Non-dominated Sorting Differential Evolution Research Articles

Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake

The effective distribution of critical relief in post disaster plays a crucial role in post-earthquake rescue operations. The location of distribution centers and vehicle routing in the available transportation network are two of the most challenging issues in emergency logistics. This paper constructs a nonlinear integer open location-routing model for relief distribution problem considering travel time, the total cost, and reliability with split delivery. It proposes the non-dominated sorting genetic algorithm and non-dominated sorting differential evolution algorithm to solve the proposed model. A case study on the Great Sichuan Earthquake in China expounds the application of the proposed models and algorithms in practice.

Parameter estimation of a pressure swing adsorption model for air separation using multi-objective optimisation and support vector regression model

In order to successfully estimate parameters of a numerical model, multiple criteria should be considered. Multi-objective Differential Evolution (MODE) and Multi-objective Genetic Algorithm (MOGA) have proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of two population based search algorithms (Nondominated Sorting Differential Evolution (NSDE) and Nondominated Sorting Genetic Algorithm (NGAII)) when applied to parameter estimation of a pressure swing adsorption (PSA) model. Full PSA mode is a complicated dynamic processing involving all transfer phenomena (mass, heat and momentum transfer) and has proven to be successful in a wide of applications. The limitation of using full PSA models is their expensive computational requirement. The parameter estimation analysis usually needs to run the numerical model and evaluate the performance thousands of times. However, in real world applications, there is simply not enough time and resources to perform such a huge number of model runs. In this study, a computational framework, known as v-support vector regression (v-SVR) PSA model, is presented for solving computationally expensive simulation problems. Formulation of an automatic parameter estimation strategy for the PSA model is outline. The simulations show that the NSDE is able to find better spread of solutions and better convergence near the true Pareto-optimal front compared to NSGAII-one elitist MOGA that pays special attention to creating a diverse Pareto-optimal front.

Automatic calibration of a rapid flood spreading model using multiobjective optimisations

In order to successfully calibrate a numerical model, multiple criteria should be considered. Multi-objective differential evolution (MODE) and multi-objective particle swarm optimisation (MOPSO) have proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of two population based search algorithms [nondominated sorting particle swarm optimisation (NSPSO), and nondominated sorting differential evolution (NSDE)] when applied to calibration of a rapid flood spreading model (RFSM). Formulation of an automatic calibration strategy for the RFSM is outline. The simulations show that the both methods possess the ability to find the optimal Pareto front.

Limitation of Small-world Topology for Application in Non-dominated Sorting Differential Evolution

In the context of complex network theory, the small-world network is famous for the small-world phenomenon, namely six degrees of separation. Different from its wide application in the social, physical and technological network analysis, it can be combined with the mathematical optimization algorithm recently. In this paper, the limitation of small-world network topology for application in multi-objective optimization algorithm is proposed. The optimization algorithm based on small-world network topology may be suitable for solving a few single-objective optimization problems, but has limitation and unobvious effectiveness to deal with many multi-objective optimization problems. This paper takes non-dominated sorting differential evolution algorithm (NSDE) based on small-world topology to solve eight multi-objective optimization problems (MOPs) for example. Compared with early NSDE algorithm, the limitation of the efficiency of small-world topology in NSDE is validated with the Matlab simulation results of eight MOEA test functions of early 2007. The results prove that small-world topology has limitation and unobvious effectiveness to improve a multi-objective optimization algorithm, not as good as to improve a single-objective optimization algorithm.

Limitation of Small-world Topology for Application in Non-dominated Sorting Differential Evolution

In the context of complex network theory, the small-world network is famous for the small-world phenomenon, namely six degrees of separation. Different from its wide application in the social, physical and technological network analysis, it can be combined with the mathematical optimization algorithm recently. In this paper, the limitation of small-world network topology for application in multi-objective optimization algorithm is proposed. The optimization algorithm based on small-world network topology may be suitable for solving a few single-objective optimization problems, but has limitation and unobvious effectiveness to deal with many multi-objective optimization problems. This paper takes non-dominated sorting differential evolution algorithm (NSDE) based on small-world topology to solve eight multi-objective optimization problems (MOPs) for example. Compared with early NSDE algorithm, the limitation of the efficiency of small-world topology in NSDE is validated with the Matlab simulation results of eight MOEA test functions of early 2007. The results prove that small-world topology has limitation and unobvious effectiveness to improve a multi-objective optimization algorithm, not as good as to improve a single-objective optimization algorithm.

Optimum culture medium composition for rhamnolipid production by pseudomonas aeruginosa AT10 using a novel multi‐objective optimization method

AbstractBACKGROUND: Rhamnolipid is a biosurfactant that finds wide applications in pharmaceuticals and beauty products. Pseudomonas aeruginosa is a producer of rhamnolipids, and the process can be implemented under laboratory‐scale conditions. Rhamnolipid concentration depends on medium composition namely, carbon source concentration, nitrogen source concentration, phosphate content and iron content. In this work, existing data7 were used to develop an artificial neural network‐based response surface model (ANN RSM) for rhamnolipid production by pseudomonas aeruginosa AT10. This ANN RSM model is integrated with non‐dominated sorting differential evolution (DE) to identify the optimum medium composition for this process.RESULTS: Different strategies for optimization of culture medium composition for this process were evaluated, and the best determined to be an ANN model combined with DE involving a combination of Naïve and Slow and ε‐constrained techniques. The optimal culture medium is determined to have carbon source concentration of 49.86 g dm−3, nitrogen source concentration of 4.99 g dm−3, phosphate content of 1.42 g dm−3, and iron content of 17.12 g dm−3. The maximum rhamnolipid activity was found to be 18.07 g dm−3, which compares favorably with that previously reported (18.66 g dm−3), and is in fact closer to the experimentally determined value of 16.50 g dm−3.CONCLUSION: This method has distinct advantages over methods using statistical regression models, and can be used for optimization of other multi‐objective biosurfactant production processes. © 2012 Society of Chemical Industry

Multi-objective biogeography based optimization for optimal PMU placement

The paper proposes a multi-objective biogeography based optimization (MO-BBO) algorithm to design optimal placement of phasor measurement units (PMU) which makes the power system network completely observable. The simultaneous optimization of the two conflicting objectives such as minimization of the number of PMUs and maximization of measurement redundancy are performed. The Pareto optimal solution is obtained using the non-dominated sorting and crowding distance. The compromised solution is chosen using a fuzzy based mechanism from the Pareto optimal solution. Simulation results are compared with Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Non-dominated Sorting Differential Evolution (NSDE). Developed PMU placement method is illustrated using IEEE standard systems to demonstrate the effectiveness of the proposed algorithm.

Memetic Elitist Pareto Differential Evolution algorithm based Radial Basis Function Networks for classification problems

This paper presents a new multi-objective evolutionary hybrid algorithm for the design of Radial Basis Function Networks (RBFNs) for classification problems. The algorithm, MEPDEN, Memetic Elitist Pareto evolutionary approach based on the Non-dominated Sorting Differential Evolution (NSDE) multi-objective evolutionary algorithm which has been adapted to design RBFNs, where the NSDE algorithm is augmented with a local search that uses the Back-propagation algorithm. The MEPDEN is tested on two-class and multiclass pattern classification problems. The results obtained in terms of Mean Square Error (MSE), number of hidden nodes, accuracy (ACC), sensitivity (SEN), specificity (SPE) and Area Under the receiver operating characteristics Curve (AUC), show that the proposed approach is able to produce higher prediction accuracies with much simpler network structures. The accuracy and complexity of the network obtained by the proposed algorithm are compared with Memetic Eilitist Pareto Non-dominated Sorting Genetic Algorithm based RBFN (MEPGAN) through statistical tests. This study showed that MEPDEN obtains RBFNs with an appropriate balance between accuracy and simplicity, outperforming the other method considered.

Sensitivity analysis and automatic calibration of a rainfall–runoff model using multi-objectives

The development of numerical model parameter sensitivity analysis (SA) has focused mainly on the selection of a single-objective measure of the distance between the model-simulated output and the data. However, practical experience with sensitivity analysis suggests that no single objective function is adequate to measure the ways in which the model fails to match the important characteristics of the observed data. In order to successfully measure parameter sensitivity of a numerical model, multiple criteria should be considered. Sensitivity analysis of a rainfall–runoff model is performed using the local sensitivity method (Morris method) and multi- objective analysis. Formulation of SA strategy for the MIKE/NAM rainfall–runoff model is outline. The SA scheme includes multiple objectives that measure different aspects of the hydrograph: (1) overall influence, and (2) parameter interaction. The SA is given as a set of Pareto ranks from a multi-objective viewpoint. In order to successfully calibrate the numerical model, multiple criteria should be considered. Multi-objective Differential Evolution (MODE) has proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of the population-based search algorithm (Non-dominated Sorting Differential Evolution (NSDE)) when applied to the rainfall–runoff model. The method has been applied for calibration of a test catchment and compared on validation data. The simulations show that the NSDE method possesses the ability to finding the optimal Pareto front and keeping a good diversity in the obtained front for the model calibration.

Multi-objective optimal PMU placement using a non-dominated sorting differential evolution algorithm

Phasor measurement unit plays a great role in wide-area measurement system (WAMS) in power system. Based on analysis of observability of each bus while one of PMUs fails and under the precondition of full network observability, this paper presents a multi-objective optimal model of PMU placement with the objectives of minimization of the number of PMU and maximization of the N − 1 measurement reliability. A new NSDE algorithm, which is an organic integration of Pareto non-dominated sorting operation and differential evolution algorithm, is designed for the model. It improved individual crowding mechanism and mutation strategy effectively. Illustrative results on the 14- and 39-bus IEEE systems are presented to show the superiorities of this algorithm.

Differential EvolutionによるSAWフィルタの多目的最適設計

The structural design of Surface Acoustic Wave (SAW) filters is formulated as a constrained multi-objective optimization problem. Then three Evolutionary Multi-criterion Optimization (EMO) algorithms based on Differential Evolution (DE), namely, Multi-Objective DE (MODE), Non-dominated Sorting DE (NSDE), and Generalized DE 3 (GDE3), are applied to the three- and two-objective optimization problems of a balanced SAW filter. In order to compare the performances of the above EMO algorithms, several criteria including hypervolume are evaluated. As a result, it is shown that the performance of the EMO algorithm depends on the number of objective functions. Besides, in order to clarify the tradeoff relationship among the objective functions of the three-objective optimization problem, Principal Component Analysis (PCA) is employed.

Non-uniform rational B-spline-based minimum cost trajectory planning for autonomous robots

This paper proposes a new novel trajectory planning method by using two evolutionary algorithms namely Elitist non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE) for an autonomous robot manipulator (STANFORD robot) whose workspace includes several obstacles. The aim of the problem is to minimise a multicriterion cost function with actuator constraints, joint limits and obstacle avoidance constraints by considering dynamic equations of motion. Trajectories are defined by non uniform rational B-spline (NURBS) functions. This is a nonlinear constrained optimisation problem with 6 objective functions, 32 constraints and 288 variables. The multicriterion cost function is a weighted balance of transfer time, mechanical energy of the actuators, singularity avoidance, penalty function to guarantee the collision free motion, joint jerks and joint accelerations. All types of obstacles (fixed, moving and oscillating obstacles) are present in the workspace of the robot. The results obtained from NSGA-II and DE are compared and analysed.