Multi-objective Differential Evolution Research Articles

Retracted: Multiobjective Differential Evolution Clustering Algorithm Based on Multimedia Information in Working Mechanism Innovation for Traditional Chinese Medicine

Retracted: Multiobjective Differential Evolution Clustering Algorithm Based on Multimedia Information in Working Mechanism Innovation for Traditional Chinese Medicine

Retracted: Medical Multimedia Image Analysis of Scoliosis in Children Aged 3–7 Years Based on Adaptive Multiobjective Differential Evolution Algorithm

Retracted: Medical Multimedia Image Analysis of Scoliosis in Children Aged 3–7 Years Based on Adaptive Multiobjective Differential Evolution Algorithm

Optimal Design of Voltage Reference Circuit and Ring Oscillator Circuit Using Multiobjective Differential Evolution Algorithm

This paper deals with the optimal design of different VLSI circuits, namely, the CMOS voltage reference circuit and the CMOS ring oscillator (RO). The optimization technique used here is the multiobjective differential evolution algorithm (MDEA). All the circuits are designed for 90 nm technology. The main objective of the CMOS voltage reference circuit is to minimize the voltage variation at the output. The targeted value of the reference voltage is 550 mV. A CMOS ring oscillator (RO) is designed depending on the performance parameters such as power consumption and phase noise. The optimal transistor sizing of each circuit is obtained from MDEA. Each circuit is implemented in SPICE by taking the optimal dimensions of the transistors, and the performance parameters are achieved. The designed voltage reference circuit achieves a reference voltage of 550 mV with 600 nW power dissipation. The reference voltage variation of 8.18% is observed due to temperature variation from −40°C to + 125°C. The MDEA-based optimal design of RO oscillates at 2.001 GHz frequency, has a phase noise of −87 dBc/Hz at 1 MHz offset frequency, and consumes 71 μW power. This work mainly aims to optimize the MOS transistors’ sizes using MDEA for better circuit performance parameters. SPICE simulation has been carried out by using the optimal values of MOS transistor sizes to exhibit the performance parameters of the circuit. Simulation results establish that design specifications are closely met. SPICE results show that MDEA is a better technique for the optimal design of the above-mentioned VLSI circuits.

An Integrated Model for Multi-Mode Resource-Constrained Multi-Project Scheduling Problems Considering Supply Management with Sustainable Approach in the Construction Industry under Uncertainty Using Evidence Theory and Optimization Algorithms

In this study, the multi-mode resource-constrained multi-project scheduling problems (MMRCMPSPs) considering supply management and sustainable approach in the construction industry under uncertain conditions have been investigated using evidence theory to mathematical modeling and solving by multi-objective optimization algorithms. In this regard, a multi-objective mathematical model has been proposed, in which the first objective function aims to maximize a weighted selection of projects based on economic, environmental, technical, social, organizational, and competitive factors; the second objective function is focused on maximizing profit, and the third objective function is aimed at minimizing the risk of supply management. Moreover, various components, such as interest rates, carbon penalties, and other implementation limitations and additional constraints, have also been considered in the modeling and mathematical relationships to improve the model’s performance and make it more relevant to real-world conditions and related issues, leading to better practical applications. In the mathematical modeling adopted, the processing time of project activities has been considered uncertain, and the evidence theory has been utilized. This method can provide a flexible and rational approach based on evidence and knowledge in the face of uncertainty. In addition, to solve the proposed multi-objective mathematical model, metaheuristic optimization algorithms, such as the differential evolution (DE) algorithm based on the Pareto archive, have been used, and for evaluating the results, the non-dominated sorting genetic algorithm II (NSGA-II) has also been employed. Furthermore, the results have been compared based on multi-objective evaluation criteria, such as quality metric (QM), spacing metric (SM), and diversity metric (DM). It is worth noting that to investigate the performance and application of the proposed model, multiple evaluations have been conducted on sample problems with different dimensions, as well as a case study on residential apartment construction projects by a contracting company. In this respect, the answers obtained from solving the model using the multi-objective DE algorithm were better and superior to the NSGA-II algorithm and had a more favorable performance. Generally, the results indicate that using the integrated multi-objective mathematical model in the present research for managing and scheduling multi-mode resource-constrained multi-project problems, especially in the construction industry, can lead to an optimal state consistent with the desired objectives and can significantly improve the progress and completion of projects.

Multiobjective Differential Evolution With Speciation for Constrained Multimodal Multiobjective Optimization

This paper proposes a novel differential evolution algorithm for solving constrained multimodal multiobjective optimization problems (CMMOPs), which may have multiple feasible Pareto optimal solutions with identical objective vectors. In CMMOPs, due to the coexistence of multimodality and constraints, it is difficult for current algorithms to perform well in both objective and decision spaces. The proposed algorithm uses speciation mechanism to induce niches preserving more feasible Pareto optimal solutions and adopts an improved environment selection criterion to enhance diversity. The algorithm can not only obtain feasible solutions but also retain more well-distributed feasible Pareto optimal solutions. Moreover, a set of constrained multimodal multiobjective test functions is developed. All these test functions have multimodal characteristics and contain multiple constraints. Meanwhile, this paper proposes a new indicator, which comprehensively considers the feasibility, convergence, and diversity of a solution set. The effectiveness of the proposed method is verified by comparing with the state-of-the-art algorithms on both test functions and real-world location-selection problem.

Traffic Signal Optimization Based on Fuzzy Control and Differential Evolution Algorithm

Urban traffic congestion is often concentrated at urban intersections. An urban road traffic signal control system is needed to prevent problems such as driving delays caused by frequent traffic congestions on trunk lines, exhaust emissions owing to frequent start and stop of vehicles, and fuel wastage due to long idling times. Maximizing the traffic capacity of an intersection and reducing the delay rate of vehicles has always been a problem for traffic control research. The coordinated control of urban traffic signals is regarded as a multi-objective optimization problem. A mathematical model for urban trunk traffic is studied herein. An average delay model, average queue length model, total delay calculation model for vehicles at intersections, and vehicle exhaust emission model are established to obtain an optimization model for a new traffic trunk coordinated control system. In addition, our study combines the fuzzy control theory with the adaptive sequencing mutation multi-objective differential evolution algorithm (FASM-MDEA). This new optimization method for traffic signal control at urban intersections is proposed as a solution for the traffic flow optimization model to solve the problem of traffic signal coordination and control of urban trunk lines. The simulation results demonstrate the effectiveness of the model optimization algorithm proposed in this study.

A New Hybrid Algorithm Based on Improved MODE and PF Neighborhood Search for Scheduling Task Graphs in Heterogeneous Distributed Systems

Multi-objective task graph scheduling is a well-known NP-hard problem that plays a significant role in heterogeneous distributed systems. The solution to the problem is expected to optimize all scheduling objectives. Pretty large state-of-the-art algorithms exist in the literature that mostly apply different metaheuristics for solving the problem. This study proposes a new hybrid algorithm comprising an improved multi-objective differential evolution algorithm (DE) and Pareto-front neighborhood search to solve the problem. The novelty of the proposed hybrid method is achieved by improving DE and hybridizing it with the neighborhood search method. The proposed method improves the performance of differential evolution by applying appropriate solution representation as well as effective selection, crossover, and mutation operators. Likewise, the neighborhood search algorithm is applied to improve the extracted Pareto-front and speed up the evolution process. The effectiveness and performance of the developed method are assessed over well-known test problems collected from the related literature. Meanwhile, the values of spacing and hyper-volume metrics are calculated. Moreover, the Wilcoxon signed method is applied to carry out pairwise statistical tests over the obtained results. The obtained results for the makespan, reliability, and flow-time of 50, 18, and 41, respectively, by the proposed hybrid algorithm in the study confirmed that the developed algorithm outperforms all proposed methods considering the performance and quality of objective values.

Energy Management in Microgrids with Renewable Energy Sources and Demand Response

This manuscript presents a unique method for stochastic management of renewable energy sources using Micro Grid (MG). This method is based on the demand reduction function to provide a demand side reserve to supply electricity to consumers. To reduce peak demand and energy costs, a typical MG for distributed generation (DG) is used to schedule 24-hour power. The optimal generation scheduling problem is solved as both single-objective and multi-objective optimization problems. Differential Evolution and Multi-Objective Differential Evolution are used to minimize operating costs and environmental emissions, which consider equality and inequality constraints to find the best way to allocate power among the many units connected to MG. Power allocation using DE is shown to be more cost effective and environmentally friendly compared to Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) based technique.

Multiobjective Differential Evolution for Feature Selection in Classification.

Feature selection aims to reduce the number of features and improve the classification accuracy, which is an essential step in many real-world problems. Multiple feature subsets with different features selected can achieve similar or even the same objective values (e.g., maximize the classification accuracy and minimize the number of selected features). This means the optimal feature subsets of a classification problem may not be unique. However, most existing feature selection methods do not take into consideration finding multiple optimal feature subsets. In this article, a multiobjective differential evolution approach is developed to search for multiple optimal feature subsets. The contributions are three-fold. First, to provide a good starting point, an initialization method considering feature relevance is proposed. Second, a clustering method is used to divide the whole population into multiple subpopulations. In each of these subpopulations, a subarchive utilizes a developed crowding distance to ensure diversity by considering both the search space and the objective space. Finally, the nondominated solutions from all the subarchives are retained in another archive to guide the evolutionary feature selection process, together with an improved hypervolume contribution indicator. The experiments on 14 datasets of varying difficulty show that the proposed approach can evolve a better Pareto front of feature subsets compared with seven other state-of-the-art methods as well as find different feature subsets with similar or the same classification performance.

Multistate-Constrained Multiobjective Differential Evolution Algorithm With Variable Neighborhood Strategy.

Multiobjective differential evolution (DE) algorithm (MODE) has been widely used in multiobjective optimization problems. However, due to the complex feasible regions, the optimization efficiency of MODE may decrease when solving constrained multiobjective problems. It is challenging to promote the evolution of population with few feasible solutions. In this article, a multistate-constrained MODE with variable neighborhood strategy (MSCMODE-VNS) is proposed to enhance the optimization effectiveness with complex feasible regions. First, a variable neighborhood DE strategy, based on a specially designed convergence indicator, is designed to accelerate the generation of feasible solutions. Second, a multistate population updating strategy with a comprehensive solution evaluation mechanism is devised to update the population of the next generation to improve the performance of solutions. Third, the convergence analysis, based on the probability theory, is derived to verify the effectiveness of the proposed MSCMODE-VNS algorithm. Finally, experimental results indicate that MSCMODE-VNS can achieve a satisfactory performance on three benchmark test suites and two real-world-constrained multiobjective problems.

Machine learning and particle swarm inspired success history based adaptive multi-objective differential evolution for optimization of heaving buoy point absorber

Success-History-Based Parameter Adaptation Multi-Objective Differential Evolution (SHAMODE) has shown excellent performance recently compared to other multi-objective evolutionary algorithms (MOEAs) and therefore caught the interest of researchers lately. The SHAMODE framework employs historical memory of control parameters, which stores set values of control parameters that have performed well in the past generation and produces new set values of the parameter by directly sampling the parameter space close to one of these stored pairs. Since the algorithm's performance depends on the problem to be optimized, this paper proposes an enhanced version of SHAMODE that is compatible with optimizing the multi-objective wave energy converter problem. The improved version of SHAMODE is achieved by incorporating competing machine learning algorithms, Particle Swarm Optimization, and a modified bubble-net attacking method formula of the Whale optimization algorithm from its original form. Simulations and comparisons are used to verify the proposed method's performance based on some famous multi-objective problem (MOP) benchmark functions. The results reveal that the proposed algorithm performs better than other algorithms that have been recently developed. In addition, the suggested technique is used to optimize the multi-objective wave energy converter model in order to maximize the annual production of electric energy while minimizing the per-unit energy cost.

A novel multimodal multi-objective optimization algorithm for multi-robot task allocation

Multi-robot task allocation (MRTA) is widely used in various fields and plays an important role in some complex task environments due to its ability to distribute parallel processing tasks. However, the multi-robot cooperative system is susceptible to actual environments or preferences of decision-makers. Therefore, providing enough solutions/schemes in the MRTA is important. To improve the reliability and feasibility of obtained solution set, an improved multimodal multi-objective differential evolution algorithm hybrid with a simulated annealing algorithm (IMMODE-SA) is proposed to solve MRTA problems in this study. In the proposed IMMODE-SA, a novel population initialization method is used to improve the population quality, and a redundant solution deletion method is employed to delete redundant solutions during the search process. Moreover, a simulated annealing algorithm is utilized to improve the exploitation capability in the last generation of evolutionary process. To verify the performance of the proposed algorithm, extensive simulation experiments are conducted on three MRTA instances. Experimental results show that the proposed algorithm performs better than other competitors on MRTA instances in terms of Hypervolume (HV). Also, the validity of the proposed algorithm is demonstrated via three experiments and experimental analysis results indicate that the IMMODE-SA can provide more equivalent optimal schemes to decision makers. Finally, it is crucial to solve MRTA problems with time window constraints.

A Novel Mutation-based Differential Evolution Algorithm for Solving Real-World Optimization Problems

In today's environment, evolutionary algorithms play a key role in solving optimization problems in mathematical models and applications. This article introduces a multi-objective differential evolution algorithm that extends the single-objective differential evolution (DE) algorithm to solve optimization problems in mathematical models and applications. Many existing algorithms face issues with diversity loss and convergence rate. To address these problems, this article proposes a novel mutation operator called ubiquitination mutation for DE, which has been added to the DE method. The proposed approach was tested on three real-world optimization problems: the next release problem, the multiline distance minimization problem, and data clustering. Results indicate that the proposed mutation operator outperformed state-of-the-art algorithms. In addition, the proposed approach provided better solutions in both single- and multi-objective platforms for various real-world problems.

Multi-objective optimization of fed-batch bioreactor for lysine production

ABSTRACT Lysine production via the fermentation process is one of the most economical production routes that involves simultaneous conflicting objectives. Two multi-objective differential evolution algorithms MODE-III and MODE-III-IMS are used to obtain the optimal control parameters of the lysine bioreactor. Two conflicting objectives, namely yield and productivity, are studied. Singular and constant feeding policies using both algorithms are studied, and respective Pareto fronts are reported. Tournament selection and penalty constraint handling methods are used, and their performances are compared for both algorithms. The higher bound of feeding rate (2.0 L/s) is found to be the best feeding rate compared to other feeding rates. The MODE-III-IMS algorithm converged to the Pareto front faster than the MODE-III algorithm. The COPRAS method is used to carry out the Pareto ranking, and the best optimal solution is reported. The decision tree method is used to predict and report the best optimal solution with acceptable accuracy.

WITHDRAWN: Short term optimal scheduling of a virtual power plants integrated with electrothermal hybrid energy storage system using an effective adaptive multi-objective differential evolution algorithm

virtual power plants (VPPs) in the power distribution grid play an important role in balancing the power and heat generation and consumption in residential, commercial, and industrial sectors. This study proposes VPPs for risk-averse energy exchange of resources and customers in the presence of the hybrid storage system. An appropriate energy management program is presented to make a balance between generators and consumers in VPPs considering generation uncertainties including electricity demand and price forecasting in the electricity market and renewable energy uncertainties. Hence, monetary exchange methods such as day-ahead agreements are proposed for energy exchange among VPPs. The expanded exchange structure of the suggested framework simplifies the renewable energy's sources to the electricity market despite its small-scale and non-dispatchable features. Also, a novel model is presented for short-term programing of virtual power plant considering technical and economic uncertainties. Given that VPPs can enter the electricity market based on time-of-use (TOU) pricing strategy and participation in demand response (DR) program, minimizing the expected cost of energy generation and environmental pollution is considered as the objective function. A multi-objective efficient model of energy management employing the machine speed scaling mechanism is suggested. An effective adaptive multi-objective differential evolution (AMODE) algorithm is presented to solve the multi-objective optimization problem. AMODE usages a novel Fitness Evaluation Mechanism (FEM) using dynamic reference point and fuzzy association randomness study to evaluate solutions in the evolutionary population by implementing the conditional value at risk (CVaR) method for risk management. The simulation studies and sensitivity analysis results are evaluated to confirm the effectiveness of the proposed model on a VPP in the island and grid-connected modes with and without participation in DR program. Finally, the conceptual results are discussed.

Reinforcement-Learning-Based Multi-Objective Differential Evolution Algorithm for Large-Scale Combined Heat and Power Economic Emission Dispatch

As social and environmental issues become increasingly serious, both fuel costs and environmental impacts should be considered in the cogeneration process. In recent years, combined heat and power economic emission dispatch (CHPEED) has become a crucial optimization problem in power system management. In this paper, a novel reinforcement-learning-based multi-objective differential evolution (RLMODE) algorithm is suggested to deal with the CHPEED problem considering large-scale systems. In RLMODE, a Q-learning-based technique is adopted to automatically adjust the control parameters of the multi-objective algorithm. Specifically, the Pareto domination relationship between the offspring solution and the parent solution is used to determine the action reward, and the most-suitable algorithm parameter values for the environment model are adjusted through the Q-learning process. The proposed RLMODE was applied to solve four CHPEED problems: 5, 7, 100, and 140 generating units. The simulation results showed that, compared with four well-established multi-objective algorithms, the RLMODE algorithm achieved the smallest cost and smallest emission values for all four CHPEED problems. In addition, the RLMODE algorithm acquired better Pareto-optimal frontiers in terms of convergence and diversity. The superiority of RLMODE was particularly significant for two large-scale CHPEED problems.

An improved differential evolution algorithm for quantifying fraudulent transactions

Identification of fraudulent credit card transactions is a complex problem mainly due to the following factors: 1) The relative behavior of customers and fraudsters may alter over time. 2) The ratio of legitimate to fraudulent transactions is highly imbalanced, and 3) Investigators examine a small segment of transactions in a reasonable time frame. Researchers have proposed various algorithms to identify potential fraud in a new incoming transaction. However, these approaches require significant human investigator effort and are sometimes misleading. To address this issue, this paper proposes an improved multiobjective differential evolution (DE) algorithm to estimate the distribution of fraudulent transactions in a set of new incoming transactions, referred to as quantifying fraudulent transactions. Our paper has three major novelties. First, we present the problem formulation of cost-based feature selection with maximum quantification ability. Second, we improve the DE by applying effective trial vector generation algorithms to the random control parameter settings to exploit the advantage of individual DE variants. Third, we develop the maximum-relevancy-minimum-redundancy-based Pareto refining operator to enhance the self-learning ability of individuals in Pareto solutions. We compare our approach against four other modifications of DE and five state-of-the-art evolutionary algorithms on real-time credit datasets in streaming and non-streaming frameworks using hyper-volume, two-set coverage, and spread performance metrics.

Energy-aware JPEG image compression: A multi-objective approach

Customer satisfaction is crucially affected by energy consumption in mobile devices. One of the most energy-consuming parts of an application is images. This paper, first, investigates that there is a correlation between energy consumption and image quality as well as image file size. Therefore, these two can be considered as a proxy for energy consumption. In the next step, we focused on proposing a multi-objective strategy to enhance image quality and reduce image file size based on the quantisation table (QT) in JPEG image compression. To this end, we have used two general multi-objective approaches: scalarisation and Pareto-based. In this paper, we embed our strategy into five scalarisation algorithms, including energy-aware multi-objective genetic algorithm (EnMOGA), energy-aware multi-objective particle swarm optimisation (EnMOPSO), energy-aware multi-objective differential evolution (EnMODE), energy-aware multi-objective evolutionary strategy (EnMOES), and energy-aware multi-objective pattern search (EnMOPS). Also, two Pareto-based methods, including a non-dominated sorting genetic algorithm (NSGA-II) and a reference-point-based NSGA-II (NSGA-III) are used for the embedding scheme, and two Pareto-based algorithms, EnNSGAII and EnNSGAIII, are presented. With our proposed scalarisation method, user’s preferences can be set before starting the optimisation process and the algorithm generates only one solution based on the preference, while our Pareto-based approaches generate a set of solutions so that a user can select one of the preferred solutions after the optimisation process.Experimental studies show that the performance of the baseline algorithm is improved by embedding the proposed strategy into metaheuristic algorithms. In particular, EnMOGA, EnMOPS, and EnNSGA-II can perform competitively, among others. From the results, the baseline algorithm in all cases and in comparison to all algorithms yields the worst results. Among the scalarisation methods, EnMOGA and EnMOPS can achieve the first rank in 6 and 7 out of 13 cases and the second rank in 7 and 5 cases in terms of objective function. Also, EnMOES achieved the fifth or worst rank among the scalarisation algorithms. Regarding the Pareto-based algorithms, the table shows that EnNSGAII outperforms EnNSGAIII in 10 out of 13 cases in terms of hyper-volume measure, while it fails in 3 cases. Furthermore, we statistically verify the proposed algorithm’s effectiveness based on the Wilcoxon-signed rank test. Finally, a sensitivity analysis of the parameters is provided. The source code for reproducing the results is available in: https://github.com/SeyedJalaleddinMousavirad/MultiobjectiveJPEGImageCompression.

Differential evolution based on network structure for feature selection

With the accumulation of high-dimensional data, feature selection (FS) plays a significant role in tasks such as classification and clustering. Recently, many evolutionary algorithms have been developed to address FS problems from single-objective or multiobjective perspectives. However, those algorithms always ignore the complex relationships among features containing abundant available information to adjust the search direction, resulting in poor performance. To address this limitation, we propose to explore the relationship patterns hidden in feature space using the techniques of network science, and based on the exploration, we develop a new differential evolution (DE) and a new multiobjective DE (MODE) for single-objective and multiobjective FS problems, respectively. In particular, we construct a feature network to represent the complex relationships between features and propose to explore the relational patterns from the perspective of the network. After that, the features with rich information are highlighted as high-degree nodes, and some features are grouped together as clusters in the feature network. Motivated by these observations, we further propose to improve the search processes of DE and MODE and produce two network-based DEs, namely, NetG-DE and NetG-MODE. Experimental results over several datasets demonstrate that the proposed NetG-DE and NetG-MODE outperform the baseline.

A grid‐based searching algorithm for observer‐based multiobjective control of T–S fuzzy stochastic jump‐diffusion systems

Most studies on a multiobjective optimal control problem (MOCP) with nonlinear stochastic jump-diffusion system (NSJDS) constraints assume the state vector is available, but in practice, this is not necessarily the case. The observer-based MOCP is worthy of further research. Furthermore, the hybrid multiobjective differential evolution algorithm (HMODEA) is usually employed to help solve MOCPs with dynamical system constraints, and such problems often have a higher computational burden. To address these two issues, a grid-based front-squeezing searching algorithm (GBFSA) is proposed to solve the observer-based MOCP with NSJDS. Takagi-Sugeno (T-S) fuzzy model is used to approximate the NSJDS and convert the problem into an MOCP with linear matrix inequality (LMI) constraints. Then, the GBFSA efficiently searches for the Pareto front by merging the LMIs and the squeezing theorem. To automatically select a preferred Pareto controller, the minimum Manhattan distance (MMD) approch is applied. Mathematical proofs are given to show that the obtained Pareto optimal controller can concurrently stabilize the associated NSJDS and achieve the desired performance indices. In addition, computational complexity and convergence analysis are also provided.