Constrained Differential Evolution Research Articles

A constrained differential evolution algorithm for calculation of two-phase equilibria at given volume, temperature and moles

A variety of strategies including two types of direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles have been developed, which can find satisfactory solutions for the phase equilibrium calculation problem at given volume, temperature and moles (NVT-flash). However, these methods are sensitive to the initial values and depend on the objective function's derivative during calculation. To resolve these deficiencies, a constrained differential evolution algorithm (abbreviated as CDE) for calculating two-phase equilibria at given volume, temperature, and moles is presented in this paper. The total Helmholtz free energy is regarded as the objective function, and the moles vector and volume of a certain phase are taken as the decision variables. This paper deals with the constraints of the NVT-flash problem by using direct search method and exterior point method. The results of the investigations on pure substance, binary and ternary mixtures are in agreement with the published data, which proves the effectiveness in solving the NVT-flash problem and the energy attenuation characteristic of the algorithm. The proposed algorithm represents the first successful attempt to apply the meta-heuristic optimization algorithm to solve the phase equilibrium computation under NVT-flash, and it shows the promising application prospect of meta-heuristic optimization algorithms for solving the phase equilibrium calculation problems.

Surrogate-assisted optimization for anti-ship missile body configuration considering high-velocity water touching

As a crucial weapon in the sea battle, anti-ship missiles generally employ a sea-skimming penetration strategy to reduce the probability of being detected by the target radar, which greatly increases the risk of touching water caused by sensor errors or random sea conditions. To alleviate the large impact load by high-velocity water touching, a novel anti-ship missile body configuration is proposed in this paper, which is inspired by the idea of hydroplaning. A parametric geometry model is first developed to modify the configuration of the anti-ship missile body. Subsequently, a structured arbitrary Lagrange-Eulerian based Fluid-Structure Interaction (FSI) model is established to analyze the kinematics parameters of the missile body during the hydroplaning process. A missile body configuration optimization problem is then formulated to minimize the impact load considering several constraints, e.g., horizontal velocity loss, pitch angle after touching water, and inside capacity for payload. Due to the time-consuming FSI simulation, a Kriging-assisted constrained differential evolution method is utilized to optimize the missile body configuration for reducing the impact load. During the optimization process, radial basis function and Kriging are combined with evolutionary operators to lead the search to the vicinity of the optimum rapidly. The result shows that the proposed missile body configuration can reduce the impact load by 18.8% compared with the ordinary configuration. Additionally, the optimized configuration can further yield a 17.4% impact load decrease subject to all the constraints and avoid structural damage by the high-velocity water touching, which demonstrates the effectiveness and practicability of the proposed anti-ship missile body configuration and corresponding optimization framework for reducing the impact load.

Robot Dynamics Modeling with a Novel Friction Model and Extracted Feasible Parameters Using Constrained Differential Evolution

Robot Dynamics Modeling with a Novel Friction Model and Extracted Feasible Parameters Using Constrained Differential Evolution

Dexterous workspace optimization for a six degree-of-freedom parallel manipulator based on surrogate-assisted constrained differential evolution

Parallel manipulators are increasingly applied because of their high stiffness, load capacity, and motion precision. However, the workspace of a parallel manipulator is relatively small compared to that of a serial manipulator. Therefore, appropriate structural designs of parallel manipulators for maximizing the workspace are essential. This paper studies the dexterous workspace maximization problem of a six-degree-of-freedom (DOF) parallel manipulator. First, a constrained optimization model is formulated, in which, the objective is to maximize the dexterous workspace, and the constraints include several kinematic and dynamic indicators, and some general structural limitations. To address the highly constrained, computationally-expensive problem, a surrogate-assisted two-phase constrained differential evolution method is proposed. Its effectiveness and efficiency are verified by the superior performance over two surrogate-free evolutionary methods: differential evolution (DE) and genetic algorithm (GA), and two surrogate-assisted state-of-the-art evolutionary methods: modified constrained expected improvement (CEI) and the lower confidence bounding approach (PCLCB), on ten benchmark functions and the established real-word 6-DOF manipulator design optimization problem.

High‐resolution 2.5D multifocusing imaging of a crooked seismic profile in a crystalline rock environment: Results from the Larder Lake area, Ontario, Canada

ABSTRACTA high‐resolution seismic reflection transect was acquired over a hard‐rock geological setting along an existing roadway in the Larder Lake area of the Superior Craton of Canada for the Metal Earth project in 2017. This profile, as well as other Metal earth transects, primarily aims to enhance the knowledge and to better understand the subsurface geology of the Abitibi Greenstone Belt within the Canadian Shield. The complex geological settings of the study area as well as the tribulations caused by the survey geometry have made the imaging and velocity field estimation more challenging. A recently introduced 2.5D multifocusing stacking method is one potential solution for processing crooked‐line seismic data with a poor signal‐to‐noise ratio. The 2.5D multifocusing approach offers more realistic modelling of the zero‐offset wavefield by explicitly accounting for the midpoint dispersion and cross‐dip effects. The main practical problem of the 2.5D multifocusing implementation is the simultaneous determination of the optimal wavefield parameters for each image point and time location. We address this optimization problem using a multidimensional constrained differential evolution global optimization algorithm, as this improves the efficiency and accuracy of the estimation. We have also designed an efficient processing sequence for multifocusing seismic imaging. The performance of the 2.5D multifocusing procedure has been examined on a synthetic model, generated using the same real acquisition geometry. Numerical tests demonstrate that the 2.5D multifocusing technique can produce a more focused stack with the primary reflections appearing at their poststack correct locations, and the procedure can also provide reliable estimates of interface dips. Due to the importance and difficulty of imaging the data, several conventional and advanced processing strategies have been attempted on the transect, specifically: 2D phase‐shift time migration of a dip moveout corrected stack; 2D prestack Kirchhoff time migration; swath 3D poststack migration; and our 2.5D multifocusing imaging algorithm. We found that applying the 2.5D multifocusing stacking algorithm followed by a poststack time migration approach improved the resolution of the image significantly compared to all the conventional and advanced methods and identified new reflections. The 2.5D multifocusing method also focused the steeply dipping reflections more coherently, which resolved ambiguities in geological architecture by understanding the location and continuity of structures. The method also accurately extracts 3D structural information and results in an improved signal‐to‐noise ratio.

Constrained-Differential-Evolution-Based Stealthy Sparse Cyber-Attack and Countermeasure in an AC Smart Grid

As the next-generation power grids, smart grids are integrated with advanced information and communication technology (ICT) to make the grid more efficient and stable than conventional power systems. Given the mounting cyber-attack threats, these critical ICT systems create great security issues for smart grids. Additionally, the clever attackers have the ability to not only access and monitor the smart grid, but also hack it by launching well-established cyber-attacks. Thus, this article is devoted to understanding the potential stealthy cyber-attack and its countermeasure. First, this article proposes a stealthy sparse cyber-attack model in an ac smart grid by considering both the residual test-based detector and the interval-state-estimation-based detector, which is not considered in previous studies. The design model is formulated as a constrained optimization problem by minimizing the number of contaminated meters, where the characteristics of two types of detector are considered simultaneously as the constraints for the first time. A constrained differential evolution (CDE) is proposed as the solver because the optimization problem is NP-hard. Then, a generalized-cumulative-sum-based detector is developed to detect the proposed cyber-attacks, where a fractional-order state transition matrix is originally introduced into the estimator to describe the dynamics of the power system. Numerical studies illustrate the feasibility of CDE-based stealthy sparse cyber-attacks and the effectiveness of the proposed countermeasure.

Swarm UAV SAR for 3-D Imaging: System Analysis and Sensing Matrix Design

The unmanned aerial vehicle (UAV) is a low-cost and high-efficiency lightweight synthetic aperture radar (SAR)-mounted platform that can be used for a variety of military and civilian missions. Using multiple UAVs to form a swarm can break through the limitations of a single platform and has broad application prospects. In this article, swarm UAV SAR that contains tens or hundreds of UAV platforms is proposed for the first time. The concept and advantages of swarm UAV SAR are investigated, and the mission outlook is given. Afterward, the swarm UAV 3-D linear array SAR (LASAR) is illustrated, which enables high-resolution 3-D imaging in a single flight. Since the antenna array of the swarm UAV 3-D LASAR is sparse, the compressed sensing (CS) algorithm is applied, whose reconstruction performance is closely related to the correlation coefficient of the sensing matrix. Hence, the signal model of swarm UAV 3-D LASAR is derived, and the expression of the sensing matrix is deduced. The sensing matrix design in this article aims at obtaining satisfactory reconstruction performance by optimizing the distribution of the antenna elements, which directly influences the correlation coefficient of the sensing matrix. Considering the limitation of the practical conditions, the sensing matrix design problem is modeled as a constrained integer programming problem. Finally, a sensing matrix design method based on discrete constrained differential evolution (DCDE) algorithm is proposed to solve the optimization problem. Experimental results demonstrate the effectiveness and superiority of the proposed method.

An Improved Multioperator-Based Constrained Differential Evolution for Optimal Power Allocation in WSNs.

Optimal power allocation (OPA), which can be transformed into an optimization problem with constraints, plays a key role in wireless sensor networks (WSNs). In this paper, inspired by ant colony optimization, an improved multioperator-based constrained adaptive differential evolution (namely, IMO-CADE) is proposed for the OPA. The proposed IMO-CADE can be featured as follows: (i) to adaptively select the proper operator among different operators, the feedback of operators and the status of individuals are considered simultaneously to assign the selection probability; (ii) the constrained reward assignment is used to measure the feedback of operators; (iii) the parameter adaptation is used for the parameters of differential evolution. To extensively evaluate the performance of IMO-CADE, it is used to solve the OPA for both the independent and correlated observations with different numbers of sensor nodes. Compared with other advanced methods, simulation results clearly indicate that IMO-CADE yields the best performance on the whole. Therefore, IMO-CADE can be an efficient alternative for the OPA of WSNs, especially for WSNs with a large number of sensor nodes.

Low-speed airfoil optimization using constrained differential evolution

Nowadays, algorithms designed to optimize the shape of an airfoil are being developed by many researchers. In this paper, to achieve an optimum shape configuration, a methodology based on an evolutionary algorithm is proposed. The main objective is to find the optimum shape of a known airfoil that gives the best aerodynamic performance for a fixed lift coefficient. For the airfoil parametrization, the class-shape method is used to develop a well-behaved geometry. The paper underlines the implementation of a constrained differential evolutionary algorithm using the free penalty scheme by varying the coefficients of the shape parametrization function. The aim is to obtain a better aerodynamic performance for a predetermined lift coefficient by imposing a fixed maximum airfoil thickness interval. The method is a general optimization procedure and can be implemented in a wide range of engineering design problems.

A constrained differential evolution algorithm to solve UAV path planning in disaster scenarios

Disasters have caused significant losses to humans in the past decades. It is essential to learn about the disaster situation so that rescue works can be conducted as soon as possible. Unmanned aerial vehicle (UAV) is a very useful and effective tool to improve the capacity of disaster situational awareness for responders. In the paper, UAV path planning is modelled as the optimization problem, in which fitness functions include travelling distance and risk of UAV, three constraints involve the height of UAV, angle of UAV, and limited UAV slope. An adaptive selection mutation constrained differential evolution algorithm is put forward to solve the problem. In the proposed algorithm, individuals are selected depending on their fitness values and constraint violations. The better the individual is, the higher the chosen probability it has. These selected individuals are used to make mutation, and the algorithm searches around the best individual among the selected individuals. The well-designed mechanism improves the exploitation and maintains the exploration. The experimental results have indicated that the proposed algorithm is competitive compared with the state-of-art algorithms, which makes it more suitable in the disaster scenario.

ε Constrained differential evolution using halfspace partition for optimization problems

There are many efficient and effective constraint-handling mechanisms for constrained optimization problems. However, most of them evaluate all the individuals, including the worse individuals, which waste a lot of fitness evaluations. In this paper, halfspace partition mechanism based on constraint violation values is proposed. Since constraint violation information of individuals in current generation are already known, the positive side of tangent line of one point as positive halfspace is defined. A point is treated as potential point if it locates in the intersect region of two positive halfspaces. Hence, the region includes all these points has greater possibility to obtain smaller constraint violation. Only when the offspring locates in this area, the actual objective function value and constraint violation will be calculated. The estimated worse individuals will be omitted without calculating actual constraint violation and fitness function value. Four engineering optimization and a case study with the grinding optimization process are studied. The experimental results verify the effectiveness of the proposed mechanism.

Adaptive Constrained Differential Evolution Algorithm by Using Generalized Opposition-Based Learning

Differential evolution is a global optimization algorithm based on greedy competition mechanism, which has the advantages of simple structure, less control parameters, higher reliability and convergence. Combining with the constraint-handling techniques, the constraint optimization problem can be efficiently solved. An adaptive differential evolution algorithm is proposed by using generalized opposition-based learning (GOBL-ACDE), in which the generalized opposition-based learning is used to generate initial population and executes the generation jumping. And the adaptive trade-off model is utilized to handle the constraints as the improved adaptive ranking mutation operator is adopted to generate new population. The experimental results show that the algorithm has better performance in accuracy and convergence speed comparing with CDE, DDE, A-DDE and. And the effect of the generalized opposition-based learning and improved adaptive ranking mutation operator of the GOBL-ACDE have been analyzed and evaluated as well.

Optimization of the Prismatic Core Sandwich Panel under Buckling Load and Yield Stress Constraints using an Improved Constrained Differential Evolution Algorithm

In this study, weight optimization of the prismatic core sandwich panel under transverse and longitudinal loadings has been independently investigated. To solve the optimization problems corresponding to the mentioned loadings, a new Improved Constrained Differential Evolution (ICDE) algorithm based on the multi-objective constraint handling method is implemented. The constraints of the problems are buckling load and yield stress. By comparing the results of the ICDE with those obtained by the other evolutionary algorithms based on the penalty function method in the previous studies, it is discerned that the results of the transverse loading obtained in this study are equal to those of the previous works, but the results of the ICDE in the longitudinal loading are better.

An improved constrained differential evolution for optimal design of steel frames with discrete variables

New metaheuristic algorithms have been shown to be robust and effective for engineering optimization problems. Differential Evolution (DE), which is one of the most famous optimization approaches developed for optimal design problems with continuous design variables, is, in fact, inappropriate for constrained problems containing discrete design variables. In this article, an improved constrained differential evolution (iCDE) algorithm is proposed for optimization of steel frames with discrete design variables, followed by comprehensive testing of iCDE to validate the results. In order to make iCDE more efficient, two novel mutation approaches are proposed and tested. Three benchmark structural optimization problems are evaluated by the algorithm and compared against those reported in the literature obtained by GA, ACO, IACO, ICA, HS, and SBO. The total weight of the frame is considered as the objective function and the cross sections of the elements are taken as design variables. Constraints are based on the stress and displacement requirements conforming to the AISC-LRFD specifications. Moreover, to demonstrate the robustness of the algorithm, eight benchmark test functions of CEC-2017 are evaluated. The results show that the iCDE algorithm is computationally efficient and robust enough to find the global optima.

Individual-dependent feasibility rule for constrained differential evolution

Benefiting from its efficiency and quick convergence, the feasibility rule (FR) is well-known for its ability to solve constrained optimization problems (COPs). However, it is highly criticized for its heavy preference for constraints. Thus, an individual-dependent feasibility rule (IDFR) was designed by alleviating the preference from two aspects. Some information of constraints, which might be nonsignificant, is depressed. By contrast, some promising information of objective function is leveraged. The extent of information is individual-dependent. To further enhance the diversity, a two-phase diversity strategy was developed. Due to their numerous merits, two differential evolution (DE) operators were selected as components of the search algorithm. By the above process, we proposed a constrained DE (i.e., IDFRDE). To the best of our knowledge, we made the first attempt to improve FR from the individual perspective. IDFR is more robust than FR while keeping the same computational time complexity. However, it would converge slower than FR on some easy COPs. Experiments on three widely used benchmarks show that: 1) IDFRDE outperforms or gets similar results comparing with other known algorithms; 2) IDFR is more effective than FR on complex COPs; 3) both, the search algorithm and the diversity strategy are important to IDFRDE.

Joint cooperative spectrum sensing and primary user emulation attack detection in cognitive radio networks using fuzzy conditional entropy maximization

AbstractCooperative spectrum sensing (CSS) in cognitive radio system shows improved performance on spectrum sensing but, at the same time, faces a common threat called primary user emulation attack (PUEA) that impersonates the primary user (PU). This work explores joint PU and PUEA detection on CSS as a multiclass hypothesis using fuzzy conditional entropy maximization. To meet the goal, a multithreshold approach is suggested using a constrained differential evolution algorithm search to determine an optimal set of fuzzy function parameters, which maximizes the conditional entropy on the energy values. The proposed work also investigates the performance of CSS in presence of a group of malicious users (as PUEA), which generates signals and directly sends the same to the fusion center. Numerical results through simulation illustrate the efficacy of the proposed scheme in terms of both reliable PU detection in presence or absence of PUEA/malicious user and separate detection of falsifying PU and energy consumption in CSS. Simulation results show that the proposed scheme offers ∼17.54% and ∼39.39% higher detection probability of PU over the existing works in presence of PUEA.

Structural Reliability Assessment Based on the Improved Constrained Differential Evolution Algorithm

In this work, the reliability analysis is employed to take into account the uncertainties in a structure. Reliability analysis is a tool to compute the probability of failure corresponding to a given failure mode. In this study, one of the most commonly used reliability analysis method namely first order reliability method is used to calculate the probability of failure. Since finding the most probable point (MPP) or design point is a constrained optimization problem, in contrast to all the previous studies based on the penalty function method or the preference of the feasible solutions technique, in this study one of the latest versions of the differential evolution metaheuristic algorithm named improved (μ+λ)-constrained differential evolution (ICDE) based on the multi-objective constraint-handling technique is utilized. The ICDE is very easy to implement because there is no need to the time-consuming task of fine tuning of the penalty parameters. Several test problems are used to verify the accuracy and efficiency of the ICDE. The statistical comparisons revealed that the performance of ICDE is better than or comparable with the other considered methods. Also, it shows acceptable convergence rate in the process of finding the design point. According to the results and easier implementation of ICDE, it can be expected that the proposed method would become a robust alternative to the penalty function based methods for the reliability assessment problems in the future works.

Optimal trajectory planning of free-floating space manipulator using differential evolution algorithm

The existence of the path dependent dynamic singularities limits the volume of available workspace of free-floating space robot and induces enormous joint velocities when such singularities are met. In order to overcome this demerit, this paper presents an optimal joint trajectory planning method using forward kinematics equations of free-floating space robot, while joint motion laws are delineated with application of the concept of reaction null-space. Bézier curve, in conjunction with the null-space column vectors, are applied to describe the joint trajectories. Considering the forward kinematics equations of the free-floating space robot, the trajectory planning issue is consequently transferred to an optimization issue while the control points to construct the Bézier curve are the design variables. A constrained differential evolution (DE) scheme with premature handling strategy is implemented to find the optimal solution of the design variables while specific objectives and imposed constraints are satisfied. Differ from traditional methods, we synthesize null-space and specialized curve to provide a novel viewpoint for trajectory planning of free-floating space robot. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a free-floating spacecraft and demonstrate the feasibility and effectiveness of the proposed method.

An incorporated constrained differential evolution algorithm and its application on parameter identification of machine joint surfaces

An incorporated constrained differential evolution algorithm and its application on parameter identification of machine joint surfaces

An incorporated constrained differential evolution algorithm and its application on parameter identification of machine joint surfaces

In this paper, an incorporated constrained differential evolution algorithm based on Invasive Weed Optimisation (IWCDE) had been proposed. The IWCDE algorithm is based on the standard differential evolution algorithm and incorporates the Invasive Weed Optimisation Algorithm. The IWCDE algorithm proposed the new mutation strategy and the strategy of 'Infeasible individual evolution'. The proposed algorithm was compared with several other evolutionary algorithms, the results showed that the proposed algorithm could overcome the premature convergence efficiently and had better global convergence and robustness. Finally, the paper established the optimisation model of parameter identification on machine joint surfaces, solved the problem by the IWCDE algorithm.