that is guaranteed to find the local optimal colour map. This hybrid approach is shown to outperform various commonly used colour quantisation algorithms on a set of standard images.

A Kinematics Based Heuristic Approach for Molecular Conformational Search

This paper presents our developed Kinematics Differential Evolution (kDE) approach to model flexible biological molecules of different type, size and shape through the rapid identification of low-energy molecular conformations. One of the main benefits of our proposed methodology is that a population of alternative low-energy solutions is provided for each tested molecular structure compared with a single low-energy solution usually obtained by traditional molecular modeling approaches. This population includes a number of different molecular conformations that attain the same low energy value and hence correspond to an energetic state with high probability of occurrence. Results show that the kDE model provides a set of molecular structures similar to those obtained by traditional molecular dynamics.

A differential evolution approach for protein structure optimisation using a 2D off-lattice model

Protein structure optimisation is a well-known problem in bioinformatics. This work applies an evolutionary algorithm to solve the protein structure optimisation problem based on the AB off-lattice model. Three different implementations of the differential evolution (DE) algorithm were developed, a sequential and two parallel. The parallel implementations (master-slave and ring-island) showed superior performance than the sequential one. Experiments were done using a benchmark of toy sequences with 13 to 55 monomers long. Results of the DE implementations were compared with other works in the literature. Good results were achieved for most sequences, not achieving the optimal values, but competitive with other specialised methods. Overall results encourage further research towards the use of knowledge-based operators to improve performance of DE.

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.

Multi-objective optimization of cutting parameters in turning process using differential evolution and non-dominated sorting genetic algorithm-II approaches

Optimization techniques using evolutionary algorithm (EA) are becoming more popular in engineering design and manufacturing activities because of the availability and affordability of high-speed computers. In this work, an attempt was made to solve multi-objective optimization problem in turning by using multi-objective differential evolution (MODE) algorithm and non-dominated sorting genetic algorithm(NSGA-II). Optimization in turning means determination of the optimal set of machining parameters to satisfy the objectives within the operational constraints. These objectives may be minimum tool wear, maximum metal removal rate or any weighted combination of both. The main machining parameters which are considered as variables of the optimization are cutting speed, feed rate, and depth of cut. The optimum set of these three input parameters is determined for a particular job-tool combination of EN24 steel and tungsten carbide during a single-pass turning which minimizes the tool wear and maximizes the metal removal rate after satisfying the constraints of temperature and surface roughness. The regression models, developed for tool wear, temperature, and surface roughness were used for the problem formulation. The non-dominated solution set obtained from MODE was compared with NSGA-II using the performance metrics and reported

Optimization of Adiabatic Styrene Reactor: A Hybrid Multiobjective Differential Evolution (H-MODE) Approach

In this study, a hybrid strategy of multiobjective differential evolution (hybrid-MODE) algorithm is proposed that consists of an evolutionary algorithm for global search and a deterministic algorithm for local search. To begin, the proposed algorithm is tested for its performance using a benchmark test function (KUR) as case study 1 with the nondominated sorting genetic algorithm-II (NSGA-II) (both binary- and real-coded versions), strength Pareto evolutionary algorithm (SPEA), Pareto archived evolutionary strategy (PAES), multiobjective differential evolution (MODE), and an improved strategy of MODE algorithms. Subsequently, the multiobjective optimization of an industrial adiabatic styrene reactor is carried out as case study 2, employing a prevalidated model using the hybrid-MODE algorithm and an improved strategy of MODE. Four cases (three sets of two-objective optimization, cases 1−3, and one set of three-objective optimization, case 4) are considered consisting of simultaneous maximization of styrene productivity, selectivity, and yield with four decision variables and two constraints. The proposed algorithm converges to a better set of nondominated solutions (possibly a Pareto front) as compared to the nondominated solutions obtained using NSGA and an improved strategy of MODE algorithms. The limitations of previous studies are reported in terms of key decision variables. The hybrid strategy of MODE is found to converge to the true Pareto front more rapidly (in fewer function evaluations), resulting in a well-diversified Pareto front as compared to the stand-alone evolutionary approach.

A multi-objective differential evolutionary approach toward more stable gene regulatory networks

Models are of central importance in many scientific contexts. Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles of living systems. Biological models, such as gene regulatory models, can help us better understand interactions among genes and how cells regulate their production of proteins and enzymes. One feature shared among living systems is their ability to cope with perturbations and remain stable, a property that is the result of evolutionary fine-tuning over many generations. In this study we use random Boolean networks (RBNs) as an abstract model of gene regulatory systems. By applying Differential Evolution (DE), an evolution-based optimization technique, we produce networks with increased stability. DE requires relatively few user-specified parameters, has fast convergence and does not rely on initial conditions to find the global minima within multi-dimensional search spaces. The stability of networks is evaluated by taking parameters such as their network sensitivity, attractor cycle length and number of attractor basins into account. In this study we present an evolutionary approach to produce networks with specific properties (high stability) starting from chaotic regimes. From this chaotic regime and randomly generated classical RBNs with static input degree, our evolutionary approach is able to produce networks with homogenous Boolean functions and highly structured state spaces.

Electromagnetic optimization based on an improved diversity‐guided differential evolution approach and adaptive mutation factor

PurposeThe purpose of this paper is to show, on a widely used benchmark problem, that adaptive mutation factors and attractive/repulsive phases guided by population diversity can improve the search ability of differential evolution (DE) algorithms.Design/methodology/approachAn adaptive mutation factor and attractive/repulsive phases guided by population diversity are used within the framework of DE algorithms.FindingsThe paper shows that the combined use of adaptive mutation factors and population diversity in order to guide the attractive/repulsive behavior of DE algorithms can provide high‐quality solutions with small standard deviation on the selected benchmark problem.Research limitations/implicationsAlthough the chosen benchmark is considered to be representative of typical electromagnetic problems, different test cases may give less satisfactory results.Practical implicationsThe proposed approach appears to be an efficient general purpose stochastic optimizer for electromagnetic design problems.Originality/valueThis paper introduces the use of population diversity in order to guide the attractive/repulsive behavior of DE algorithms.

A Differential Evolution Based on Double Populations for Constrained Multi-Objective Optimization Problem

An improved differential evolution approach is given first,and a new algorithm based on double popumations for Constrained Multi-objective Optimization Problem(CMOP)is presented.In the proposed algorithm,two populations are adopted,one is for the feasible solutions found during the evolution,and the other is for infeasible solutions with better performance which are allowed to participate in the evolution with the advantage of avoiding difficulties such as constructing penalty function and deleting infeasible solutions directly.In addition,the time complexity of the proposed algorithm,NSGA-Ⅱand SPEA are compared,which show the best is NSGA-Ⅱ,followed by SPEA and the proposed algorithm simultaneously.The experiments on benchmarks indicate that the proposed algorithm is superior to NSGA-Ⅱin the measure of GD and SP.

Solution of inverse radiative transfer problems in two-layer participating media with differential evolution

In the present work the differential evolution approach (DE) is used for the estimation of radiative properties in two-layer participating media. This physical phenomenon is modelled by an integro-differential equation known as the Boltzmann equation. A review of the optimization technique used is presented. The direct radiative transfer problem is solved by using the collocation method. Then, case studies are presented aimed at illustrating the efficiency of the methodology used in the treatment of an inverse problem of radiative transfer. The results obtained from the solution of the inverse problem are compared with those obtained from a hybridization of simulated annealing and Levenberg–Marquardt methods. The preliminary results indicate that the proposed approach characterizes a promising methodology for the present type of inverse problem.

Application of enhanced discrete differential evolution approach to unit commitment problem

This paper proposes a discrete binary differential evolution (DBDE) approach to solve the unit commitment problem (UCP). The proposed method is enhanced by priority list based on the unit characteristics and heuristic search strategies to handle constraints effectively. The implementation of the proposed method for UCP consists of three stages. Firstly, the DBDE based on priority list is applied for unit scheduling when neglecting the minimum up/down time constraints. Secondly, repairing strategies are used to handle the minimum up/down time constraints and decommit excess spinning reserve units. Finally, heuristic unit substitution search and gray zone modification algorithm are used to improve optimal solution further. Furthermore, the effects of two crucial parameters on performance of the DBDE for solving UCP are studied as well. To verify the advantages of the method, the proposed method is tested and compared to the other methods on the systems with the number of units in the range of 10–100. Numerical results demonstrate that the proposed method is superior to other methods reported in the literature.

Parameter estimation of chaotic system with time-delay: A differential evolution approach

It is an important issue to estimate parameters of chaotic system in nonlinear science. In this paper, parameter estimation problem of chaotic system with time-delay is considered. Parameters and time-delay are estimated together by treating time-delay as an additional parameter. The parameter estimation problem is converted to an multi-dimensional optimization problem. A differential evolution (DE) algorithm, which possess a powerful searching capability for finding the solutions for a given optimization problem, is applied to solve this optimization problem. Two illustrative examples are given to verify the effectiveness of the proposed method.

Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems

Evolutionary algorithms (EAs) are general-purpose stochastic search methods that use the metaphor of evolution as the key element in the design and implementation of computer-based problems solving systems. During the past two decades, EAs have attracted much attention and wide applications in a variety of fields, especially for optimization and design. EAs offer a number of advantages: robust and reliable performance, global search capability, little or no information requirement, and others. Among various EAs, differential evolution (DE), which characterized by the different mutation operator and competition strategy from the other EAs, has shown great promise in many numerical benchmark problems and real-world optimization applications. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. To improve the global optimization property of DE, in this paper, a DE approach based on measure of population's diversity and cultural algorithm technique using normative and situational knowledge sources is proposed as alternative method to solving the economic load dispatch problems of thermal generators. The traditional and cultural DE approaches are validated for two test systems consisting of 13 and 40 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Simulation results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving economic load dispatch problems.

Differential evolution optimization combined with chaotic sequences for image contrast enhancement

Evolutionary Algorithms (EAs) are stochastic and robust meta-heuristics of evolutionary computation field useful to solve optimization problems in image processing applications. Recently, as special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used in various designs of EAs. Three differential evolution approaches based on chaotic sequences using logistic equation for image enhancement process are proposed in this paper. Differential evolution is a simple yet powerful evolutionary optimization algorithm that has been successfully used in solving continuous problems. The proposed chaotic differential evolution schemes have fast convergence rate but also maintain the diversity of the population so as to escape from local optima. In this paper, the image contrast enhancement is approached as a constrained nonlinear optimization problem. The objective of the proposed chaotic differential evolution schemes is to maximize the fitness criterion in order to enhance the contrast and detail in the image by adapting the parameters using a contrast enhancement technique. The proposed chaotic differential evolution schemes are compared with classical differential evolution to two testing images. Simulation results on three images show that the application of chaotic sequences instead of random sequences is a possible strategy to improve the performance of classical differential evolution optimization algorithm.

Improved Multiobjective Differential Evolution (MODE) Approach for Purified Terephthalic Acid (PTA) Oxidation Process

Evolutionary algorithms (EAs), which are basically the population-based search algorithms, are becoming increasingly popular for solving highly nonlinear and complex optimization problems (both the single-objective and multiobjective problems). Multiobjective Differential Evolution (MODE), which is an extension of Differential Evolution (DE) to multiobjective optimization, has been successfully applied to a few chemical process industrial problems. This article presents multiobjective optimization of p-xylene oxidation in the manufacturing process of industrial Purified Terephthalic Acid (PTA) oxidation using MODE, its improved strategy, i.e., Elitist-Multiobjective Differential Evolution (E-MODE), and NSGA-II. E-MODE algorithm includes the concept of elitism as present in NSGA-II. Four industrially important cases are studied from the multiobjective optimization point of view. The effect of six decision variables identified, namely, catalyst concentration, vent oxygen content, % water in solvent, feed xylene rate, temperature of reactor, and total feed rate, on the formulated objective function for the four cases is studied. The corresponding Pareto optimal sets (i.e., sets of equally good nondominated solutions) are obtained. All decision variables, corresponding to the Pareto optimal solutions, are plotted against each of the objectives. Comparison among the Pareto optimal fronts of four cases is also carried out. Pareto solutions obtained in this study (using MODE, E-MODE, and NSGA-II) lie on same (Global) Pareto front. However, MODE is able to cover a better range than E-MODE and NSGA-II. The results obtained are useful to a plant engineer for possible improvement in the process design decisions.

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.