Multi-objective Differential Evolution Algorithm Research Articles

Application of Differential Evolution algorithms to multi-objective optimization problems in mixed-oxide fuel assembly design

Multi-objective optimization of nuclear engineering fuel assembly design problems is particularly difficult due to the highly non-linear interactions of a large number of possible variables. In addition, effective optimization algorithms are often highly problem-dependent and require extensive tuning, which reduces their applicability to the real world. To address this issue, Differential Evolution (DE) algorithms have been proposed as a new and effective method for heterogeneous fuel assembly optimization design problems. This paper presents the first complete study to investigate their applicability and performance. Firstly, two multi-objective DE algorithms have their performance compared against an Evolutionary Algorithm (EA) from the literature in optimizing a CORAIL mixed-oxide (MOX) fuel assembly for maximum plutonium content and minimum power peaking factor. Statistical analysis of the results shows the DE algorithms exhibit superior performance to the EA. The DE algorithms are then used to optimize a MOX fuel assembly with gadolinia poison, with results showing DE produces assembly designs comparable in performance to those in the literature. Finally, a sensitivity study is conducted on the control parameters of the better performing of the DE algorithms. Results indicate DE performance remains consistent for a wide range of values of both control parameters, suggesting the algorithm is able to perform effectively without requiring user expertise or effort to find the ‘optimal’ control parameter settings.

Optimum Pareto design of vehicle vibration model excited by non-stationary random road using multi-objective differential evolution algorithm with dynamically adaptable mutation factor

Optimum Pareto design of vehicle vibration model excited by non-stationary random road using multi-objective differential evolution algorithm with dynamically adaptable mutation factor

Multi-objective optimization-based updating of predictions during excavation

In this paper, an efficient multi-objective optimization (MOOP)-based updating framework is established, which involves (1) the development of an enhanced multi-objective differential evolution algorithm with good searching ability and high convergence speed, (2) the development of an enhanced anisotropic elastoplastic model considering small-strain stiffness with its implementation into a finite element code, and (3) the proposal of an identification procedure for parameters using field measurements followed by an updating procedure. The proposed updating framework is verified with a well-documented excavation case where the small-strain stiffness, the anisotropy of elasticity, the anisotropy of yield surface for natural clays, and the parameters of the supporting structures and diaphragm wall are consecutively updated during the staged excavation process. The advantages of the proposed updating framework compared to the Bayesian updating on the same case are also illustrated.

A hybrid forecasting system based on fuzzy time series and multi-objective optimization for wind speed forecasting

Wind speed forecasting is fundamental to the dispatching, controllability, and stability of the power grid. As a challenging but essential work, wind speed forecasting has attracted significant attention from researchers and managers. However, traditional forecasting models sometimes fail to capture data features owing to the randomness and intermittency of wind speed, and the models always focus only on improving accuracy, which is one-sided. Motivated by these problems, in this study, a novel hybrid forecasting system consisting of three modules (a data preprocessing module, optimization module, and forecasting module) is developed to improve the forecasting accuracy and stability. In the data preprocessing module, an effective denoising technique is used to produce a smoother sequence. A fuzzy time series method optimized by a multi-objective differential evolution algorithm that balances the conflict between forecasting accuracy and stability is developed in the next two modules to perform the forecasting. Several experimental results covering different models and wind-speed time intervals all indicate that our proposed hybrid forecasting system can achieve both satisfactory accuracy and stability with a mean absolute percentage error of below 4% in wind speed forecasting. Moreover, the statistical hypothesis test, forecasting effectiveness and grey relational degree are discussed which also demonstrate the great performance of proposed system.

Integrated Scheduling of Reheating Furnace and Hot Rolling Based on Improved Multiobjective Differential Evolution

In the hot rolling mill, a cold slab is reheated in reheating furnace and then rolled into thin coils through hot rolling process. Traditional research on hot rolling mill generally takes the two processes as two separate single-objective scheduling problems, though they are closely connected and their optimization objectives are conflicting with each other. In this paper, the integrated scheduling of the reheating furnace and hot rolling is investigated in the view of multiobjective optimization. A mixed-integer programming model with two objectives is formulated for this problem, and a multiobjective differential evolution (MODE) algorithm is developed to solve this model. To make it easy for algorithm design, a hot rolling schedule (i.e., a sequence of slabs) is used to represent a solution and for a given solution, a heuristic with consideration of energy consumption minimization is presented to obtain the schedule of reheating furnace. To achieve the balance of exploration and exploitation, a novel mutation operator with adaptive leader selection, a crossover operator with feasibility consideration, and a guided multiobjective local search are designed. Computational results based on simulated data illustrate that the integrated scheduling is superior to the traditional two-phase scheduling method used in practice and literature. Further results illustrate that the proposed MODE algorithm is effective and superior to some other multiobjective evolutionary algorithms.

Simulating Land Use Structure Optimization Based on an Improved Multi-Objective Differential Evolution Algorithm

Simulating Land Use Structure Optimization Based on an Improved Multi-Objective Differential Evolution Algorithm

Optimal feature selection for islanding detection in distributed generation

The integration of the distributed power generation into a distribution system comes with several system problems. One of the teething problems related to system protection is islanding detection. Various anti-islanding techniques based on feature evaluation were proposed in the recent past. However, they overlook the need for justifying the selection of a particular detection feature among all the possible measures. In this study, a wrapper feature selection approach is proposed where a modified multi-objective differential evolution algorithm is coupled with a kernel-based extreme learning machine classifier. To select the optimum features, five standard objective functions have been considered, such as dependability, security, accuracy, F-measure, and the number of features. About 1864 cases have been generated from the designed IEEE 13 bus system to extract the sensitive features. IEEE 1547 standards have been considered while designing and testing the IEEE 13 bus system against islanding. The selected optimal features detect the islanded condition decisively for both synchronous and inverter-based distributed generators. The features also validate their performance under noisy environment accurately with lesser computational time.

A multi objective approach for placement of multiple DGs in the radial distribution system

Insertion of distributed generation (DG) in existing distribution system has effectively improved its performance and operation. Many different approaches for the planning of distribution system with DG insertion are presented by researchers. In this paper a multi objective approach has been proposed to maximize the mutual benefits of both the distribution system operator and DG owner. The contradictory relationship between reduction in MVA rating of DGs and reduction of power losses of the system is the motivation for this multi-objective approach. The best compromised size of DGs in MVA, their operating power factors and positions are obtained to reduce the system active power loss along with the reduction of DGs size. The 69-bus and 85-bus radial distribution system are considered as test systems. The Pareto-front of non-dominated solutions is obtained by using multi-objective differential evolution (MODE) optimization algorithm. The performance of MODE algorithm is also compared with that of multi-objective particle swarm optimization (MOPSO) algorithm. The different system operating indices such as active power loss, reactive power loss and voltage deviation are evaluated to show the effect of the best compromised solution of DGs placement in distribution system.

Differential evolution algorithm applied to wireless sensor distribution on different geometric shapes with area and energy optimization

Sensor distribution is a significant issue in wireless sensor networks and has been frequently sub-optimally solved by several heuristic algorithms. This research applies multi-objective differential evolution algorithm to jointly optimize the sensors distribution over diverse area shapes, increase the coverage area and reduce the network energy at the same time. A case base and different scenarios with constraints are considered. The restrictions are based on the boundaries of the delimited areas to prevent their centers to be close to the given boundaries, and on the area of interest by reducing the overlap among the covered areas of the nodes. At the end, the shortest distance between the initial node positions and the final node positions is determined finding which node should go in which position using the Hungarian algorithm. Finally, a minimum spanning tree among the nodes is also obtained. The results for different sensor network sizes from 9 up to 56 sensors and different sizes of target areas are presented (fitness, coverage area, energy and needed generations). The computed results show that the right combination of the control parameters leads to an optimized energy and a total coverage area of at least 87% of the target area.

Elitism-based multi-objective differential evolution with extreme learning machine for feature selection: a novel searching technique

ABSTRACTThe features related to the real world data may be redundant and erroneous in nature. The vital role of feature selection (FS) in handling such type of features cannot be ignored in the area of computational learning. The two most commonly used objectives for FS are the maximisation of the accuracy and minimisation of the number of features. This paper presents an Elitism-based Multi-objective Differential Evolution algorithm for FS and the novelty lies in the searching process which uses Minkowski Score (MS) and simultaneously optimises three objectives. The MS is considered as the third objective to keep track of the feature subset which is capable enough to produce a good classification result even if the average accuracy is poor. Extreme Learning Machine because of its fast learning speed and high efficiency has been considered with this multi-objective approach as a classifier for FS. Twenty-one benchmark datasets have been considered for performance evaluation. Moreover, the selected feature subsets are tested using 10-fold cross-validation. A comparative analysis of the proposed approach with two classical models, three single objective algorithms, and four multi-objective algorithms has been carried out to test the efficacy of the model.

A multiobjective DEA model to assess the eco-efficiency of agricultural practices within the CF + DEA method

Reducing environmental impacts while maintaining high production levels is a challenge for environmentally sustainable agricultural production, which is more complex compared to other production systems. In this sense, it is important to measure environmental impacts and agricultural production in order to implement improvement plans. Moreover, it is relevant to add flexibility in the decision-making process for carrying out such implementations. The use of the Life Cycle Assessment + Data Envelopment Analysis (LCA + DEA) approach provides a tool to assess the eco-efficiency of units, considering environmental impacts, determining best practices and obtaining a single target for each inefficient unit. In this study, in order to add the necessary flexibility to the decision-making process, a multiobjective DEA model (MORO-D) is used, which provides a set of targets for each inefficient unit. According to their operational/managerial needs or limitations, the decision maker can choose a suitable target. This model is introduced within the four-step method for the Carbon Footprint (CF) + DEA approach, which leads to a new version of this method. We illustrated this new version assessing the eco-efficiency of organic blueberry (Vaccinium corymbosum) orchards. As a way to support the decision-making process, criteria for selecting one target from the set of targets are proposed. The results and also the advantages of the new version of the four-step method over the previous one are discussed. When consulted, the producers highlighted the advantages of having multiple alternatives due to the changing market conditions and they were more predisposed to select the easiest to implement. To the best of our knowledge, this is the first multiobjective model used within the LCA + DEA approach.

Multiobjective Optimization for a Wireless Ad Hoc Sensor Distribution on Shaped-Bounded Areas

Resource efficiency in wireless ad hoc networks has become a widely studied NP-problem. This problem may be suboptimally solved by heuristic strategies, focusing on several features like the channel capacity, coverage area, and more. In this work, maximizing coverage area and minimizing energy consumption are suboptimally adjusted with the implementation of two of Storn/Price’s Multiobjective Differential Evolution (DE) algorithm versions. Additionally, their extended representations with the use of random-M parameter into the mutation operator were also evaluated. These versions optimize the initial random distribution of the nodes in different shaped areas, by keeping the connectivity of all the network nodes by using the Prim–Dijkstra algorithm. Moreover, the Hungarian algorithm is applied to find the minimum path distance between the initial and final node positions in order to arrange them at the end of the DE algorithm. A case base is analyzed theoretically to check how DE is able to find suboptimal solutions with certain accuracy. The results here computed show that the inclusion of random-M and completion of the algorithm, where the area is pondered with 60% and the energy is pondered with 40%, lead to energy optimization and a total coverage area higher than 90%, by considering the best results on each scenario. Thus, this work shows that the aforementioned strategies are feasible to be applied on this problem with successful results. Finally, these results are compared against two typical bioinspired multiobjective algorithms, where the DE algorithm shows the best tradeoff.

Adaptive multi objective differential evolution with fuzzy decision making in preventive and corrective control approaches for voltage security enhancement

This paper presents a multi objective differential evolution (MODE) based voltage security enhancement through combined preventive-corrective control strategy. Load shedding, generation rescheduling and optimal utilization of FACTS devices are considered for security enhancement. Maximum l-index of load buses is taken as the indicator of voltage stability. Minimization of cost of FACTS devices, minimization of amount of load shedding along with improvement in voltage stability are the objectives of this multi objective optimization problem. The optimal location of FACTS devices are selected using modal analysis technique. The buses for load shedding are selected based on the minimum eigen value of load flow Jacobian. The proposed MODE algorithm employs DE/randSF/1/bin strategy scheme with self tuned parameter which employs binomial crossover and difference vector based mutation. A fuzzy based decision making algorithm is employed to get the best compromise solution from the non dominated solutions. The proposed MODE is also tested with statistical performance metrices. The proposed methodology is implemented on IEEE 30 bus and IEEE 57 bus test systems. The proposed MODE method provides better solutions in the pareto optimal front than the other optimization techniques such as MOGA and NSGA II under combined preventive–corrective control approach. In IEEE 30 bus system, the amount of load shedding is reduced by 40% and voltage stability is improved by 15% and in IEEE 57 bus system, the amount of load shedding is reduced by 15.4% and voltage stability is improved by 13% by the proposed approach. Hence the simulation results show that the proposed approach provides considerable reduction in the amount of load shedding and enhancement of voltage stability by including generation rescheduling and utilization of FACTS devices.

A multi-objective differential evolution algorithm for parallel batch processing machine scheduling considering electricity consumption cost

The manufacturing industry consumes massive amounts of energy and produces great numbers of greenhouse gases every year. Recently, an increasing attention has been paid to the energy efficiency of the manufacturing industry. This paper considers a parallel batch processing machine (BPM) scheduling problem in the presence of dynamic job arrivals and a time-of-use pricing scheme. The objective is to simultaneously minimize makespan, a measure of production efficiency and minimize total electricity cost (TEC), an indicator for environmental sustainability. A BPM is capable of processing multiple jobs at a time, which has wide applications in many manufacturing industries such as electronics manufacturing facilities and steel-making plants. We formulate this problem as a mixed integer programming model. Considering the problem is strongly NP-hard, a multi-objective differential evolution algorithm is proposed for effectively solving the problem at large scale. The performance of the proposed algorithm is evaluated by comparing it to the well-known NSGA-II algorithm and another multi-objective optimization algorithm AMGA. Experimental results show that the proposed algorithm performs better than NSGA-II and AMGA in terms of solution quality and distribution.

Fitness partition-based multi-objective differential evolutionary algorithm and its application to the sodium gluconate fermentation process

The operating conditions of the fermentation process of sodium gluconate play a key role in the quality and quantity of its production. The fermentation process is highly nonlinear and dynamic, and several objects must be considered. To implement a global and efficient optimization for the fermentation process, a fitness partition-based multi-objective differential evolutionary algorithm (FPMDE) is proposed. In the FPMDE algorithm, the information in the target space, which expresses some superiority message, is used to guide the evolutionary process. Namely, according to the fitness values, the target space is divided into some sub-region, and then some optimal directions are extracted for individuals to search for the optimal region and finally approximate the Pareto front. Experimental results on 20 benchmark functions show its advantage in convergence and diversity compared with 5 other state-of-art algorithms. Further, three objective functions for the fermentation process of sodium gluconate are proposed, and the FPMDE algorithm is applied to obtain its Pareto front; the conversion rates and utilization rate of equipment has been improved. It is shown that the FPMDE can optimize the conditions of the production of sodium gluconate effectively and efficiently.

Evolutionary Multiobjective Clustering and Its Applications to Patient Stratification.

Patient stratification has a major role in enabling efficient and personalized medicine. An important task in patient stratification is to discover disease subtypes for effective treatment. To achieve this goal, the research on clustering algorithms for patient stratification has brought attention from both academia and medical community over the past decades. However, existing clustering algorithms suffer from realistic restrictions such as experimental noises, high dimensionality, and poor interpretability. In particular, the existing clustering algorithms usually determine clustering quality using only one internal evaluation function. Unfortunately, it is obvious that one internal evaluation function is hard to be fitted and robust for all datasets. Therefore, in this paper, a novel multiobjective framework called multiobjective clustering algorithm by fast search and find of density peaks is proposed to address those limitations altogether. In the proposed framework, a parameter candidate population is evolved under multiple objectives to select features and evaluate clustering densities automatically. To guide the multiobjective evolution, five cluster validity indices including compactness, separation, Calinski-Harabasz index, Davies-Bouldin index, and Dunn index, are chosen as the objective functions, capturing multiple characteristics of the evolving clusters. Multiobjective differential evolution algorithm based on decomposition is adopted to optimize those five objective functions simultaneously. To demonstrate its effectiveness, extensive experiments have been conducted, comparing the proposed algorithm with 45 algorithms including nine state-of-the-art clustering algorithms, five multiobjective evolutionary algorithms, and 31 baseline algorithms under different objective subsets on 94 datasets featuring 35 real patient stratification datasets, 55 synthetic datasets based on a real human transcription regulation network model, and four other medical datasets. The numerical results reveal that the proposed algorithm can achieve better or competitive solutions than the others. Besides, time complexity analysis, convergence analysis, and parameter analysis are conducted to demonstrate the robustness of the proposed algorithm from different perspectives.

A multi-objective multicast routing optimization based on differential evolution in MANET

PurposeThe purpose of this paper is to propose a multi-objective differential evolution algorithm named as MOMR-DE to resolve multicast routing problem. In mobile ad hoc network (MANET), multicast routing is a non-deterministic polynomial -complete problem that deals with the various objectives and constraints. Quality of service (QoS) in the multicast routing problem mainly depends on cost, delay, jitter and bandwidth. So the cost, delay, jitter and bandwidth are always considered as multi-objective for designing multicast routing protocols. However, mobile node battery energy is finite and the network lifetime depends on node battery energy. If the battery power consumption is high in any one of the nodes, the chances of network’s life reduction due to path breaks are also more. On the other hand, node’s battery energy had to be consumed to guarantee high-level QoS in multicast routing to transmit correct data anywhere and at any time. Hence, the network lifetime should be considered as one objective of the multi-objective in the multicast routing problem.Design/methodology/approachRecently, many metaheuristic algorithms formulate the multicast routing problem as a single-objective problem, although it obviously is a multi-objective optimization problem. In the MOMR-DE, the network lifetime, cost, delay, jitter and bandwidth are considered as five objectives. Furthermore, three QoS constraints which are maximum allowed delay, maximum allowed jitter and minimum requested bandwidth are included. In addition, we modify the crossover and mutation operators to build the shortest-path multicast tree to maximize network lifetime and bandwidth, minimize cost, delay and jitter.FindingsTwo sets of experiments are conducted and compared with other algorithms for these problems. The simulation results show that our proposed method is capable of achieving faster convergence and is more preferable for multicast routing in MANET.Originality/valueIn MANET, most metaheuristic algorithms formulate the multicast routing problem as a single-objective problem. However, this paper proposes a multi-objective differential evolution algorithm to resolve multicast routing problem, and the proposed algorithm is capable of achieving faster convergence and more preferable for multicast routing.

Optimal shape design of multi-layered IPMSM using adaptive dynamic Taylor Kriging model

PurposeThis paper aims to propose a numerically efficient multi-objective optimization strategy, which can improve both the efficiency and performance during the optimization process.Design/methodology/approachThis paper discusses the multi-objective optimization algorithm by combining multi-objective differential evolution (MODE) algorithm with an adaptive dynamic Taylor Kriging (ADTK) model.FindingsThe proposed approach is validated through application to an analytic example and applied to a shape optimal design of a multi-layered interior permanent magnet synchronous motor for torque ripple reduction while maintaining the average torque.Originality/valueThe ADTK model selects its basis functions adaptively and dynamically so that it may have better accuracy than any other Kriging models. Through adaptive insertion of new sampling data, it guarantees minimum required sampling data for a desired fitting accuracy.

Multiobjective economic-environmental power dispatch with stochastic wind-solar-small hydro power

Economic-environmental power dispatch is one of the most popular bi-objective non-linear optimization problems in power system. Classical economic power dispatch problem is formulated with only thermal generators often ignoring security constraints of the network. But importance of reduction in emission is paramount from environmental sustainability perspective and hence penetration of more and more renewable sources into the electrical grid is encouraged. However, most common forms of renewable sources are intermittent and uncertain. This paper proposes multiobjective economic emission power dispatch problem formulation and solution incorporating stochastic wind, solar and small-hydro (run-of-river) power. Weibull, lognormal and Gumbel probability density functions are used to calculate available wind, solar and small-hydro power respectively. Some conventional generators of the standard IEEE 30-bus system are replaced with renewable power sources for study purpose. Network security constraints such as transmission line capacities and bus voltage limits are also taken into consideration alongwith constraints on generator capabilities and prohibited operating zones for the thermal units. Decomposition based multiobjective evolutionary algorithm and summation based multiobjective differential evolution algorithm are applied to the problem under study. An advanced constraint handling technique, superiority of feasible solutions, is integrated with both the multiobjective algorithms to comply with system constraints. The simulation results of both the algorithms are summarized, analyzed and compared in this study.

A self-adaptive mating restriction strategy based on survival length for evolutionary multiobjective optimization

Abstract Mating restriction plays an important role in improving the performance of the multiobjective evolutionary algorithms. However, research on mating restriction is still insufficient, and in most cases, the same mating restriction strategy is set for all individuals without consideration of individual quality. To effectively alleviate the above problems, this paper proposes a self-adaptive mating restriction strategy based on survival length (MRSL). Based on the information of neighbourhood relationship extracted by clustering, mating parents are selected from the neighbours for exploitation or from the whole population for exploration, which is controlled by the mating restriction probability. Furthermore, considering different individuals are in need of different search space, each individual has a separate mating restriction probability. Additionally, the survival length of the individual is proposed to define and update the mating restriction probability self-adaptively at each generation. The survival length of the individual represents the number of survival generations over the last certain period of time. A multiobjective differential evolutionary algorithm called MDESL is proposed by using MRSL, and compared with five representative algorithms on several test instances. The experimental results validate the superiority of MDESL over the comparison algorithms.