A vague-set-based fuzzy multi-objective decision making model for bidding purchase

A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans according to their experience and preferences, and these assessments may be expressed as linguistic terms, which are then converted to fuzzy numbers. The resulting decision matrices are then transformed to objective membership grade matrices. The lower bound of satisfaction and upper bound of dissatisfaction are used to determine each bidding plan’s supporting, opposing, and neutral objective sets, which together determine the vague value of a bidding plan. Finally, a score function is employed to rank all bidding plans. A new score function based on vague sets is introduced in the model and a novel method is presented for calculating the lower bound of sat- isfaction and upper bound of dissatisfaction. In a vague-set-based fuzzy multi-objective decision making model, different valua- tions for upper and lower bounds of satisfaction usually lead to distinct ranking results. Therefore, it is crucial to effectively contain DMs’ arbitrariness and subjectivity when these values are determined.

Improved Fuzzification Method for Multi-Objective Decision-Making and Its Application in Evaluation of Highway Planning

A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.

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.

A multi-objective decision-making method for the treatment scheme of landslide hazard

The treatment engineering of landslide hazard is a complicated systemengineering. The selecting treatment scheme is influenced by many factors such as technology,economics, environment, and risk. The decision-making of treatment schemes of landslide hazard is aproblem of comprehensive judgment with multi-hierarchy and multi-objective. The traditional analysishierarchy process needs identity test. The traditional analysis hierarchy process is improved bymeans of optimal transfer matrix here. An improved hierarchy decision-making model for the treatmentof landslide hazard is set up. The judgment matrix obtained by the method can naturally meet therequirement of identity, so the identity test is not necessary. At last, the method is applied tothe treatment decision-making of the dangerous rock mass at the Slate Mountain, and its applicationis discussed in detail.

Control Method of Effect of Robust Optimization in Multi-Player Multi-Objective Decision-Making

In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on as the background of this research. They deal with the common quantities of their products, but due to their different environments, the optimal production quantity of one part can be unacceptable to another part and it may suffer a heavy loss. To avoid that kind of unacceptable situations, the common production quantities should be acceptable to all parts in one supply chain. Therefore, the motivation of this research is the necessity of the method to find the production quantities that make all decision makers acceptable is needed. However, it is difficult to find the production quantities that make all decision makers acceptable. Moreover, their acceptable ranges do not always have common ranges. In the decision making of car design, there are similar situations to this type of decision making. The performance of a car consists of purposes such as fuel efficiency, size and so on. Improving one purpose makes another worse and the relationship between these purposes is tradeoff. In these cases, Suriawase process is applied. This process consists of negotiations and reviews of the requirements of the purposes. In the step of negotiations, the requirements of the purposes are share among all decision makers and the solution that makes them as satisfied as possible. In the step of reviews of the requirements, they are reviewed based on the result of the negotiation if the result is unacceptable to some of decision makers. Therefore, through the iterations of the two steps, the solution that makes all decision makers satisfied is obtained. However, in the previous research, the effects that one decision maker reviews requirements in Suriawase process are quantified, but the mathematical model to modify the ranges of production quantities of all decision makers simultaneously is not shown. Therefore, in this research, based on Suriawase process, the mathematical model of multi-player multi-objective decision making is proposed. The mathematical model of multi-player multi-objective decision making by using linear physical programming (LPP) and robust optimization (RO) in the previous research is the basis of the methods of this research. LPP is one of the multi-objective optimization methods and RO is used to make the balance of the preference levels among decision makers. In LPP, the preference ranges of all objective functions are needed, so as the hypothesis of this research. In the research referred in this research, the method to control the effect of RO is not shown. If the effect of RO is too big, the average of the preference level becomes worse. The purpose of this research is to reproduce the mathematical model of multi-player multi-objective decision making based on Suriawase process and propose the method to control the effect of RO. In the proposed model, a set of the solutions of the negotiation problem is obtained and it is proved by the result of the numerical experiment. Therefore, the conclusion that the proposed model is available to obtain a set of the solutions of the negotiation problems in supply chain.

Multi-Objective Optimization Algorithm for Grouping Decision Variables Based on Extreme Point Pareto Frontier

The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Build orientation determination of multi-feature mechanical parts in selective laser melting via multi-objective decision making

Selective laser melting(SLM)is a unique additive manufacturing(AM)category that can be used to manufacture mechanical parts.It has been widely used in aerospace and automotive using metal or alloy powder.The build orientation is crucial in AM because it affects the as-built part,including its part accuracy,surface roughness,support structure,and build time and cost.A mechanical part is usually composed of multiple surface features.The surface features carry the production and design knowledge,which can be utilized in SLM fabrication.This study proposes a method to determine the build orientation of multi-feature mechanical parts(MFMPs)in SLM.First,the surface features of an MFMP are recognized and grouped for formulating the particular optimization objectives.Second,the estimation models of involved optimization objectives are established,and a set of alternative build orientations(ABOs)is further obtained by many-objective optimization.Lastly,a multi-objective decision making method integrated by the technique for order of preference by similarity to the ideal solution and cosine similarity measure is presented to select an optimal build orientation from those ABOs.The weights of the feature groups and considered objectives are achieved by a fuzzy analytical hierarchy process.Two case studies are reported to validate the proposed method with numerical results,and the effectiveness comparison is presented.Physical manufacturing is conducted to prove the performance of the proposed method.The measured average sampling surface roughness of the most crucial feature of the bracket in the original orientation and the orientations obtained by the weighted sum model and the proposed method are 15.82,10.84,and 10.62μm,respectively.The numerical and physical validation results demonstrate that the proposed method is desirable to determine the build orientations of MFMPs with competitive results in SLM.

Stability Analysis and Efficiency Improvement of a Multi-converter System Using Multi-objective Decision Making

Multi-converter system is mainly used in advanced automotive systems.Different converters and inverters are taking part in automotive systems to provide different voltage levels in a multi-converter system.It involves constant voltage load(CVL),constant power load(CPL)and other loads.The CPL in such systems offers negative impedance characteristic and it creates a destabilizing effect on the main converter.The effect of destabilization can be reduced by increasing the CVL or inserting parasitic components.Attempts have been made by authors to improve the stability by using parasitics of different components such as switch,diode and inductor.Influence of insertion of parasitics including the series equivalent resistance of the filter capacitor and variation in CVL on the performance of main converter is mathematically analyzed and conflicting behavior between system stability and efficiency is observed.The optimum solution between these two functions is obtained by using multi-objective decision making(MODM)by varying parasitics of different components and CVL.An attempt has been made to demonstrate the effect of CVL load and the parasitics on the stability and efficiency of the main converter,experimentally.

Stress-assisted corrosion mechanism of 3Ni steel by using gradient boosting decision tree machining learning method

Traditional 3Ni weathering steel cannot completely meet the requirements for offshore engineering development,resulting in the design of novel 3Ni steel with the addition of microalloy elements such as Mn or Nb for strength enhancement becoming a trend.The stress-assisted corrosion behavior of a novel designed high-strength 3Ni steel was investigated in the current study using the corrosion big data method.The information on the corrosion process was recorded using the galvanic corrosion current monitoring method.The gradi-ent boosting decision tree(GBDT)machine learning method was used to mine the corrosion mechanism,and the importance of the struc-ture factor was investigated.Field exposure tests were conducted to verify the calculated results using the GBDT method.Results indic-ated that the GBDT method can be effectively used to study the influence of structural factors on the corrosion process of 3Ni steel.Dif-ferent mechanisms for the addition of Mn and Cu to the stress-assisted corrosion of 3Ni steel suggested that Mn and Cu have no obvious effect on the corrosion rate of non-stressed 3Ni steel during the early stage of corrosion.When the corrosion reached a stable state,the in-crease in Mn element content increased the corrosion rate of 3Ni steel,while Cu reduced this rate.In the presence of stress,the increase in Mn element content and Cu addition can inhibit the corrosion process.The corrosion law of outdoor-exposed 3Ni steel is consistent with the law based on corrosion big data technology,verifying the reliability of the big data evaluation method and data prediction model selection.

Cognitive interference decision method for air defense missile fuze based on reinforcement learning

To solve the problem of the low interference success rate of air defense missile radio fuzes due to the unified interference form of the traditional fuze interference system,an interference decision method based Q-learning algorithm is proposed.First,dividing the distance between the missile and the target into multiple states to increase the quantity of state spaces.Second,a multidimensional motion space is utilized,and the search range of which changes with the distance of the projectile,to select parameters and minimize the amount of ineffective interference parameters.The interference effect is determined by detecting whether the fuze signal disappears.Finally,a weighted reward function is used to determine the reward value based on the range state,output power,and parameter quantity information of the interference form.The effectiveness of the proposed method in selecting the range of motion space parameters and designing the discrimination degree of the reward function has been verified through offline experiments involving full-range missile rendezvous.The optimal interference form for each distance state has been obtained.Compared with the single-interference decision method,the proposed decision method can effectively improve the success rate of interference.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

A modified back analysis method for deep excavation with multi-objective optimization procedure

Real-time prediction of excavation-induced displacement of retaining pile during the deep excavation process is crucial for construction safety.This paper proposes a modified back analysis method with multi-objective optimization procedure,which enables a real-time prediction of horizontal displacement of retaining pile during construction.As opposed to the traditional stage-by-stage back analysis,time series monitoring data till the current excavation stage are utilized to form a multi-objective function.Then,the multi-objective particle swarm optimization (MOPSO) algorithm is applied for parameter identification.The optimized model parameters are immediately adopted to predict the excavation-induced pile deformation in the continuous construction stages.To achieve efficient parameter optimization and real-time prediction of system behavior,the back propagation neural network (BPNN) is established to substitute the finite element model,which is further implemented together with MOPSO for automatic operation.The proposed approach is applied in the Taihu tunnel excavation project,where the effectiveness of the method is demonstrated via the comparisons with the site monitoring data.The method is reliable with a prediction accuracy of more than 90%.Moreover,different optimization algorithms,including non-dominated sorting genetic algorithm (NSGA-II),Pareto Envelope-based Selection Algorithm II (PESA-II) and MOPSO,are compared,and their influences on the prediction accuracy at different excavation stages are studied.The results show that MOPSO has the best performance for high dimensional optimization task.

A Class of Optimization Method for Bilevel Multi-objective Decision Making Problem with the Help of Satisfactoriness

In the paper, it is discussed that the method on how to transform the multi-person bilevel multi-objective decision making problem into the equivalent generalized multi-objective decision making problem by using Kuhn-Tucker sufficient and necessary condition. In order to embody the decision maker′s hope and transform it into single-objective decision making problem with the help of ε-constraint method. Then we can obtain the global optimal solution by means of simulated annealing algorithm.

Attribute Reduction Method Based on Sequential Three-Branch Decision Model

Attribute reduction is a research hotspot in rough set theory. Traditional heuristic attribute reduction methods add the most important attribute to the decision attribute set each time, resulting in multiple redundant attribute calculations, high time consumption, and low reduction efficiency. In this paper, based on the idea of sequential three-branch decision classification domain, attributes are treated as objects of three-branch division, and attributes are divided into core attributes, relatively necessary attributes, and unnecessary attributes using attribute importance and thresholds. Core attributes are added to the decision attribute set, unnecessary attributes are rejected from being added, and relatively necessary attributes are repeatedly divided until the reduction result is obtained. Experiments were conducted on 8 groups of UCI datasets, and the results show that, compared to traditional reduction methods, the method proposed in this paper can effectively reduce time consumption while ensuring classification performance.

A reduced combustion mechanism of ammonia/diesel optimized with multi-objective genetic algorithm

For the deep understanding on combustion of ammonia/diesel,this study develops a reduced mechanism of ammonia/diesel with 227 species and 937 reactions.The sub-mechanism on ammonia/interactions of N-based and C-based species(N—C)/NOx is optimized using the Non-dominated Sorting Genetic Algorithm II(NSGA-II)with 200 generations.The optimized mechanism(named as 937b)is validated against combustion characteristics of ammonia/methane(which is used to examine the accuracy of N—C interactions)and ammonia/diesel blends.The ignition delay times(IDTs),the laminar flame speeds and most of key intermediate species during the combustion of ammonia/methane blends can be accurately simulated by 937b under a wide range of conditions.As for ammonia/diesel blends with various diesel energy fractions,reasonable predictions on the IDTs under pressures from 1.0 MPa to5.0 MPa as well as the laminar flame speeds are also achieved by 937b.In particular,with regard to the IDT simulations of ammonia/diesel blends,937b makes progress in both aspects of overall accuracy and computational efficiency,compared to a detailed ammonia/diesel mechanism.Further kinetic analysis reveals that the reaction pathway of ammonia during the combustion of ammonia/diesel blend mainly differs in the tendencies of oxygen additions to NH_2 and NH with different equivalence ratios.

Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

Multi-objective global optimization approach predicted quasi-layered ternary TiOS crystals with promising photocatalytic properties

Titanium dioxide(TiO_(2))has attracted considerable research attentions for its promising applications in solar cells and photocatalytic devices.However,the intrinsic challenge lies in the relatively low energy conversion efficiency of TiO_(2),primarily attributed to the substantial band gaps(exceeding 3.0 eV)associated with its rutile and anatase phases.Leveraging multi-objective global optimization,we have identified two quasi-layered ternary Ti-O-S crystals,composed of titanium,oxygen,and sulfur.The calculations of formation energy,phonon dispersions,and thermal stability confirm the chemical,dynamical and thermal stability of these newly discovered phases.Employing the state-of-art hybrid density functional approach and many-body perturbation theory(quasiparticle GW approach and Bethe-Salpeter equation),we calculate the optical properties of both the TiOS phases.Significantly,both phases show favorable photocatalytic characteristics,featuring band gaps suitable for visible optical absorption and appropriate band alignments with water for effective charge carrier separation.Therefore,ternary compound TiOS holds the potential for achieving high-efficiency photochemical conversion,showing our multi-objective global optimization provides a new approach for novel environmental and energy materials design with multicomponent compounds.

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.

DeepSurNet-NSGA II:Deep Surrogate Model-Assisted Multi-Objective Evolutionary Algorithm for Enhancing Leg Linkage in Walking Robots

This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.