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When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In recent years, electric vehicle charging stations (EVCSs) have been deployed very fast, which offer a platform for the energy coordination between electric vehicles (EVs) and the electricity distribution system (DS). This paper presents an energy management method for the operation of EVCSs and DS while considering their interaction. In this method, we first use a quality-of-service constrained decision model for EVCSs, which is formulated based on the network calculus theory. Then, the DS aims to maximize its utility by scheduling charging plans for EVCSs. Afterwards, a game based on the supply function equilibrium (SFE) model is adopted to analyze the energy interaction, in which each EVCS is regarded as the leader, and the DS as the follower. In this way, an optimization problem with equilibrium constraints is established. Moreover, a hybrid optimization algorithm based on differential evolution and interior point method is used to obtain the equilibrium solution of the SFE game. Finally, simulation studies verify the effectiveness of proposed interactive energy management method. [ABSTRACT FROM AUTHOR]

Nonlinear equations system (NES) arises commonly in science and engineering. Repulsion techniques are considered to be the effective methods to locate different roots of NES. In general, the repulsive radius needs to be given by the user before the run. However, its optimal parameter setting is difficult and problem-dependent. To alleviate this drawback, in this paper, we first propose a dynamic repulsion technique, and then a general framework based on the dynamic repulsion technique and evolutionary algorithms (EAs) is presented to effectively solve NES. The major advantages of our framework are: 1) the repulsive radius is controlled dynamically during the evolutionary process; 2) multiple roots of NES can be simultaneously located in a single run; 3) the diversity of the population is preserved due to the population reinitialization; and 4) different repulsion techniques and different EAs can be readily integrated into this framework. To extensively evaluate the performance of our framework, we choose 42 problems with diverse features as the test suite. In addition, some representative differential evolution and particle swarm optimization variants are incorporated into the framework. Our method is also compared with other state-of-the-art methods. Experimental results indicate that the dynamic repulsion technique can improve the performance of the original repulsion technique with static repulsive radius. Moreover, the proposed method is able to yield better results compared with other methods. [ABSTRACT FROM AUTHOR]

As the mutation strategy and algorithmic parameters in differential evolution (DE) are sensitive to the problems being solved, a hot research topic is to adaptively control the strategy and parameters according to the requirements of the problem. In the literature, most adaptive DE use either historical experiences of the population or heuristic information of the individuals to promote adaptation. In this paper, we develop a novel variant of adaptive DE, utilizing both the historical experience and heuristic information for the adaptation. In this novel historical and heuristic DE (HHDE), each individual dynamically adjusts its mutation strategy and associated parameters not only by learning from previous successful experience of the whole population, but also according to heuristic information related with its own current state. These help the algorithm select a more suitable mutation strategy and determinate better parameters for each individual in different evolutionary stages. The performance of the proposed HHDE is extensively evaluated on 30 benchmark functions with different dimensions. Experimental results confirm the competitiveness of the proposed algorithm to a number of DE variants. [ABSTRACT FROM AUTHOR]

Energy storage systems (ESSs) play a significant role in performance improvement of future electric traction systems. This paper investigates an ESS based on supercapacitors for trams as a reliable technical solution with considerable energy saving potential. Operating the ESS onboard a tram brings the following benefits: reduction of peak power demands, decrease of power consumption, improvement of performance, and efficiency. Whereas the commonly used ESS power management (PM) has been dealing only with PM without vehicle position knowledge, the main emphasis of the presented research is put on position-based Takagi–Sugeno fuzzy (T-S fuzzy) PM for human-driven trams with an ESS. The tram position, located by, e.g., a Global Positioning System module, is used to predict future energy demands and power flows. This information is used in the preparation of the supercapacitor energy level and its power flow control. The optimal ESS power flow with respect to the tram position is a very complex problem. Therefore, soft computing techniques are used in this paper. The main part of the proposed ESS PM is the T-S fuzzy controller. The T-S fuzzy reduces problem dimensionality using expert knowledge represented by the rules. The output membership functions were optimized by differential evolution. The designed ESS PM was verified on real traffic data. [ABSTRACT FROM PUBLISHER]

Design of electromagnetic devices has multimodal, multidimensional, and constrained characteristics. Metaheuristic approaches are good choices for tackling these design problems owing to their simulation-based property. As many electromagnetic design problems require a long computing time to solve (even on modern computers) and many heuristic approaches have been created, the major goal of this paper is to improve the effectiveness and robustness of existing approaches. This paper proposes an algorithm with the ensemble of two composite differential evolution (DE) ingredients. One ingredient is biased toward exploration and the other is biased toward exploitation. The probability of choosing which ingredient to search for new solutions is adaptively updated based on the previous performance of each ingredient. The algorithm is applied to solve a loudspeaker design problem with promising performance when compared with DE, artificial bee colony, two improved artificial bee colony algorithms, and a randomly choosing ingredients algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes an improved hybrid method to compute the parameters of the two-diode model of photovoltaic (PV) module. Unlike previous methods, it attains the speed of the analytical approach by utilizing only datasheet information. Furthermore, its accuracy is not compromised as it does not require simplifications in its computation. Four parameters are determined analytically, while the remaining three are optimized by using an evolutionary algorithm, i.e., the differential evolution. The speed is improved because the parameters are optimized only once, i.e., at standard test condition, while the values at other conditions are computed analytically. Furthermore, a procedure to guide the initial conditions of the Newton–Raphson iteration is introduced. For validation, the algorithm is compared to other established computational methods for mono-, polycrystalline, and thin film modules. When evaluated against the experimental data, the mean absolute error is improved by one order of magnitude, while the speed is increased by approximately threefold. The standard deviation of the decision parameters over 100 independent runs is less than 0.1—which suggests that the optimization process is very consistent. Due to its speed and accuracy, the method is envisaged to be useful as a computational engine in PV simulator. [ABSTRACT FROM PUBLISHER]

Existing differential evolution (DE) algorithms often face two challenges. The first is that the optimization performance is significantly affected by the ad hoc configurations of operators and parameters for different problems. The second is the long runtime for real-world problems whose fitness evaluations are often expensive. Aiming at solving these two problems, this paper develops a novel double-layered heterogeneous DE algorithm and realizes it in cloud computing distributed environment. In the first layer, different populations with various parameters and/or operators run concurrently and adaptively migrate to deliver robust solutions by making the best use of performance differences among multiple populations. In the second layer, a set of cloud virtual machines run in parallel to evaluate fitness of corresponding populations, reducing computational costs as offered by cloud. Experimental results on a set of benchmark problems with different search requirements and a case study with expensive design evaluations have shown that the proposed algorithm offers generally improved performance and reduced computational time, compared with not only conventional and a number of state-of-the-art DE variants, but also a number of other distributed DE and high-performing evolutionary algorithms. The speedup is significant especially on expensive problems, offering high potential in a broad range of real-world applications. [ABSTRACT FROM PUBLISHER]

Large-scale design optimization of electric machines is oftentimes practiced to achieve a set of objectives, such as the minimization of cost and power loss, under a set of constraints, such as maximum permissible torque ripple. Accordingly, the design optimization of electric machines can be regarded as a constrained optimization problem (COP). Evolutionary algorithms (EAs) used in the design optimization of electric machines including differential evolution (DE), which has received considerable attention during recent years, are unconstrained optimization methods that need additional mechanisms to handle COPs. In this paper, a new optimization algorithm that features combined multi-objective optimization with differential evolution (CMODE) has been developed and implemented in the design optimization of electric machines. A thorough comparison is conducted between the two counterpart optimization algorithms, CMODE and DE, to demonstrate CMODE’s superiority in terms of convergence rate, diversity and high definition of the resulting Pareto fronts, and its more effective constraint handling. More importantly, CMODE requires a lesser number of simultaneous processing units which makes its implementation best suited for state-of-the-art desktop computers reducing the need for high-performance computing systems and associated software licenses. [ABSTRACT FROM PUBLISHER]

The dynamic economic dispatch problem is a high-dimensional complex constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost. Over the last few decades, a number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, the performance of evolutionary algorithms is highly dependent on a number of factors, such as the control parameters, diversity of the population, and constraint-handling procedure used. In this paper, a self-adaptive differential evolution and a real-coded genetic algorithm are proposed to solve the dynamic dispatch problem. In the algorithm design, a new heuristic technique is introduced to guide infeasible solutions towards the feasible space. Moreover, a constraint-handling mechanism, a dynamic relaxation for equality constraints, and a diversity mechanism are applied to improve the performance of the algorithms. The effectiveness of the proposed approaches is demonstrated on a number of dynamic economic dispatch problems for a cycle of 24 h. Their simulation results are compared with each other and state-of-the-art algorithms, which reveals that the proposed method has merit in terms of solution quality and reliability. [ABSTRACT FROM AUTHOR]

Sensor network localization based on connectivity can be modeled as a nonconvex optimization problem. However, current models only consider the convex constraints, i.e., connections among the nodes. The proposed method considers not only the connection constraints but the disconnection constraints, which are nonconvex in nature, as well. It is argued that the connectivity-based localization problem should be represented as an optimization problem with both convex and nonconvex constraints. In this paper, an algorithm combining a modified differential evolution (DE) algorithm and heuristics is presented for the situation in which the communication range value is unknown. The developed algorithm has a new crossover procedure, with refined procedures to produce a new generation of individuals/candidates. A “single node treatment” procedure is also designed for the search procedure to formulate a new set of coordinate locations to jump out from the local minimum. The final solution can reach the most suitable configuration of the unknown nodes (nodes without knowing their location) because all the information on the constraints has been used. Simulation results have shown that better solutions can be obtained when compared with other convex-constraint methods. The proposed method also gets better results than other general nonconvex optimization methods. [ABSTRACT FROM AUTHOR]

Concurrent minimization of project time and project cost is an important issue in construction planning and management. Tradeoff optimization between these two variables is necessary to maximize overall construction project benefit. This paper presents a two-phase differential evolution (DE) model to resolve these problems. This model is able to effectively consider both time–cost effects and resource constraints. First, we introduce a novel multiple-objective algorithm, the chaotic initialized multiple objective differential evolution with adaptive-mutation strategy-based time–cost tradeoff, to determine the execution mode that best optimizes the time–cost balance. Subsequently, we introduce a DE-based resource-constrained method to generate a feasible schedule. A real construction case study is then used to illustrate the application of the proposed algorithm. Performance comparisons done with the nondominated sorting genetic algorithm, multiple objective particle swarm optimization, and multiple objective differential evolution further verify the efficiency and effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]