Multi-Strategy Assisted Multi-Objective Whale Optimization Algorithm for Feature Selection

In classification problems,datasets often contain a large amount of features,but not all of them are relevant for accurate classification.In fact,irrelevant features may even hinder classification accuracy.Feature selection aims to alleviate this issue by minimizing the number of features in the subset while simultaneously minimizing the classification error rate.Single-objective optimization approaches employ an evaluation function designed as an aggregate function with a parameter,but the results obtained depend on the value of the parameter.To eliminate this parameter’s influence,the problem can be reformulated as a multi-objective optimization problem.The Whale Optimization Algorithm(WOA)is widely used in optimization problems because of its simplicity and easy implementation.In this paper,we propose a multi-strategy assisted multi-objective WOA(MSMOWOA)to address feature selection.To enhance the algorithm’s search ability,we integrate multiple strategies such as Levy flight,Grey Wolf Optimizer,and adaptive mutation into it.Additionally,we utilize an external repository to store non-dominant solution sets and grid technology is used to maintain diversity.Results on fourteen University of California Irvine(UCI)datasets demonstrate that our proposed method effectively removes redundant features and improves classification performance.The source code can be accessed from the website:https://github.com/zc0315/MSMOWOA.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection

Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.

A Portfolio Selection Method Based on Pattern Matching with Dual Information of Direction and Distance

Pattern matching method is one of the classic classifications of existing online portfolio selection strategies. This article aims to study the key aspects of this method—measurement of similarity and selection of similarity sets, and proposes a Portfolio Selection Method based on Pattern Matching with Dual Information of Direction and Distance (PMDI). By studying different combination methods of indicators such as Euclidean distance, Chebyshev distance, and correlation coefficient, important information such as direction and distance in stock historical price information is extracted, thereby filtering out the similarity set required for pattern matching based investment portfolio selection algorithms. A large number of experiments conducted on two datasets of real stock markets have shown that PMDI outperforms other algorithms in balancing income and risk. Therefore, it is suitable for the financial environment in the real world.

Multi-objective optimization in highway pavement maintenance and rehabilitation project selection and scheduling:A state-of-the-art review

The motivation for cost-effective management of highway pavements is evidenced not only by the massive expenditures associated with these activities at a national level but also by the consequences of poor pavement condition on road users.This paper presents a state-of-the-art review of multi-objective optimization(MOO)problems that have been formulated and solution techniques that have been used in selecting and scheduling highway pavement rehabilitation and maintenance activities.First,the paper presents a taxonomy and hierarchy for these activities,the role of funding sources,and levels of jurisdiction.The paper then describes how three different decision mechanisms have been used in past research and practice for project selection and scheduling(historical practices,expert opinion,and explicit mathematical optimization)and identifies the pros and cons of each mechanism.The paper then focuses on the optimization mechanism and presents the types of optimization problems,formulations,and objectives that have been used in the literature.Next,the paper examines various solution algorithms and discusses issues related to their implementation.Finally,the paper identifies some barriers to implementing multi-objective optimization in selecting and scheduling highway pavement rehabilitation and maintenance activities,and makes recommendations to overcome some of these barriers.

Enhanced Multi-Objective Grey Wolf Optimizer with Lévy Flight and Mutation Operators for Feature Selection

The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized.While it is a multi-objective problem,current methods tend to treat feature selection as a single-objective optimization task.This paper presents enhanced multi-objective grey wolf optimizer with Lévy flight and mutation phase(LMuMOGWO)for tackling feature selection problems.The proposed approach integrates two effective operators into the existing Multi-objective Grey Wolf optimizer(MOGWO):a Lévy flight and a mutation operator.The Lévy flight,a type of random walk with jump size determined by the Lévy distribution,enhances the global search capability of MOGWO,with the objective of maximizing classification accuracy while minimizing the number of selected features.The mutation operator is integrated to add more informative features that can assist in enhancing classification accuracy.As feature selection is a binary problem,the continuous search space is converted into a binary space using the sigmoid function.To evaluate the classification performance of the selected feature subset,the proposed approach employs a wrapper-based Artificial Neural Network(ANN).The effectiveness of the LMuMOGWO is validated on 12 conventional UCI benchmark datasets and compared with two existing variants of MOGWO,BMOGWO-S(based sigmoid),BMOGWO-V(based tanh)as well as Non-dominated Sorting Genetic Algorithm II(NSGA-II)and Multi-objective Particle Swarm Optimization(BMOPSO).The results demonstrate that the proposed LMuMOGWO approach is capable of successfully evolving and improving a set of randomly generated solutions for a given optimization problem.Moreover,the proposed approach outperforms existing approaches in most cases in terms of classification error rate,feature reduction,and computational cost.

Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R &D Project Portfolio Selection

This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.

Enhancing Hyper-Spectral Image Classification with Reinforcement Learning and Advanced Multi-Objective Binary Grey Wolf Optimization

Hyperspectral(HS)image classification plays a crucial role in numerous areas including remote sensing(RS),agriculture,and the monitoring of the environment.Optimal band selection in HS images is crucial for improving the efficiency and accuracy of image classification.This process involves selecting the most informative spectral bands,which leads to a reduction in data volume.Focusing on these key bands also enhances the accuracy of classification algorithms,as redundant or irrelevant bands,which can introduce noise and lower model performance,are excluded.In this paper,we propose an approach for HS image classification using deep Q learning(DQL)and a novel multi-objective binary grey wolf optimizer(MOBGWO).We investigate the MOBGWO for optimal band selection to further enhance the accuracy of HS image classification.In the suggested MOBGWO,a new sigmoid function is introduced as a transfer function to modify the wolves’position.The primary objective of this classification is to reduce the number of bands while maximizing classification accuracy.To evaluate the effectiveness of our approach,we conducted experiments on publicly available HS image datasets,including Pavia University,Washington Mall,and Indian Pines datasets.We compared the performance of our proposed method with several state-of-the-art deep learning(DL)and machine learning(ML)algorithms,including long short-term memory(LSTM),deep neural network(DNN),recurrent neural network(RNN),support vector machine(SVM),and random forest(RF).Our experimental results demonstrate that the Hybrid MOBGWO-DQL significantly improves classification accuracy compared to traditional optimization and DL techniques.MOBGWO-DQL shows greater accuracy in classifying most categories in both datasets used.For the Indian Pine dataset,the MOBGWO-DQL architecture achieved a kappa coefficient(KC)of 97.68%and an overall accuracy(OA)of 94.32%.This was accompanied by the lowest root mean square error(RMSE)of 0.94,indicating very precise predictions with minimal error.In the case of the Pavia University dataset,the MOBGWO-DQL model demonstrated outstanding performance with the highest KC of 98.72%and an impressive OA of 96.01%.It also recorded the lowest RMSE at 0.63,reinforcing its accuracy in predictions.The results clearly demonstrate that the proposed MOBGWO-DQL architecture not only reaches a highly accurate model more quickly but also maintains superior performance throughout the training process.

Fuzzy Multi-Objective Decision Model of Supplier Selection with Preference Information

Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different suppliers. In this paper, a new multi-objective decision model with preference information of supplier is established. A practical example of supplier selection problem utilizing this model is studied. The result demonstrates the feasibility and effectiveness of the methods proposed in the paper.

Do Search and Selection Operators Play Important Roles in Multi-Objective Evolutionary Algorithms:A Case Study

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.

Spectroscopic Multicomponent Analysis Using Multi-objective Optimization for Variable Selection

The multiple determination tasks of chemical properties are a classical problem in analytical chemistry. The major problem is concerned in to find the best subset of variables that better represents the compounds. These variables are obtained by a spectrophotometer device. This device measures hundreds of correlated variables related with physicocbemical properties and that can be used to estimate the component of interest. The problem is the selection of a subset of informative and uncorrelated variables that help the minimization of prediction error. Classical algorithms select a subset of variables for each compound considered. In this work we propose the use of the SPEA-II （strength Pareto evolutionary algorithm II）. We would like to show that the variable selection algorithm can selected just one subset used for multiple determinations using multiple linear regressions. For the case study is used wheat data obtained by NIR （near-infrared spectroscopy） spectrometry where the objective is the determination of a variable subgroup with information about E protein content （%）, test weight （Kg/HI）, WKT （wheat kernel texture） （%） and farinograph water absorption （%）. The results of traditional techniques of multivariate calibration as the SPA （successive projections algorithm）, PLS （partial least square） and mono-objective genetic algorithm are presents for comparisons. For NIR spectral analysis of protein concentration on wheat, the number of variables selected from 775 spectral variables was reduced for just 10 in the SPEA-II algorithm. The prediction error decreased from 0.2 in the classical methods to 0.09 in proposed approach, a reduction of 37%. The model using variables selected by SPEA-II had better prediction performance than classical algorithms and full-spectrum partial least-squares.

Path Selection of Multimodal Transport Based on Multi-Objective Mixed Integer Programming

Based on “One Belt and One Road”, this paper studies the path selection of multimodal transport by using the method of multi-objective mixed integer programming. Therefore, this paper studies the factors of transportation time, transportation cost and transportation safety performance, and establishes a mathematical model. In addition, the method of multi-objective mixed integer programming is used to comprehensively consider the different emphasis and differences of customers on cargo transportation. Then we use planning tools of Microsoft Excel to solve path selection and to determine whether the chosen path is economical and reliable. Finally, a relatively complex road network is built as an example to verify the accuracy of this planning method.

Optimal Test Points Selection Based on Multi-Objective Genetic Algorithm

A new approach to select anoptimal set of test points is proposed. The described method uses fault-wise table and multi-objective genetic algorithm to find the optimal set of test points. First, the fault-wise table is constructed whose entries are measurements associated with faults and test points. The selection of optimal test points is transformed to the selection of the columns that isolate the rows of the table. Then, four objectives are described according to practical test requirements. The multi-objective genetic algorithm is explained. Finally, the presented approach is illustrated by a practical example. The results indicate that the proposed method can efficiently and accurately find the optimal set of test points and is practical for large scale systems.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

Weapons equipment portfolios selection based on equipment system contribution rates

Equipment selection is an essential work in the research and development planning of equipment.The scientific and rational development of weapons equipment portfolios is of considerable significance to the optimization of equipment architecture design,the adequate resources allocation,and the joint combat performance.From the system view,this paper proposes a method of weapons equipment portfolios selection(WEPS)based on the contribution rate of weapon systems,providing a new idea for weapon equipment portfolio selection.Firstly,we analyze the WEPS problem and the concept of the contribution rate under the systems background.Secondly,we propose a combat network modeling method for weapon equipment systems based on the function chain.Thirdly,we propose a WEPS method based on the contribution rate,fully considering the correlation relationships between potential weapons and the old weapon systems by the combat network model,under the limitation of capability demands and budget resources,with the objective to maximally increasing the combat ability of weapon systems.Finally,we make a case study with a specific WEPS problem where the whole calculation processes and results are analyzed and exhibited to verify the feasibility and effectiveness of the proposed method model.

Service-oriented weapon systems of system portfolio selection method

Weapon system portfolio selection is an important combinatorial problem that arises in various applications,such as weapons development planning and equipment procurement,which are of concern to military decision makers.However,the existing weapon system-of-systems(SoS)is tightly coupled.Because of the diversity and connectivity of mission requirements,it is difficult to describe the direct mapping relationship from the mission to the weapon system.In the latest service-oriented research,the introduction of service modules to build a service-oriented,flexible,and combinable structure is an important trend.This paper proposes a service-oriented weapon system portfolio selection method,by introducing service to serve as an intermediary to connect missions and system selection,and transferring the weapon system selection into the service portfolio selection.Specifically,the relation between the service and the task is described through the service-task mapping matrix;and the relation between the service and the weapon system is constructed through the servicesystem mapping matrix.The service collaboration network to calculate the flexibility and connectivity of each service portfolio is then established.Through multi-objective programming,the optimal service portfolios are generated,which are further decoded into weapon system portfolios.

System portfolio selection based on GRA method under hesitant fuzzy environment

The hesitant fuzzy set(HFS) is an important tool to deal with uncertain and vague information.In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data;it is usually described by qualitative information and expressed as multiple possible values.We propose a method of equipment system portfolio selection under hesitant fuzzy environment.The hesitant fuzzy element(HFE) is used to describe the index and attribute values of the equipment system.The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system.The hesitant fuzzy grey relational analysis(GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree.Based on the score and hesitation degree of the equipment system,two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.

Weapon system portfolio selection based on structural robustness

The system portfolio selection is a fundamental frontier issue in the development planning and demonstration of weapon equipment.The scientific and reasonable development of the weapon system portfolio is of great significance for optimizing the design of equipment architecture,realizing effective resource allocation,and increasing the campaign effectiveness of integrated joint operations.From the perspective of system-ofsystems,this paper proposes a unified framework called structure-oriented weapon system portfolio selection(SWSPS)to solve the weapon system portfolio selection problem based on structural invulnerability.First,the types of equipment and the relationship between the equipment are sorted out based on the operation loop theory,and a heterogeneous combat network model of the weapon equipment system is established by abstracting the equipment and their relationships into different types of nodes and edges respectively.Then,based on the combat network model,the operation loop comprehensive evaluation index(OLCEI)is introduced to quantitatively describe the structural robustness of the combat network.Next,a weapon system combination selection model is established with the goal of maximizing the operation loop comprehensive evaluation index within the constraints of capability requirements and budget limitations.Finally,our proposed SWSPS is demonstrated through a case study of an armored infantry battalion.The results show that our proposed SWSPS can achieve excellent performance in solving the weapon system portfolio selection problem,which yields many meaningful insights and guidance to the future equipment development planning.

Portfolio selection: a fuzzy-ANP approach

This study developed specific criteria and a fuzzy analytic network process(FANP)to assess and select portfolios on the Tehran Stock Exchange(TSE).Although the portfolio selection problem has been widely investigated,most studies have focused on income and risk as the main decision-making criteria.However,there are many other important criteria that have been neglected.To fill this gap,first,a literature review was conducted to determine the main criteria for portfolio selection,and a Likert-type questionnaire was then used to finalize a list of criteria.Second,the finalized criteria were applied in an FANP to rank 10 different TSE portfolios.The results indicated that profitability,growth,market,and risk are the most important criteria for portfolio selection.Additionally,portfolios 6,7,2,4,8,1,5,3,9,and 10(A6,A7,A2,A4,A8,A1,A5,A3,A9,and A10)were found to be the best choices.Implications and directions for future research are discussed.

Scenario-based approach for project portfolio selection in army engineering and manufacturing development

The decisions concerning portfolio selection for army engineering and manufacturing development projects determine the benefit of those projects to the country concerned.Projects are typically selected based on ex ante estimates of future return values,which are usually difficult to specify or only generated after project launch.A scenario-based approach is presented here to address the problem of selecting a project portfolio under incomplete scenario information and interdependency constraints.In the first stage,the relevant dominance concepts of scenario analysis are studied to handle the incomplete information.Then,a scenario-based programming approach is proposed to handle the interdependencies to obtain the projects,whose return values are multi-criteria with interval data.Finally,an illustrative example of army engineering and manufacturing development shows the feasibility and advantages of the scenario-based multi-objective programming approach.