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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]

This paper proposes an evolutionary algorithm-based energy-saving control strategy to control a highly nonlinear and time-varying active magnetic bearing (AMB) positioning system that considers energy efficiency and control performance simultaneously. Most AMB control schemes use a bias current with a superimposed control current to improve the linearity and dynamic performance of the system. However, the bias current causes power losses even if no electromagnetic force is required. As such, a recurrent wavelet fuzzy neural network with adaptive differential evolution (RWFNN-ADE)-based dynamic bias current control strategy is proposed in this paper so as to minimize the energy consumed by an AMB without altering its positioning performance and robustness. To begin with, this paper analyzes the operation principle of the AMB positioning system with a differential driving mode. Subsequently, the proposed RWFNN-ADE control scheme, in which the control current and bias current are controlled by the RWFNN and ADE, respectively, is introduced in detail. Finally, the experimental results demonstrate the high-accuracy control and significant energy-saving performances of the proposed RWFNN-ADE-controlled AMB positioning system. In the tests corresponding to operation periods of 10 and 50 s, the energy improvements compared to the baseline values were 20.24% and 17.65%, respectively, in nominal cases, and 18.89% and 18.68%, respectively, in parameter variation cases, for the proposed control strategy. [ABSTRACT FROM AUTHOR]

Real-time taxi–passenger matching plays a critical role in modern taxi dispatch systems. Currently, the greedy strategy is widely adopted, which limits the quality of the service (QoS) and the profit of the entire system. There are two crucial tasks in this system: 1) the pairwise prioritization and 2) the matching of taxi–passenger pairs. In this paper, we develop a two-stage taxi–passenger matching system to deal with these two tasks. In the first stage, we design a fuzzy controller to assign a priority score to each taxi–passenger pair in real time. To ensure its performance on providing good QoS and profit, the fuzzy controller is optimized by an offline differential evolution algorithm. New individual representation is designed to optimize the membership functions and fuzzy rule base simultaneously. To accelerate the optimization process, the algorithm is implemented in a parallel way. Then, in the second stage, considering the priority scores as weights in the bipartite graph of taxi and passenger sets, we further apply a polynomial Kuhn–Munkres algorithm to find the maximum weight perfect matching in the bipartite graph. Simulated results validate the effectiveness of the proposed algorithm, which is able to enhance the QoS provided by the taxi system and improve the profit gained by the taxi service company. [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]

Owing to environmental concerns, the energy-efficient subway train scheduling problem is necessary in subway operation management. This paper designs an approximate dynamic programming (DP) approach for energy-efficient subway train scheduling problem with time-dependent demand. The train traffic model is proposed with the dynamic equations for the evolution of train headway, train passenger loads, and the energy consumption along the subway line. For the dynamic changing of the onboard passengers with time, the total train energy usage is modeled as the sum of energy consumptions from the traction system and auxiliary facilities. A nonlinear DP problem is formulated to generate a near optimal timetable to realize the tradeoff among the utilization of trains, passenger waiting time, service levels, and energy consumption. To overcome the curse of dimensionality in this optimization problem, we construct an approximate DP framework, where the conceptions of states, policies, state transitions, and reward function are introduced. And this algorithm is able to converge to a good solution with a short time compared to the genetic algorithm and differential evolution algorithm. Finally, the numerical experiments are given to demonstrate the effectiveness of the proposed model and algorithm. [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]

This paper presents a control strategy based on model reduction and online intelligent calculation for a planar ${n}$ -link underactuated manipulator with a passive first joint (PA $^{{n-1}}$ for short) to realize its control objective, which is to move its end-point from an initial position to a target position. First, two active links of the planar PA $^{{n-1}}$ manipulator are chosen to be the active links of a planar virtual passive–active–active (PAA) manipulator, which guarantees that the geometric reachable range of the planar virtual PAA manipulator is the same as that of the planar PA $^{{n-1}}$ manipulator. The planar PA $^{{n-1}}$ manipulator is reduced to the planar virtual PAA manipulator by keeping the states of two active links in their initial values and controlling the states of the remaining ${n-3}$ active links to zero. Then, the planar virtual PAA manipulator is equivalent to two planar virtual Acrobots by adopting two-stage control method. Based on two sets of angle constraint relationships corresponding to two planar virtual Acrobots, an online differential evolution algorithm is employed to obtain all link target angles of the planar virtual PAA manipulator. Next, two Lyapunov functions, each of which is constructed based on the active link angle of one planar virtual Acrobot, are used to design controllers to realize the system control objective. Finally, Simulation results of a planar PAA-active manipulator demonstrate the effectiveness of the proposed control strategy. [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]

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]

This paper presents a hybrid differential evolution (DE) with quantum-behaved particle swarm optimization (QPSO) for the unmanned aerial vehicle (UAV) route planning on the sea. The proposed method, denoted as DEQPSO, combines the DE algorithm with the QPSO algorithm in an attempt to further enhance the performance of both algorithms. The route planning for UAV on the sea is formulated as an optimization problem. A simple method of pretreatment to the terrain environment is proposed. A novel route planner for UAV is designed to generate a safe and flyable path in the presence of different threat environments based on the DEQPSO algorithm. To show the high performance of the proposed method, the DEQPSO algorithm is compared with the real-valued genetic algorithm, DE, standard particle swarm optimization (PSO), hybrid particle swarm with differential evolution operator, and QPSO in terms of the solution quality, robustness, and the convergence property. Experimental results demonstrate that the proposed method is capable of generating higher quality paths efficiently for UAV than any other tested optimization algorithms. [ABSTRACT FROM AUTHOR]