Using differential evolution for combinatorial optimization: A general approach

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

A self-competitive mutation strategy for Differential Evolution algorithms with applications to Proportional–Integral–Derivative controllers and Automatic Voltage Regulator systems

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Regulation-based formulas and improved Differential Evolution(DE) algorithm is used to optimize PID parameters. In order to improve the global search ability and the convergence rate of the common DE algorithm, self-adaptive method is introduced to obtain DE parameters. On the other hand, initial population quality of DE algorithm has important influence on convergence of the algorithm. So the regulation-based formulas are used to guide the production of initial population, which is good to improve the convergence rate and realize obtaining of PID parameters completely adaptive without any personal experience. The simulation is developed on steam temperature system of cycle fluidized bed boiler with serious parameter uncertainties and many disturbance and long-time delay. The results show that the improved DE algorithm has higher optimal speed, small amount of calculation and effective optimization of parameters. The proposed method has better control quality and system robustness.

Parameters setting is an important problem of evolution algorithms, include differential evolution algorithm. It has an effect on the performance of evolution algorithms. Although there is only three control parameters in differential evolution (DE) algorithm, the parameters setting is also a difficult problem. Self-adaptation is highly beneficial for adjusting the control parameters, especially when done without any user interaction. This paper presents differential evolution algorithm, called (AdaptDE), which use self-adaptive mechanisms applied to the control parameters. It can get the optimal control parameters for different optimization problem without user interaction. Experimental results indicate that AdaptDE algorithm is efficient and feasible. It is superior to jDE algorithm and FADE algorithm on the quality of solution.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

The paper considers dimensional synthesis of a path generator four-bar linkage by applying the modified Differential Evolution (DE) algorithm. During the search of the space, the DE algorithm may skip the right solution and lead to premature convergence. If the step is reduced, the search space is reduced as well, so that convergence becomes slower. Search efficiency may be achieved by including Lévy Flight in the DE algorithm. Namely, when the DE algorithm identifies the space of best solution, then a Levý Flight step is used for local search in that region, which significantly increases the exploitation capability and allows obtaining a very efficient solution of the optimization problem. The algorithm was tested with three examples of dimensional synthesis of a path generator four-bar linkage. The proposed algorithm can be very efficiently applied to solving very complex optimization problems.

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. In terms of the objective function, most existing research has been focused on the makespan criterion. However, in contemporary manufacturing systems, due‐date‐related performances are more important because they are essential for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a hybrid differential evolution (DE) algorithm is proposed for the problem. To enhance the overall search efficiency, a neighborhood property of the problem is discovered, and then a tree search procedure is designed and embedded into the DE framework. According to the extensive computational experiments, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness objective.

A differential evolution algorithm with intersect mutation operator

In response to the low accuracy exhibited by the Storm Water Management Model (SWMM), we propose an enhanced Differential Evolution and Bayesian Optimization Algorithm (DE-BOA) . This algorithm integrates the global search capability of the differential evolution algorithm with the local search capability of the Bayesian optimization algorithm, which enables a more comprehensive exploration of the vector solution space. A comparative analysis of various types of rainfall events is conducted. For model calibration and validation, a drainage subzone in Jinshazhou, Guangzhou City, is selected as the research subject. In total, 20 specific rainfall events are selected, and the DE-BOA algorithm outperforms the manual calibration, differential evolution algorithm, and Bayesian optimization algorithm regarding model calibration accuracy. Furthermore, the DE-BOA algorithm exhibits robust adaptability to rainfall events characterized by multiple peaks and higher precipitation levels, with Nash–Sutcliffe Efficiency coefficient values surpassing 0.90. This study’s findings could hold significant reference value for dynamically updating model parameters, thereby enhancing the model simulation performance and improving the accuracy of the urban intelligent water management platform.

Dynamic optimization of a continuous polymer reactor aims to decide optimal trajectories of control input variables so that the transition time, required to reach the desired steady state from the initial state during startup or grade-change operation, is minimized. The problem is challenging because of its highly nonlinear dynamics and multimodal properties. The proposed modified differential evolution (MDE) algorithm is different from differential evolution algorithms in the sense that MDE employs a local search to enhance the computational efficiency and modified heuristic constraints to systematically reduce the size of the search space. The algorithm is illustrated by several case studies using the dynamic optimization problem of a continuous methyl methacrylate−vinyl acetate copolymerization reactor. The case studies have shown that the proposed algorithm offers faster speed, flexible implementation, and higher robustness to find the global optimum than differential evolution algorithms.

This paper is concerned with the discrete combinatorial optimization problem. A novel set-based differential evolution (SBDE) algorithm for traveling salesman problem (TSP) is proposed and evaluated. SBDE is based on a set-based representation scheme that enables SBDE to characterize the discrete search space of TSP. The candidate solution, vector and the arithmetical operator in SBDE are redefined. Numerical experiments are carried out using the TSPLIB of test TSP problems. The obtained results show that the proposed approach is effective in quality for solving TSP.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.