Proposed Differential Evolution Algorithm Research Articles

DE3D-NURBS: A differential evolution-based 3D path-planner integrating kinematic constraints and obstacle avoidance

This work presents a novel path planner, DE3D-NURBS, for 3D path planning considering the maximum and minimum climb/dive angle and the maximum curvature imposed by a robot, such as an autonomous fixed-wing aircraft. To deal with this constrained problem, we propose a Differential Evolution (DE) based algorithm, assuming the partitioning of feasible and infeasible individuals and a novel mutation operator. This solution can provide a short differentiable smooth path, directly parameterized by a kth-order Non-Uniform Rational B-Spline (NURBS) curve, a generalization of B-spline curves. This representation provides more flexibility to satisfy essential kinematic constraints and to take into account obstacles and topography. This path can guide an Unmanned Aerial Vehicle (UAV) through a set of desired robot configurations (position and orientation) in 3D space. The simulation results provide a more comprehensive insight into the capabilities of the proposed planner to generate feasible paths, considering simple scenarios in a free obstacle environment and also complex scenarios. Such scenarios include topographic environments, narrow passages such as a tunnel, and a solution for closed-loop missions in a modular approach. We also provide a comparative benchmark with other nature-inspired algorithms. These results serve as a baseline for evaluating the effectiveness of the proposed DE algorithm in complex and challenging case studies.

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

The Differential Evolution (DE) algorithm is a powerful and simple optimizer for solving various optimization problems. Based on the literature, DE has shown suitable performance in exploring search spaces and locating global optimums. However, it is typically slow in extracting the problem solution. In this paper, the exploration ability of the DE algorithm is augmented with a competitive control parameter ω based on the value of the objective function of the mutating members. A new mutation strategy is introduced, subtracting weaker members from superior weaker ones. The proposed DE algorithm, which is referred to as the self-competitive DE, has been employed for solving real-world optimization problems. Several DE algorithms are enhanced with the proposed parameter ω, and the efficiencies of the resulting enhanced algorithms are tested. Furthermore, the optimal Proportional–Integral–Derivative (PID) controller tuning for an Automatic Voltage Regulator (AVR) system is used to investigate the effectiveness of the proposed strategy in solving real-world optimization problems. Simulation results demonstrate a good performance of the proposed parameter ω over several other well-known DE algorithms.

Protein–ligand docking using differential evolution with an adaptive mechanism

The protein–ligand docking problem plays a crucial role in the drug discovery process and remains challenging in bioinformatics. A successful protein–ligand docking approach depends on two key factors: an efficient search strategy and an effective scoring function. In this study, we attempt to use an adaptive differential evolution (DE) algorithm as the search strategy. The search ability of the proposed DE algorithm is improved by incorporating a parameter adaptation scheme and a modified mutation strategy. In addition, the scoring function of the classical AutoDock Vina suite is employed as the fitness function of the proposed approach. Finally, the performance of the adaptive DE method in solving the protein–ligand docking problem is evaluated on 40 test docking instances. The experimental results and statistical analysis demonstrate the effectiveness of the proposed adaptive DE algorithm compared with five other classical evolutionary algorithms. The results of this study reveal that employing powerful evolutionary algorithms, such as adaptive DE, contributes to solving the protein–ligand docking problem.

Differential Evolution in Robust Optimization Over Time Using a Survival Time Approach

This study presents an empirical comparison of the standard differential evolution (DE) against three random sampling methods to solve robust optimization over time problems with a survival time approach to analyze its viability and performance capacity of solving problems in dynamic environments. A set of instances with four different dynamics, generated by two different configurations of two well-known benchmarks, are solved. This work also introduces a comparison criterion that allows the algorithm to discriminate among solutions with similar survival times to benefit the selection process. The results show that the standard DE holds a good performance to find ROOT solutions, improving the results reported by state-of-the-art approaches in the studied environments. Finally, it was found that the chaotic dynamic, disregarding the type of peak movement in the search space, is a source of difficulty for the proposed DE algorithm.

Optimisation of cost efficient robotic assembly line using metaheuristic algorithms

Robotic assembly lines (RALs) are utilised due to the flexibility it provides to the overall production system. Industries mainly focus on reducing the operation costs involved. From the literature survey it can be seen that only few research has been reported in the area of cost related optimisation in RALs. This paper focuses on proposing a new model in RALs with the main objective of maximising line efficiency by minimising total assembly line cost. The proposed model can be used production managers to balance a RAL in an efficient manner. Since simple assembly line balancing problem is classified as NP-hard, proposed problem due to additional constraints also falls under the same category. Particle swarm optimisation (PSO) and differential evolution (DE) are applied as the optimisation tool to solve this problem. The performances of this proposed algorithm are tested on a set of reported benchmark problems. From the comparative study, it is found that the proposed DE algorithm obtain better solutions for the majority of the problems tested. [Received: 2 July 2018; Revised: 16 December 2018; Revised: 8 May 2019; Accepted: 2 August 2019]

An adaptive differential evolution algorithm to optimal multi-level thresholding for MRI brain image segmentation

Segmentation is an important method for MRI medical image analysis as it can provide the radiologists with noninvasive information about a patient that is crucial to the diagnostic process. The efficiency of such a computer-aided diagnosis system relies on the accuracy of an adopted image segmentation method. Multi-level thresholding is a segmentation method that has been widely adopted in medical image analysis in recent studies, where selecting the optimal thresholds has a pivotal role in determining the efficiency and the accuracy of the segmentation algorithm. While some well-known methods, such as Kapur’s and Otsu’s, are proven effective for bi-level thresholding, multi-level thresholding remains a challenge as it is computationally expensive. Evolutionary algorithms, such as Differential Evolution (DE), have the potential to address this problem, as they can find sufficiently good solutions with manageable computational effort. While a number of DE solutions have been proposed for multi-level thresholding, they are not stable, in that, when the number of thresholds increases, the algorithm efficiency decreases due to the imbalance between exploration and exploitation. In this paper, we propose a DE solution that achieves a good balance between exploration and exploitation through a new adaptive approach and new mutation strategies. The new adaptive approach can generate optimal solutions in assigning populations by measuring the quality of candidate solutions to evaluate the efficiency of different parts of the proposed DE algorithm. The new mutation methods harness Mantegna Lévy and Cauchy distributions, as well as Cotes’ Spiral to improve global search, and to further balance between exploitation and exploration. We further experimentally compare the proposed DE algorithm, referred to as Adaptive Differential Evolution with Lévy Distribution (ALDE), against three DE benchmark algorithms on T2 weighted MRI brain images. Our results show that ALDE can, not only obtain optimal thresholds at a reasonable computational cost, but more importantly, clearly outperforms the benchmark algorithms.

U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm

The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within a fixed given cycle time), where the aim is to minimize the number of workstations. After establishing the method, the results from previous research studies were compared with the results from this study. For the UALBP, two groups of benchmark problems were used for the experiments: (1) For the medium-sized UALBP (21–45 tasks), it was found that the DE algorithm DE/best/2 to Exponential Crossover 1 produced better solutions when compared to the other metaheuristic methods: it could generate 25 optimal solutions from a total of 25 instances, and the average time used for the calculation was 0.10 seconds/instance; (2) for the large-scale UALBP (75–297 tasks), it was found that the basic DE algorithm and improved differential evolution algorithm generated better solutions, and DE/best/2 to Exponential Crossover 1 generated the optimal solutions and achieved the minimum solution search time when compared to the other metaheuristic methods: it could generate 36 optimal solutions from a total of 62 instances, and the average time used for the calculation was 4.88 seconds/instance. From the comparison of the DE algorithms, it was found that the improved differential evolution algorithm generated optimal solutions with a better solution search time than the search time of the basic differential evolution algorithm. The basic and improved DE algorithm are the effective methods for balancing UALBP-1 when compared to the other metaheuristic methods.

An implementation of differential evolution algorithm for a single product and single period multi-echelon supply chain network model

In this paper, five variants of Differential Evolution (DE) algorithms are proposed to solve the multi-echelon supply chain network optimization problem. Supply chain network composed of different stages which involves products, services and information flow between suppliers and customers, is a value-added chain that provides customers products with the quickest delivery and the most competitive price. Hence, there is a need to optimize the supply chain by finding the optimum configuration of the network in order to get a good compromise between several objectives. The supply chain problem utilized in this study is taken from literature which incorporates demand, capacity, raw-material availability, and sequencing constraints in order to maximize total profitability. The performance of DE variants has been investigated by solving three stage multi-echelon supply chain network optimization problems for twenty demand scenarios with each supply chain settings. The objective is to find the optimal alignment of procurement, production, and distribution while aiming towards maximizing profit. The results show that the proposed DE algorithm is able to achieve better performance on a set of supply chain problem with different scenarios those obtained by well-known classical GA and PSO.

Differential Evolution algorithm for contingency analysis-based optimal location of FACTS controllers in deregulated electricity market

In this paper, a novel heuristic optimization algorithm called differential evolution (DE) technique has been proposed to solve the optimal location of FACTS devices in deregulated electricity market using contingency analysis. The proposed approach deals with the optimal injection of real and reactive power using FACTS devices with an aim to minimize the total system cost, the total number of overloads, excess power flow, the severity of overload and real power loss of the network. To enhance the search behavior of the DE approach, the scaling factor and crossover parameters are empirically selected. To show the superiority of the proposed DE approach and as a step ahead to prove its novelty, the same optimization problem is solved using evolutionary programming method, and the results are compared. The results indicate the proposed DE algorithm is superior in terms of final solution quality, efficiency, convergence rate and robustness. A sample four-bus system and 24-bus EHV southern region of Indian grid system has been considered to illustrate the proposed methodology.

A new differential evolution algorithm for solving multimodal optimization problems with high dimensionality

Differential evolution (DE) is an efficient intelligent optimization algorithm which has been widely applied to real-world problems, however poor in solution quality and convergence performance for complex multimodal optimization problems. To tackle this problem, a new improving strategy for DE algorithm is presented, in which crossover operator, mutation operator and a new local variables adjustment strategy are integrated together to make the DE more efficient and effective. An improved dynamic crossover rate is adopted to manage the three operators, so to decrease the computational cost of DE. To investigate the performance of the proposed DE algorithm, some frequently referred mutation operators, i.e., DE/rand/1, DE/Best/1, DE/current-to-best/1, DE/Best/2, DE/rand/2, are employed, respectively, in proposed method for comparing with standard DE algorithm which also uses the same mutation operators as our method. Three state-of-the-art evolutionary algorithms (SaDE, CoDE and CMAES) and seven large-scale optimization algorithms on seven high-dimensional optimization problems of CEC2008 are compared with the proposed algorithm. We employ Wilcoxon Signed-Rank Test to further test the difference significance of performance between our algorithm and other compared algorithms. Experimental results demonstrate that the proposed algorithm is more effective in solution quality but with less CPU time (e.g., when dimensionality equals 1000, its mean optimal fitness is less than \(1\hbox {e}{-}9\) and the CPU time reduces by about 19.3% for function Schwefel 2.26), even with a very small population size, no matter which mutation operator is adopted.

An Improved Differential Evolution Algorithm and Its Application to Large-Scale Artificial Neural Networks

A new differential evolution (DE) algorithm is presented in this paper. The proposed algorithm monitors the evolutionary progress of each individual and assigns appropriate control parameters depends on whether the individual is successfully evolved or not. We conducted the performance evaluation on CEC 2014 benchmark problems and confirmed that the proposed algorithm outperformed than the conventional DE algorithm. In addition, we apply the proposed DE algorithm as an optimization technique of training large scale multilayer perceptron. We conducted the performance evaluation on an artificial neural network that has approximately 1,000 weights and confirmed again that the proposed algorithm performed better than the conventional DE algorithm. As a result, we proposed a new DE algorithm that has better optimization performance for solving large-scale global optimization problems.

Engineering optimization by constrained differential evolution with nearest neighbor comparison

It has been proposed to utilize nearest neighbor comparison to reduce the number of function evaluations in unconstrained optimization. The nearest neighbor comparison omits the function evaluation of a point when the comparison can be judged by its nearest point in the search population. In this paper, a constrained differential evolution (DE) algorithm is proposed by combining the ε constrained method to handle constraints with the nearest neighbor comparison method. The algorithm is tested using five benchmark engineering design problems and the results indicate that the proposed DE algorithm is able to find good results in a much smaller number of objective function evaluations than conventional DE and it is competitive to other state-of-the-art DE variants.

Constraint Consensus Mutation-Based Differential Evolution for Constrained Optimization

Until now, numerous mutation strategies have been introduced as search operators within the differential evolution (DE) algorithm. These operators are designed mainly to improve fitness value while also maintaining diversity in the population, but they do not directly act to reduce constraint violations of constrained problems. Interestingly, the so-called constraint handling techniques, used with most evolutionary algorithms, are not a part of the actual search process. Instead, the constraint violations are only considered in the ranking and selection of individuals for participation in the search process. This paper introduces a new DE mutation operator that incorporates a mechanism, based on constraint consensus, that can directly help to reduce the constraint violations during the evolutionary search process. The proposed DE algorithm has been tested on a set of well-known constrained benchmark problems. The experimental results show that the proposed algorithm is able to obtain better solutions, compared to the standard DE algorithm, with significantly reduced computational effort. The algorithm also outperforms state-of-the-art algorithms.

Differential Evolution for Urban Transit Routing Problem

The urban transit routing problem (UTRP) involves the construction of route sets on existing road networks to cater for the transit demand efficiently. This is an NP-hard problem, where the generation of candidate route sets can lead to a number of potential routes being discarded on the grounds of infeasibility. This paper presents a new repair mechanism to complement the existing terminal repair and the make-small-change operators in dealing with the infeasibility of the candidate route set. When solving the UTRP, the general aim is to determine a set of transit route networks that achieves a minimum total cost for both the passenger and the operator. With this in mind, we propose a differential evolution (DE) algorithm for solving the UTRP with a specific objective of minimizing the average travel time of all served passengers. Computational experiments are performed on the basis of benchmark Mandl’s Swiss network. Computational results from the proposed repair mechanism are comparable with the existing repair mechanisms. Furthermore, the combined repair mechanisms of all three operators produced very promising results. In addition, the proposed DE algorithm outperformed most of the published results in the literature.

Differential Evolution with Population and Strategy Parameter Adaptation

Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality.

A PAPR Reduction Method Based on Differential Evolution

High peak-to-average ratio power (PAPR) is a critical practical problem for an OFDM system. Many techniques, such as clipping and filtering (ICF), cognitive clipping, have been proposed to deal with the issue. However, it needs to determine the relationship between error vector magnitude (EVM) and clipping ratio (CR). In this paper, we formulate a universal PAPR optimization model with EVM constraint, and propose a differential evolution (DE) algorithm with a time complexity of 2 ( log ) O N N . The optimization parameter of the new approach is clipping noise. The EVM constraint guarantees proper receiver operation that is specified by most modern communication standards. The proposed DE algorithm employs the noise vector as the population. It adjusts three crucial control parameters to minimize cost function which is the amount of PAPR reduction. Simulation results show that our proposed method can offer good performance in PAPR and bit error rate (BER).

On the Parameter Determination of a Stress Relaxation Model Based on Creep Equations Using Differential Evolution Algorithm

A robust and efficient parameter identification method of the stress relaxation model based on Altenbach-Gorash-Naumenko creep equations is discussed. The differential evolution (DE) algorithm with a modified forward-Euler scheme is used in the identification procedure. Besides its good convergence properties and suitability for parallelization, initial guesses close to the solutions are not required for the DE algorithm. The parameter determination problem of the stress relaxation model is based on a very broad range specified for each parameter. The performance of the proposed DE algorithm is compared with a step-by-step model parameter determination technology and the genetic algorithm (GA). The model parameters of 12Cr-1Mo-1W-1/4V stainless steel bolting material at 550°C have been determined, and the creep and stress relaxation behaviors have been calculated. Results indicate that the optimum solutions can be obtained more easily by DE algorithm than others.

Ensemble of differential evolution algorithms for electromagnetic target recognition problem

In this study, an ensemble of differential evolution (DE) algorithms is presented to classify electromagnetic targets in resonance scattering region. The algorithm aims to synthesize a special incident signal for each target, which is defined as the main discrimination feature in the given target recognition method. In the proposed algorithm, the amplitudes of basis functions and the duration of this incident signal are optimised to give minimum late-time scattered signal's energy, which is the main fitness function of the algorithm. The proposed DE algorithm is applied to a target set consisting of lossless dielectric spheres and correct recognition rates for both noiseless and noisy signals are obtained. The results for both developed DE algorithm and other DE variants of traditional DE, adaptive differential evolution with optional external archive (JADE), jDE are also given to compare the algorithms and show the effectiveness of the proposed one.

Transceiver Design for Distributed STBC Based AF Cooperative Networks in the Presence of Timing and Frequency Offsets

In multi-relay cooperative systems, the signal at the destination is affected by impairments such as multiple channel gains, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs). In this paper we account for all these impairments and propose a new transceiver structure at the relays and a novel receiver design at the destination in distributed space-time block code (DSTBC) based amplify-and-forward (AF) cooperative networks. The Cramer-Rao lower bounds and a least squares (LS) estimator for the multi-parameter estimation problem are derived. In order to significantly reduce the receiver complexity at the destination, a differential evolution (DE) based estimation algorithm is applied and the initialization and constraints for the convergence of the proposed DE algorithm are investigated. In order to detect the signal from multiple relays in the presence of unknown channels, MTOs, and MCFOs, novel optimal and sub-optimal minimum mean-square error receiver designs at the destination node are proposed. Simulation results show that the proposed estimation and compensation methods achieve full diversity gain in the presence of channel and synchronization impairments in multi-relay AF cooperative networks.

Differential evolution algorithm for multi-commodity and multi-level of service hub covering location problem

Article history: Received 10 August 2012 Received in revised format 14 September 2012 Accepted September 27 2012 Available online 28 September 2012 The hub location problem involves a network of origins and destinations over which transportation takes place. There are many studies associated with finding the location of hub nodes and the allocation of demand nodes to these located hub nodes to transfer the only one kind of commodity under one level of service. However, in this study, carrying different commodity types from origin to destination under various levels of services (e.g. price, punctuality, reliability or transit time) is studied. Quality of services experienced by users such as speed, convenience, comfort and security of transportation facilities and services is considered as the level of service. In each system, different kinds of commodities with various levels of services can be transmitted. The appropriate level of service that a commodity can be transmitted through is chosen by customer preferences and the specification of the commodity. So, a mixed integer programming formulation for single allocation hub covering location problem, which is based on the idea of transferring multi commodity flows under multi levels of service is presented. These two are applied concepts, multi-commodity and multi-level of service, which make the model's assumptions closer to the real world problems. In addition, a differential evolution algorithm is designed to find near-optimal solutions. The obtained solutions using differential evolution (DE) algorithm (upper bound), where its parameters are tuned by response surface methodology, are compared with exact solutions and computed lower bounds by linear relaxation technique to prove the efficiency of proposed DE algorithm. © 2012 Growing Science Ltd. All rights reserved