Search

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]

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]

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]

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]

Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate. [ABSTRACT FROM AUTHOR]

In evolutionary computation, balancing the diversity and convergence of the population for multiobjective evolutionary algorithms (MOEAs) is one of the most challenging topics. Decomposition-based MOEAs are efficient for population diversity, especially when the branch partitions the objective space of multiobjective optimization problem (MOP) into a series of subspaces, and each subspace retains a set of solutions. However, a persisting challenge is how to strengthen the population convergence while maintaining diversity for decomposition-based MOEAs. To address this issue, we first define a novel metric to measure the contributions of subspaces to the population convergence. Then, we develop an adaptive strategy that allocates computational resources to each subspace according to their contributions to the population. Based on the above two strategies, we design an objective space partition-based adaptive MOEA, called OPE-MOEA, to improve population convergence, while maintaining population diversity. Finally, 41 widely used MOP benchmarks are used to compare the performance of the proposed OPE-MOEA with other five representative algorithms. For the 41 MOP benchmarks, the OPE-MOEA significantly outperforms the five algorithms on 28 MOP benchmarks in terms of the metric hypervolume. [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]

Randomized neural networks (NNs), such as random vector functional link (RVFL) and extreme learning machine (ELM), have been widely applied in various classification problems owing to their computational efficiency and universal approximation capability. However, such approaches are designed for regular Euclidean data and lack the ability to generalize to complex structured data. Moreover, their randomly generated parameters often lead to a suboptimal decision boundary with a growing requirement of hidden neurons. In this article, we first propose a plain framework, termed randomized graph convolutional networks (RGCNs), to generalize the classic randomized NNs to the non-Euclidean domain. Then, a hybrid framework called evolution-driven RGCN (EvoRGCN) is presented by using adaptive differential evolution with novelty search strategy to seek the globally optimal graph embedding for the plain RGCN. Finally, we recast the classic ELM and RVFL under the proposed frameworks, resulting in four novel semi-supervised models, including the plain models [i.e., graph convolutional extreme learning machines (GCELMs) and graph convolutional RVFL (GCRVFL)] and the optimized models (i.e., O-GCELM and O-GCRVFL). We show that our approaches are the natural generalization of the traditional randomized NNs in the non-Euclidean domain. Furthermore, our approaches not only retain the advantages of the classic approaches but also enable them to handle graph data. We compare our approaches against many existing methods across regular datasets and graph benchmarks, demonstrating that the proposed approaches dramatically outperform the compared methods with better generalization ability and robustness. Particularly, we quantitatively show the performance ranking of different randomized NNs, i.e., O-GCRVFL $> $ O-GCELM $\approx $ GCRVFL $> $ GCELM $\approx $ RVFL $> $ ELM. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

A growing number of organizations are hosting their software applications in distributed data centers (DCs) in the cloud, for faster response time and higher energy efficiency. The dramatic increase of user tasks, however, poses a significant challenge on DC providers to retain users’ expectations on both aspects. To tackle this challenge, this work first formulates the problem into a constrained biobjective optimization problem. A biobjective algorithm, named simulated-annealing-based adaptive differential evolution (SADE), is presented to simultaneously reduce both the response time of tasks and energy cost. Meanwhile, a method of minimal Manhattan distance is adopted to search for a final knee, for achieving a good balance between response time minimization and energy cost reduction. Experimental results on real-life datasets, i.e., the electricity prices and tasks collected from a Google cluster trace, have proved that SADE yields less task response time and lower energy cost compared with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

JADE is a differential evolution (DE) algorithm and has been shown to be very competitive in comparison with other evolutionary optimization algorithms. However, it suffers from the premature convergence problem and is easily trapped into local optima. This article presents a novel JADE variant by incorporating chaotic local search (CLS) mechanisms into JADE to alleviate this problem. Taking advantages of the ergodicity and nonrepetitious nature of chaos, it can diversify the population and thus has a chance to explore a huge search space. Because of the inherent local exploitation ability, its embedded CLS can exploit a small region to refine solutions obtained by JADE. Hence, it can well balance the exploration and exploitation in a search process and further improve its performance. Four kinds of its CLS incorporation schemes are studied. Multiple chaotic maps are individually, randomly, parallelly, and memory-selectively incorporated into CLS. Experimental and statistical analyses are performed on a set of 53 benchmark functions and four real-world optimization problems. Results show that it has a superior performance in comparison with JADE and some other state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]