Automatic SWMM parameter calibration method based on the differential evolution and Bayesian optimization algorithm

Hybrid metaheuristic algorithms have become popular for solving complex problems that are very challenging to overcome with conventional methods in recent years. This paper presents a hybrid algorithm called DE-ACO that combines Differential Evolution (DE) and Ant Colony Optimization (ACO) algorithms. The main idea is to use the Differential Evolution (DE) algorithm for a good starting point for Ant Colony Optimization (ACO) algorithm. A benchmark of six well-known test functions is employed to check the performances of the proposed approach in terms of convergence rate, quality of optimum solutions and computing time. The results obtained show that the performances of the hybrid algorithm outperform significantly the DE and ACO algorithms.

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

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.

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.

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

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.

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 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.

A differential evolution algorithm with intersect mutation operator

The differential evolution (DE) optimization algorithm predominantly relies on elite individuals and random difference to direct evolution. Although the strategy is clear and easy to implement, identifying a suitable direction for the DE mutation strongly depends on the direction information provided beforehand. To address this, we present a neighbor-induced mutation operator that simulates the neighbor-induced movement of Antarctic krill to guide the evolution direction in a natural manner. Additionally, center dispersion is proposed to disperse the population and redistribute individual positions to escape search stagnation, inspired by the spreading out of krill around newly discovered food. Comprising the new operator and the center dispersion pattern, this paper proposes a neighbor-induced DE algorithm with dispersion pattern (NDEd). The results of the comparative experiments verify the effectiveness of the neighbor-induced mutation operator and the dispersion pattern. Further, experimental results from 28 test functions of CEC2013 demonstrate that NDEd performs better compared to the other classic DE algorithms.

The problem of trajectory planning and obstacle avoidance in redundant robots is addressed in this paper. Four variants of Particle Swarm Optimization (PSO) and a Differential Evolution (DE) algorithm are proposed to solve this problem. Simulation experiments on a 5 degree-of-freedom (DOF) robot manipulator in an environment with static obstacles are conducted. The manipulator is required to move from a start position to a goal position with minimum error while avoiding collision with the obstacles in the workspace. The performance of the proposed algorithms is compared with the results reported in the literature and the comparative results are presented. It is observed that qPSO-C performs better in free space and PSO-C performs better in environment with obstacles in terms of minimizing error average convergence time. The performance of DE improves when the number of obstacles increases.

Several contemporary algorithms, including cuckoo search (CS), were applied to the CEC 2017 problem set, which includes a wide variety of 120 very difficult subproblems. We found that the algorithms were ineffective, especially when the number of dimensions was high. We configured several usage patterns of Linnik flight with the inverse of the golden ratio (1/Φ) to replace Lévy flight in CS, resulting in a new search mechanism that increased the efficiency of the CS algorithm. The impacts of each Linnik flight usage pattern were evaluated using the CEC 2017. The experimental results showed that: 1) CS variants that used Linnik flight were more capable than CS variants that used Lévy flight and 2) CS variants that used a mixture of Linnik flight and quantum-behaved mechanisms were even more capable. The primary effect of Linnik flight is the strengthening of the ranking, while that of the quantum-behaved mechanisms is a decreased error. A chaotic-initialized quantum-Linnik flight CS (CQLCS) algorithm is proposed. Among the 66 competitive methods applied to the CEC 2017, CQLCS ranked first and won the contemporary competitive algorithms section, which also included several advanced variants of differential evolution (DE) and particle swarm optimization (PSO) algorithms. The CQLCS could potentially be improved further by adjusting the probability of the occurrence of Linnik flight. The processes for building improved variants were analyzed to discover how, or if, this improvement could be achieved. Finally, the CQLCS algorithm required fewer lines of code to run than did the DE and PSO variants.

During recent decades, evolutionary algorithms have been widely studied in optimization problems. The multi-objective whale optimization algorithm based on multi-leader guiding is proposed in this paper, which attempts to offer a proper framework to apply whale optimization algorithm and other swarm intelligence algorithms to solving multi-objective optimization problems. The proposed algorithm adopts several improvements to enhance optimization performance. First, search agents are classified into leadership set and ordinary set by grid mechanism, and multiple leadership solutions guide the population to search the sparse spaces to achieve more homogeneous exploration in per iteration. Second, the differential evolution and whale optimization algorithm are employed to generate the offspring for the leadership and ordinary solutions, respectively. In addition, a novel opposition-based learning strategy is developed to improve the distribution of the initial population. The performance of the proposed algorithm is verified in contrast to 10 classic or state-of-the-arts algorithms on 20 bi-objective and tri-objective unconstrained problems, and experimental results demonstrate the competitive advantages in optimization quality and convergence speed. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned experiments have indicated that the proposed algorithm is comparatively effective and efficient.

The development and application of the differential evolution (DE) optimisation algorithm to the problem of worst-case analysis of nonlinear control laws for hypersonic re-entry vehicles is described. The algorithm is applied to the problem of evaluating a proposed nonlinear handling qualities clearance criterion for a detailed simulation model of a hypersonic re-entry vehicle (also known as a reusable launch vehicle (RLV)) having a full-authority nonlinear dynamic inversion (NDI) flight control law. A hybrid version of the differential evolution algorithm, incorporating local gradient-based optimisation, is also developed and evaluated. Comparisons of computational complexity and global convergence properties reveal the significant benefits which may be obtained through hybridisation of the standard differential evolution algorithm. The proposed optimisation-based approach to worst-case analysis is shown to have significant potential for improving both the reliability and efficiency of the flight clearance process for next generation RLV’s.

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