Multi-objective Differential Evolution Algorithm Research Articles

Economic and Emission Dispatch Using Ensemble Multi-Objective Differential Evolution Algorithm

In the past two decades, China’s manufacturing industry has achieved great success. However, pollution and environmental impacts have become more serious while this industry has grown. The economic and emission dispatch (EED) problem is a typical multi-objective optimization problem with conflicting fuel costs and pollution emission objectives. An ensemble multi-objective differential evolution (EMODE) is proposed to tackle the EED problem. First, the equality constraints of the problem have been transformed into inequality constraints. Next, two mutation strategies DE/rand/1 and DE/current-to-rand/1 have been implemented to improve the conventional DE. The performance of the proposed algorithm is evaluated on six test functions and the numerical results have indicated that the proposed algorithm is effective. The proposed algorithm EMODE is used to solve a series of six generators and eleven generators in the EED problem. The experimental results obtained are compared with those reported using single optimization algorithms and multi-objective evolutionary algorithms (MOEAs). The results have revealed that the proposed algorithm EMODE either matches or outperforms those algorithms. The proposed algorithm is an effective candidate to optimize the manufacturing industry of China.

Shapley value-based multi-objective data envelopment analysis application for assessing academic efficiency of university departments

This paper adopts a modified approach of data envelopment analysis (DEA) to measure the academic efficiency of university departments. In real-world case studies, conventional DEA models often identify too many decision-making units (DMUs) as efficient. This occurs when the number of DMUs under evaluation is not large enough compared to the total number of decision variables. To overcome this limitation and reduce the number of decision variables, multi-objective data envelopment analysis (MODEA) approach previously presented in the literature is applied. The MODEA approach applies Shapley value as a cooperative game to determine the appropriate weights and efficiency score of each category of inputs. To illustrate the performance of the adopted approach, a case study is conducted in a university in the Philippines. The input variables are academic staff, non-academic staff, classrooms, laboratories, research grants, and department expenditures, while the output variables are the number of graduates and publications. The results of the case study revealed that all DMUs are inefficient. DMUs with efficiency scores close to the ideal efficiency score may be emulated by other DMUs with least efficiency scores.

Selecting sustainable electric bus powertrains using multipreference evolutionary algorithms

ABSTRACTConstant improvement of vehicle technologies towards more efficient powertrains and reduced pollutant emissions, frequently leads to the increase of the vehicle or fuel costs, compromising its viability. Multi-objective optimization methods are commonly used to solve such problems, finding optimal trade-off solutions relatively conflicting objectives. Nevertheless, vehicle driving performance, is often disregarded from the optimization process or considered only as a fixed constraint. This may raise some issues, which are discussed in this paper: (a) vehicle dynamics are not improved, (b) trade-off optimal solutions are not distinguishable, (c) interesting solutions near constraints limits won´t be considered if constraints are not marginally relaxed.This paper proposes a method to optimize three electric-drive vehicle options for an urban bus, a battery electric (BEV), a fuel cell hybrid (FC-HEV) and a plug-in hybrid (FC-PHEV), aiming minimum carbon footprint, maximum financial indicator and simultaneously improved driving performance (speed, acceleration, and electric range). The carbon footprint is assessed by a life cycle (LC) approach, considering the impact of the fuel production and use, and vehicle embodied materials; while the financial assessment considers the vehicle and fuel costs. The spherical pruning multi-objective differential evolution algorithm (spMODE-II) is used in the optimization, considering different preference regions within the problem constraints and objectives. The vehicle solutions optimality and suitability are compared with other multi-objective algorithm, NSGA-II.The FC-HEV achieved the lowest LC emissions (547 g/km), and the FC-PHEV the maximum financial gain (0.19 $/km), while the BEV achieved the best trade-off of solutions.

Hardware implementation of multi-objective differential evolution algorithm: a case study of spectrum allocation in cognitive radio networks

In this paper, a hardware solution for multi-objective differential evolution (MODE) algorithm is presented. The proposed hardware is developed as a co-processor and interfaced with PowerPC440 processor of Virtex-5 field programmable gate array to accelerate execution speed on an embedded platform. It is validated by optimising four standard benchmark functions and its execution time is compared with the same algorithm running on a 32-bit PowerPC440 processor. Further, as a case study, the proposed hardware is used to solve Spectrum Allocation (SA) problem in Cognitive Radio Network (CRN). In CRN, the available licensed channels are assigned to cognitive users using SA task while satisfying the multiple objectives posed by licensed users. The MODE core is integrated with the SA objective functions and developed as a MODE-based SA (MODE-SA) co-processor on an embedded platform for distributed CRN. The MODE-SA core has attained a speedup of 50-60× compared to the PowerPC440 implementation.

Differential evolution for filter feature selection based on information theory and feature ranking

Feature selection is an essential step in various tasks, where filter feature selection algorithms are increasingly attractive due to their simplicity and fast speed. A common filter is to use mutual information to estimate the relationships between each feature and the class labels (mutual relevancy), and between each pair of features (mutual redundancy). This strategy has gained popularity resulting a variety of criteria based on mutual information. Other well-known strategies are to order each feature based on the nearest neighbor distance as in ReliefF, and based on the between-class variance and the within-class variance as in Fisher Score. However, each strategy comes with its own advantages and disadvantages. This paper proposes a new filter criterion inspired by the concepts of mutual information, ReliefF and Fisher Score. Instead of using mutual redundancy, the proposed criterion tries to choose the highest ranked features determined by ReliefF and Fisher Score while providing the mutual relevance between features and the class labels. Based on the proposed criterion, two new differential evolution (DE) based filter approaches are developed. While the former uses the proposed criterion as a single objective problem in a weighted manner, the latter considers the proposed criterion in a multi-objective design. Moreover, a well known mutual information feature selection approach (MIFS) based on maximum-relevance and minimum-redundancy is also adopted in single-objective and multi-objective DE algorithms for feature selection. The results show that the proposed criterion outperforms MIFS in both single objective and multi-objective DE frameworks. The results also indicate that considering feature selection as a multi-objective problem can generally provide better performance in terms of the feature subset size and the classification accuracy.

Optimal control for wastewater treatment process based on an adaptive multi-objective differential evolution algorithm

In this paper, for the operations of wastewater treatment processes (WWTPs), an intelligent multi-objective optimization control (IMOOC), based on an adaptive multi-objective differential evolution (AMODE) algorithm, is proposed to search for the suitable set-points to balance the treatment performance and the operational costs. In this IMOOC, the combination of an AMODE algorithm and the multi-objective critical issues helps us to fulfill all the control objectives simultaneously. To improve the optimization efficiency and achieve fast convergence, the AMODE algorithm is designed to improve the local search and the global exploration abilities: The adaptive adjustment strategies are developed to select the suitable scaling factor and crossover rate in the process of searching. Meanwhile, the multi-objective critical issues, according to the state of the processes, are given as a nonlinear multi-objective optimization problem to evaluate the operational performance of WWTPs. Therefore, once the nonlinear multi-objective optimization problem is solved at each sampling time, the most appropriate set of Pareto is selected as suitable set-points to achieve the process performance. To demonstrate the merits of our proposed method, the proposed IMOOC is applied to the Benchmark Simulation Model No. 1 of WWTPs. The results show that the proposed IMOOC effectively provides process control. The performance comparison with other algorithms also indicates that the proposed optimal strategy yields better effluent qualities and lower average operation consumption.

Exergoeconomic analysis and optimization of a solar based multigeneration system using multiobjective differential evolution algorithm

This paper presents and analyzes a multigeneration energy system that consists of a reverse osmosis desalination unit, water heater, organic Rankine cycle, photovoltaic solar collectors, and a single effect absorption chiller. In doing so, energy and exergy analysis are first performed to evaluate the performance of the system and determine the irreversibility of each component. Next, considering minimizing total cost rate and maximizing exergy efficiency as two objective functions, a multiobjective optimization approach based on differential evolution algorithm is proposed to determine the best design parameters. A self-adaptive technique is utilized to deal with the search capability, population diversity, and convergence speed of the proposed optimization algorithm. An external archive list is used to save all nondominated optimal solutions during the optimization. Dynamic crowding distance approach is employed to decrease archiving size without losing its characteristics. Furthermore, a fuzzy clustering approach is used to select the desired solution among the Pareto-optimal solutions. Simulation results are compared with two other multiobjective optimization algorithms and effectiveness of the proposed optimization method is verified using various indices. Finally, a sensitivity analysis is employed to evaluate effects of design parameters on exergy efficiency and total cost rate of the system.

A multi-objective simulation-based optimization approach for inventory replenishment problem with premium freights in convergent supply chains

In this study, a multi-objective simulation-based optimization approach is developed to solve inventory replenishment problem with premium freights in convergent supply chains. In this context, a decomposition-based multi-objective differential evolution algorithm (MODE/D) is used to determine demand forecast adjustment factor, safety stock and supplier flexibility parameters that minimize total holding cost, inbound and outbound premium freight ratios simultaneously. The proposed approach is applied a set of problem instances and the performance of the proposed approach is evaluated in comparison with the performance of non-dominated sorting genetic algorithm-II (NSGA-II). Furthermore, the proposed approach is applied to a multi-national automotive supply chain spread on Europe. The results reveal that the proposed approach is effective in solving inventory replenishment problem with premium freights in convergent supply chains.

Adaptive fuzzy neural network control of wastewater treatment process with multiobjective operation

Abstract This study investigates an adaptive fuzzy neural network control system for the multiobjective operation of wastewater treatment process (WWTP) with standard effluent quality (EQ) as well as low energy consumption (EC). The control system consists of an optimization module with the adaptive multiobjective differential evolution (AMODE) algorithm and a control module with the adaptive fuzzy neural network (AFNN). First, an AMODE algorithm, using the adaptive adjustment strategies for selecting the suitable scaling factor and crossover rate, is developed to optimize all objectives simultaneously. Then, the optimal set-points of the dissolved oxygen concentration in the fifth tank ( S O5 ) and the nitrogen nitrate concentration in the second anoxic tank ( S NO2 ) of WWTP can be obtained by the AMODE algorithm. Second, an AFNN controller, based on an adaptive second order algorithm, is employed to trace the set-points of S O5 and S NO2 for achieving the process performance. Finally, the proposed control system is applied on the Benchmark Simulation Model 1 (BSM1). The performance comparison with other algorithms indicates that the proposed control system yields better effluent qualities and lower average operation consumption.

Optimal Load Scheduling of Plug-In Hybrid Electric Vehicles via Weight-Aggregation Multi-Objective Evolutionary Algorithms

In order to protect the environment and slow down global warming trend, many governments and environmentalists are keen at promoting the use of plug-in hybrid electric vehicles (PHEVs). As a result, more and more PHEVs have been put into use. However, load peak caused by their disordered charging can be detrimental to an entire power grid. Several methods have been proposed to establish ordered PHEV charging. While focusing on single-objective load scheduling, they fail to meet the real requirements that need one to conduct multiple objective optimization. This paper formulates a multi-objective load scheduling problem to minimize two competing objectives: 1) potential serious peak-to-valley difference and 2) economic loss. When we apply existing multi-objective evolutionary algorithms (MOEAs), i.e., multi-objective particle swarm optimization (MOPSO), Nondominated Sorting Genetic Algorithm II, MOEA based on decomposition, and multi-objective differential evolutionary algorithm to solve it, because its high dimension and special conditions we find that they fail to reach the Pareto Front or converge into a relatively small area only. Therefore, we propose a weight aggregation (WA) strategy and implement a novel MOEA algorithm named WA-MOPSO by incorporating WA into MOPSO to solve the problem. Its effectiveness and efficiency to generate a Pareto front of this problem are verified and compared with those of the state-of-the-art approaches. Furthermore, WA is also combined with other MOEAs to solve the defined scheduling problem.

Elitism based Multi-Objective Differential Evolution for feature selection: A filter approach with an efficient redundancy measure

The real world data are complex in nature and addition to that a large number of features add more value to the complexity. However, the features associated with the data may be redundant and erroneous in nature. To deal with such type of features, feature selection plays a vital role in computational learning. The reduction in the dimensionality of the dataset not only reduces the computational time required for classification but also enhances the classification accuracy by removing the misleading features. This paper presents a Filter Approach using Elitism based Multi-objective Differential Evolution algorithm for feature selection (FAEMODE) and the novelty lies in the objective formulation, where both linear and nonlinear dependency among features have been considered to handle the redundant and unwanted features of a dataset. Finally, the selected feature subsets of 23 benchmark datasets are tested using 10-fold cross validation with four well-known classifiers to endorse the result. A comparative analysis of the proposed approach with seven filter approaches and two conventional as well as three metaheuristic based wrapper approaches have been carried out for validation. The result reveals that the proposed approach can be considered as a powerful filter method for feature selection in various fields.

Multi-Objective Differential Evolution for feature selection in Facial Expression Recognition systems

Feature selection using Multi-Objective Differential Evolution (DEMO) is proposed.This efficient selection is integrated in advanced Facial Emotion Recognition system.Emotion-specific and more discriminative features over all emotions selection strategies.Emotion recognition accuracy of proposed algorithm comparable to state-of-the-art.Feature selection by using DEMO enormously reduces a feature vector length. This paper proposes an efficient feature selection system applied to a Facial Expression Recognition (FER) system. This system, capable of recognizing seven prototypical emotions including neutral expression, is based on a histogram of oriented gradient descriptor (HOG) and difference feature vectors. The emotion feature selection was carried out by using an appropriately modified multi-objective differential evolution algorithm. The number of used features was minimized, while the emotion recognition accuracy of the support vector machine classifiers was maximized simultaneously. The emotion-specific features and the more discriminative features over all emotions selection strategies were developed, whereby the latter strategy proved to be more efficient using the Friedman statistical test. This person-independent FER system with proposed feature selection was validated on three commonly used evaluation databases, where the mean emotion recognition rate was 98.37% on the Cohn Kanade database, 92.75% on the JAFFE database, and 84.07% on the MMI database, while the number of used features lowered up to 89% with respect to the original difference feature vector length. Compared to the state-of-the-art, the proposed FER method offers good results, while also greatly lowering the number of used features, which, in return, minimizes the computational cost of training the classifiers. The optimization proposed in this paper can be generalized easily to a feature selection for an arbitrary multi-objective, as well as many-objective, problem.

A multi-stage dynamic soft scheduling algorithm for the uncertain steelmaking-continuous casting scheduling problem

The steelmaking-continuous casting (SCC) manufacturing system is usually regarded as a cornerstone as well as a bottleneck in a modern integrated steel company. In this study, we consider an uncertain scheduling problem that arises from the SCC manufacturing system where the processing times and arrival times are in intervals. To solve this problem, we propose a multi-stage dynamic soft scheduling (MDSS) algorithm based on an improved differential evolution. In the proposed algorithm, the uncertain SCC scheduling problem is decomposed into global and local scheduling problems. The global scheduling problem comprising cast units is solved by a dynamic multi-objective differential evolutionary algorithm based on decomposition where each solution is evaluated in the worst-case scenario. The local scheduling problem comprising charge units is solved by the knowledge-based differential evolutionary algorithm where all the solutions are sorted by the interval TOPSIS method. A modified critical ratio-based rule is also developed for real-time dispatching. Finally, computational results demonstrate that the MDSS algorithm outperforms previously described algorithms.

A Hybrid DEA-Adaboost Model in Supplier Selection for Fuzzy Variable and Multiple Objectives

Supplier selection is a critical multi-criteria decision making problem for supply chain management. With the emergence of big data, there is an urgent need for data-driven decision making methods. A hybrid DEA-Adaboost model is proposed to meet the challenge. The proposed model is split into the DEA and the learner. The fuzzy multi-objective DEA is used to build the expert database, which contains the appropriate and inappropriate suppliers. The learner is trained by Adaboost from the expert database. Thus, the DEA and derived learner are combined as the hybrid model to reduce the time consumption and computational complexities for suppliers selection. The simulation results demonstrate that the proposed model improves the accuracy compared with other two approaches.

Optimization of the p-xylene oxidation process by a multi-objective differential evolution algorithm with adaptive parameters co-derived with the population-based incremental learning algorithm

ABSTRACTDifferent operating conditions of p-xylene oxidation have different influences on the product, purified terephthalic acid. It is necessary to obtain the optimal combination of reaction conditions to ensure the quality of the products, cut down on consumption and increase revenues. A multi-objective differential evolution (MODE) algorithm co-evolved with the population-based incremental learning (PBIL) algorithm, called PBMODE, is proposed. The PBMODE algorithm was designed as a co-evolutionary system. Each individual has its own parameter individual, which is co-evolved by PBIL. PBIL uses statistical analysis to build a model based on the corresponding symbiotic individuals of the superior original individuals during the main evolutionary process. The results of simulations and statistical analysis indicate that the overall performance of the PBMODE algorithm is better than that of the compared algorithms and it can be used to optimize the operating conditions of the p-xylene oxidation process effectively and efficiently.

Optimal crop plans for a multi-reservoir system having intra-basin water transfer using multi-objective evolutionary algorithms coupled with chaos

Optimizing a multi-reservoir system is complicated, since the operation of one reservoir depends on other reservoir and may also have conflicting multiple objectives. The conflicting purposes of a multi-reservoir system requires a systematic multi-objective study. Recently, multi-objective evolutionary algorithms (MOEAs) have been widely used for the multi-objective analysis of the reservoir systems. However, the simple MOEAs result in premature convergence and local optimal solution for complex non-linear multi-objective optimization problems. To improve the performance and maintain the diversity in the population, chaos is being combined with the evolutionary algorithms for optimizing complex problems. In the present study, the chaos algorithm is coupled with MOEAs such as non-dominated genetic algorithm-II (CNSGA-II) and multi-objective differential evolution algorithm (CMODE) to derive an optimal crop planning for a multi-reservoir system having intra-basin water transfer. The model is developed with the objective of maximizing the net benefits and maximizing the crop production, subject to various physical, land and water availability constraints. The resulted optimal policy is further assessed using a simulation model and its performance is evaluated using various statistical indices. It is found that CMODE has resulted in slightly higher net benefits of Rs. 1921.77 Million and 1201.55 thousand tons of crop production with an irrigation intensity of 106.29% compared to other techniques used in this study. It has also resulted in an optimal spatial and temporal intra-basin water transfer from the upstream reservoirs to the downstream reservoir. The simulation of optimal results showed that the optimal policies obtained from CMODE performed well for longer period with less irrigation deficits. All the reservoirs in the system achieved more than 95% reliability in meeting the irrigation demands and intra-basin water transfer.

A jumping genes inspired multi-objective differential evolution algorithm for microwave components optimization problems

Exploitation and exploration are equally important for multi-objective evolutionary algorithms (MOEAs) to approximate the optimal Pareto Front (PF). However, most existing multi-objective differential evolution algorithms (MODEs) focus on exploitation with proposals of elitism methods that may result in poor diversity or sticking into local optimal front. Inspired by a biological discovery, this study proposes a jumping genes based MODE algorithm, termed as JGDE with two components. The first component is the application of jumping genes operator to MODE to promote population diversity while in the second component, an elitism leading mechanism is designed to accelerate the convergence. Experimental studies show the superiority of JGDE over other competitive algorithms in both convergence and diversity. More importantly, JGDE can deal with local optimal fronts that are difficult to handle by the existing MODEs. The studies are also further verified by the solvement of a practical microwave components optimization problem and the comparison between different optimization algorithms.

The Comparisons of Optimized Extended Kalman Filters for Speed-Sensorless Control of Induction Motors

This paper presents the comparisons of optimized extended Kalman filters (EKFs) using different fitness functions for speed-sensorless vector control of induction motors (IMs). In order to achieve high performance estimations of states/parameter by EKF algorithm, state and noise covariance matrices must be accurately selected. For this aim, instead of using time-consuming trial-and-error method to determine those covariance matrices, in this paper EKF algorithm is optimized by differential evolution algorithm (DEA) and multi-objective DEA (MODEA) with the utilization of different fitness functions. The optimally obtained set of each covariance matrices is used in EKF algorithm built on the same IM model and thus, the estimation results of the optimized EKF algorithms are compared in real-time experiments in order to conclude which fitness function is better for motion control applications.

In-Wheel Switched Reluctance Motor Design for Electric Vehicles by Using a Pareto-Based Multiobjective Differential Evolution Algorithm

In this paper, an in-wheel switched reluctance motor (IW-SRM) is designed by using a Pareto-based multiobjective differential evolution algorithm (PMODEA) for electric vehicles (EVs). The performance of the IW-SRM varies by the dimension parameters of the motor. Estimation of optimum motor dimensions is a multiobjective optimization problem. In dimension optimization of the IW-SRM for direct-driven EVs, torque, torque per motor lamination volume, and efficiency are specified as objective functions. The PMODEA is proposed for the solution of the multiobjective optimization problem as designing IW-SRM, and nondominant optimum solution set consisting of motor dimensions is obtained. This study provides flexibility to the decision maker, in selection of desired one from the existing solution set. The analysis of the selected motor is realized by considering optimum dimensions via the finite-element method (FEM). Then, the IW-SRM is manufactured, and then, the experimental results are obtained for static and dynamic analysis. FEM analysis results are compared with the experimental results. Eventually, it is observed that the results are satisfactory.

Multi-objective optimization of p -xylene oxidation process using an improved self-adaptive differential evolution algorithm

Abstract The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p -xylene (PX) to TPA is regarded as a critical and efficient chemical process in industry [1] . PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simultaneously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization problems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm (SADE) to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm (ISADE). Optimization results indicate that application of ISADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.