Fuzzy Multi-objective Optimization Research Articles

A Sustainable Production Planning Scheme for New Energy Vehicles in China

The carbon emissions of new energy vehicles (NEVs)have transited from the use stage to the production stage, indicating that the environmental impact of NEVs in the manufacturing stage cannot be ignored. To reduce carbon emissions and maintain profits, this study proposes a fuzzy multi-objective optimization model to achieve a sustainable production planning scheme for NEVs. The proposed model not only considers the maximum profits of automobile enterprises but also the minimum target of carbon emissions in the production process, to coordinate the optimal production quantity. The results show that the output of NEVs in different price ranges has different proportions. The market share of blade electric vehicles is the highest, accounting for 39% of the NEV market, and the proportion of plug-in hybrid and blade electric vehicles is increasing. The sensitivity analysis further reflects the impact of government subsidy “recession” and body lightweight on the output, carbon emissions, and annual profits of NEVs in China. Accordingly, this paper provides policy implications for achieving a sustainable production planning scheme for NEVs in China.

A Two Phases Multiobjective Trajectory Optimization Scheme for Multi-UGVs in the Sight of the First Aid Scenario.

Timely delivery of first aid supplies is significant to saving lives when an accident happens. Among the promising solutions provided for such scenarios, the application of unmanned vehicles has attracted ever more attention. However, such scenarios are often very complex, while the existing studies have not fully addressed the trajectory optimization problem of multiple unmanned ground vehicles (multi-UGVs) against the scenario. This study focuses on multi-UGVs trajectory optimization in the sight of first aid supply delivery tasks in mass accidents. A two-stage completely decoupling fuzzy multiobjective optimization strategy is designed. On the first stage, with the proposed timescale involved tridimensional tunneled collision-free trajectory (TITTCT) algorithm, collision-free coarse tunnels are build within a tridimensional coordinate system, respectively, for the UGVs as the corresponding configuration space for a further multiobjective optimization. On the second stage, a fuzzy multiobjective transcription method is designed to solve the decoupled optimal control problem (OCP) within the configuration space with the consideration of priority constrains. Following the two-stage design, the computational time is significantly reduced when achieving an optimal solution of the multi-UGV trajectory planning, which is crucial in a first aid task. In addition, other objectives are optimized with the aspiration level reflected. Simulation studies and experiments have been curried out to testify the effectiveness and the improved computational performance of the proposed design.

Numerical modelling using fuzzy multi-objective optimisation for environmental sustainability in green supply chain manufacturing

Numerical modelling using fuzzy multi-objective optimisation for environmental sustainability in green supply chain manufacturing

Sustainable crude oil desulfurization: A multi-objective fuzzy optimization for pollution prevention

The ultrasonic-assisted oxidative desulfurization (UAOD) process is employed to mitigate the environmental impact of sulfur emissions. Previous studies have focused on evaluating the efficiency of crude oil UAOD. This research assesses the desulfurization efficiency encompassing irradiation time, ultrasonic power, and oxidant amount, as well as the corresponding operational expenses, to ascertain the optimal conditions. The research employed a multi-objective fuzzy optimization (MOFO) method to assess the operational expenses of crude oil UAOD. It established the upper and lower limits and subsequently optimized the operational costs and desulfurization efficiency while accounting for uncertainties. The fuzzy model optimized the level of satisfaction on a scale from 0 (unsatisfied) to 1 (satisfied) using the max-min aggregation. The degree of satisfaction slightly decreased to 55.49 %, achieved under optimal conditions of 739.70 W ultrasonic power, 6.70 min irradiation, and 8.47 mL oxidant. This configuration yielded a desulfurization efficiency (YA) of 63.24 % at 2.02 USD/L. Compared to existing literature, the desulfurization of crude oil was found to be less efficient and less expensive. The outcomes presented by MOFO showcase economic feasibility with reduced overall operating expenses and simplified process conditions and provide valuable insights for optimizing potential large-scale UAOD processes.

Advancing gasoline desulfurization: Multi-objective fuzzy optimization in systems technology

Ultrasonic-assisted oxidative desulfurization (UAOD) is utilized to lessen environmental problems due to sulfur emissions. The process uses immiscible polar solvents and ultrasonic waves to enhance desulfurization efficiency. Prior research focused on comparing the effectiveness of UAOD for gasoline using response surface methodology. This study evaluates the desulfurization efficiency and operating costs, including ultrasonic power, irradiation time, and oxidant amount to determine optimal conditions. The study used a multi-objective fuzzy optimization (MOFO) approach to evaluate the economic viability of UAOD for gasoline. It identified upper and lower boundaries and then optimized the desulfurization efficiency and operating costs while considering uncertainty errors. The fuzzy model employed max-min aggregation to optimize the degree of satisfaction on a scale from 0 (unsatisfied) to 1 (satisfied). Optimal conditions for gasoline UAOD were found at 445.43 W ultrasonic power, 4.74 min irradiation time, and 6.73 mL oxidant, resulting in a 66.79 % satisfaction level. This yielded a 78.64 % desulfurization efficiency (YA) at an operating cost of 13.49 USD/L. Compared to existing literature, gasoline desulfurization was less efficient and less costly. The solutions provided by MOFO demonstrate not only economic viability through decreased overall operating costs and simplified process conditions, but also offer valuable insights for optimizing prospective future industrial-scale UAOD processes.

Multi-objective fuzzy green scheduling optimization method of special vehicle body-in-white prototype shop considering equipment preventive maintenance

Based on the advantages of non-contact, flexibility, and small heat-affected zone, laser processing technology is widely used in material removal, addition, modification and other manufacturing fields. However, the emission of large amounts of smoke during laser processing of metal materials will result in environmental pollution in the job shop. Additionally, the processing time of laser equipment becomes uncertain as the power decays with prolonged use. Therefore, this paper is mainly focus on a multi-objective flexible job shop fuzzy green scheduling problem to minimize the fuzzy makespan, fuzzy total energy consumption and fuzzy total smoke emission. To solve it, an improved multi-objective particle swarm optimization algorithm has been designed. Firstly, a preventive maintenance strategy is proposed to reduce the makespan and equipment failure frequency by considering periodic power attenuation of laser equipment. Next, different particle updating strategies are employed to enhance particles’ exploration capabilities. Subsequently, five neighborhood structures are introduced to improve the performance of local search. Finally, comparison experiments are conducted with an expanded common benchmark, and a production case study in a special vehicle body-in-white prototype job shop. The results effectively demonstrate the feasibility and effectiveness of the developed model and improved multi-objective particle swarm optimization algorithm.

A Probability-based Fuzzy Multi-objective Optimization for Material Selection

Abstract: In the present paper, a rational fuzzy multi-objective optimization for material selection is developed in respect of probabilistic method for multi-objective optimization, which agrees with the viewpoint of system theory for the whole optimization of a system and is the novelty of this work. The basic ideas and algorithms of fuzzy theory together with probability theory are taken as the cornerstone to perform the formulation. In the treatment, the intersection of the membership function of fuzzy numbers of alternative material performance and the membership function of fuzzy numbers of desired material performance is used as the utility of the material performance index. Thereafter, the utility of each material performance index is further used to conduct the assessment of its partial preferable probability and formulate the multi-objective optimization by means of probability theory. Moreover, a typical example is presented to provide the rational process of the probabilistic fuzzy multi-objective optimization for material selection.

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α-level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients.

A note on “A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem”

Moges et al. (Inf. Sci. 625 (2023) 457–475) proposed a method to find a Pareto-optimal solution (POS) of intuitionistic fuzzy multi-objective linear fractional optimization problem (MOLFOP). In this method, firstly, an intuitionistic fuzzy MOLFOP is transformed into a crisp MOLFOP with the help of a ranking function. Then, using the existing method (Fuzzy Sets Syst. 125 (2002) 335–342), the transformed crisp MOLFOP is transformed into a crisp multi-objective linear optimization problem (MOLOP). Finally, it is assumed that to find a POS of the considered intuitionistic fuzzy MOLFOP is equivalent to find a POS of the transformed crisp MOLOP. It is pertinent to mention that this assumption is valid only if the transformed crisp MOLFOP is equivalent to the considered intuitionistic fuzzy MOLFOP as well as the transformed crisp MOLOP is equivalent to the transformed crisp MOLFOP. In this note, a numerical example is considered to show that the transformed crisp MOLFOP is not equivalent to the considered intuitionistic fuzzy MOLFOP. Also, on the basis of the existing results (Fuzzy Sets Syst. 246 (2014) 156–159), it is pointed out that the transformed crisp MOLOP is not equivalent to the transformed crisp MOLFOP. Therefore, Moges et al.’s method is not valid and hence, the results of agricultural planning problem of Ethopia for cultivation of different crops, obtained by Moges et al. with their proposed method, are not correct.

A comparative study of fuzzy multi-objective investment project portfolio selection and optimization based on financial return and different risk measurements

Competitiveness in the global market is getting more intense. Due to resource and budget constraints, firms need to achieve their expected goals and satisfy all investment constraints under uncertainty. Selecting the set of projects among other candidates to get the most efficient portfolio requires a lot of attention from the Decision Makers (DMs) as this consideration no longer relies purely on the financial term. This problem becomes a multi-objective problem under uncertainty where the financial return and risk from uncertainty are required into the trading off consideration. Due to the financial uncertainty, the chance-constrained programming has been employed in this study for defuzzifying and solving uncertain optimization problems at a specified confidence level that is defined by the DMs. Then, various kinds of investment or financial risk measures, Lower-Semi Variance Index (LSVI), the absolute deviation with the expected FNPV, and the absolute mean-Conditional Value at Risk (CVaR) gap are provided in the selection of such risk measures to show their differences in characteristics and performances in the obtained results. Since, such problems can consist of many project candidates and complex constraints, which may grow beyond the application of the exact optimization approach, a meta-heuristic method, Genetic Algorithm (GA), is introduced to optimize this problem through designing and constructing a decision support tool for the investment portfolio selection and optimization. The applicability of the proposed comparative approach and the constructed tool are illustrated through examples.

Arsenate removal using chitosan-coated bentonite via fixed-bed system: a process integration by fuzzy optimization.

Groundwater contamination is a global concern that has detrimental effect on public health and the environment. Sustainable groundwater treatment technologies such as adsorption require attaining a high removal efficiency at a minimal cost. This study investigated the adsorption of arsenate from groundwater utilizing chitosan-coated bentonite (CCB) under a fixed-bed column setup. Fuzzy multi-objective optimization was applied to identify the most favorable conditions for process variables, including volumetric flow rate, initial arsenate concentration, and CCB dosage. Empirical models were employed to examine how initial concentration, flow rate, and adsorbent dosage affect adsorption capacity at breakthrough, energy consumption, and total operational cost during optimization. The ε-constraint process was used in identifying the Pareto frontier, effectively illustrating the trade-off between adsorption capacity at breakthrough and the cost of the fixed-bed system. The integration of fuzzy optimization for adsorption capacity and its total operating cost utilized the global solver function in LINGO 20 software. A crucial equation derived from the Box-Behnken design and a cost equation based on energy and material usage in the fixed-bed system was employed. The results from identifying the Pareto front determined boundary limits for adsorption capacity at breakthrough (ranging from 12.96 ± 0.19 to 12.34 ± 0.42μg/g) and total operating cost (ranging from 955.83 to 1106.32 USD/kg). An overall satisfaction level of 35.46% was achieved in the fuzzy optimization process. This results in a compromise solution of 12.90μg/g for adsorption capacity at breakthrough and 1052.96 USD/kg for total operating cost. Henceforth, this can allow a suitable strategic decision-making approach for key stakeholders in future applications of the adsorption fixed-bed system.

An integrated group decision making framework for business performance evaluation of performing arts enterprises with probabilistic hesitant fuzzy IDOCRIW-MOOSRA method

There is a lack of domestic and foreign research on the evaluation and improvement strategies of business performance of performing arts enterprises, especially in the context of the “restructuring” of cultural groups in China. Most of the existing studies are distributed in bulk, not only lacking in theoretical depth, but also lacking in systematization to a certain extent, which shows that the existing studies have not fully formed a mature and valuable theoretical system. The business performance evaluation of performing arts enterprises is a multiple attributes group decision making (MAGDM). This paper constructs a novel probabilistic hesitant fuzzy Multi-Objective Optimization Simple Ratio Analysis (PHF-MOOSRA) model based on the integrated determination of objective criteria weights (IDOCRIW) under the probabilistic hesitant fuzzy sets (PHFSs) for this issue. The PHFSs provides an evaluation circumstance containing more information which make the final decision-making results more accurately. Additionally, the IDOCRIW method separately and the MOOSRA method based on the MOORA method is proposed in PHFSs circumstance in this model. In the end, this model is then applied in a numerical case study for business performance evaluation of performing arts enterprises and compare this model with other existing methods.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

An iterative approach for the solution of fully fuzzy linear fractional programming problems via fuzzy multi-objective optimization

<abstract><p>The primary goal of optimization theory is to formulate solutions for real-life challenges that play a fundamental role in our daily lives. One of the most significant issues within this framework is the Linear Fractional Programming Problem (LFrPP). In practical situations, such as production planning and financial decision-making, it is often feasible to express objectives as a ratio of two distinct objectives. To enhance the efficacy of these problems in representing real-world scenarios, it is reasonable to utilize fuzzy sets for expressing variables and parameters. In this research, we have worked on the Fully Fuzzy Linear Fractional Linear Programming Problem (FFLFrLPP). In our approach to problem-solving, we simplified the intricate structure of the FFLFrLPP into a crisp Linear Programming Problem (LPP) while accommodating the inherent fuzziness. Notably, unlike literature, our proposed technique avoided variable transformation, which is highly competitive in addressing fuzzy-based problems. Our methodology also distinguishes itself from the literature in preserving fuzziness throughout the process, from problem formulation to solution. In this study, we conducted a rigorous evaluation of our proposed methodology by applying it to a selection of numerical examples and production problems sourced from the existing literature. Our findings revealed significant improvements in performance when compared to established solution approaches. Additionally, we presented comprehensive statistical analyses showcasing the robustness and effectiveness of our algorithms when addressing large-scale problem instances. This research underscores the innovative contributions of our methods to the field, further advancing the state-of-the-art in problem-solving techniques.</p></abstract>

An integrated model for rice supplier selection strategies and a comparative analysis of fuzzy multicriteria decision-making approaches based on the fuzzy entropy weight method for evaluating rice suppliers.

Rice, being a staple food in many countries, necessitates the identification of reliable suppliers to ensure a steady supply. Consequently, it is vital to establish trustworthy vendors for various types of this essential grain who can meet stringent product quality standards. This study aims to identify, analyze, rank, and select primary rice suppliers. The study emphasizes the importance of selecting and managing suitable providers to meet customer demands, proposes a ranking model for rice suppliers, and introduces developed fuzzy MCDM techniques. It proposes an integrated model for selecting rice suppliers, considering factors related to the processes before, during, and after selecting providers within a defined framework. The outcomes shows that rice supplier selection strategy can efficiently identify reliable rice suppliers, improve buyer value, reduce procurement risk, enhance efficiency, and establish strong supply chain relationships in complex decision-making processes. To assess suppliers, the study introduces two advanced integrated approaches and compares them. The fuzzy entropy weight method (EWM) was used to determine the criteria weights. The ranking of rice suppliers was achieved using a fuzzy multi-objective optimization based on ratio analysis (MOORA), fuzzy complex proportional assessment (COPRAS), and combinations of these two methods in different approaches. The methodology supports decision-makers in a rapidly evolving global environment by assisting importers, traders, suppliers, procurement, and logistics management, particularly for non-rice-cultivating countries in rice importation and supplier selection. The numerical analysis is grounded in a real-world case study of selecting rice suppliers in Jordan. The findings reveal that the various strategies yield both similar and different results. Furthermore, the integrated method is considered the most accurate for evaluating rice imports and suppliers, aligning closely with the reality of the current situation.

New preference order relationships and their application to multiobjective interval and fuzzy interval optimization problems

Recently, a method to generate preference ordering relationships in interval space, which is based on a family of automorphisms in bidimensional Euclidean space, and the family of φ-interval optimization problems were introduced in the literature. In this article both the method to generate preference ordering relationships in interval space and the family of φ-interval optimization problems are generalized, providing frameworks for dealing with families of multiobjective interval and multiobjective fuzzy interval optimization problems called the family of φ-multiobjective interval optimization problems and the family of φ-multiobjective fuzzy interval optimization problems, respectively. It is shown that those multiobjective interval and multiobjective fuzzy interval optimization problems presented in the literature, whose formulations are based on a given preference order relationship, can be seen as particular cases of a φ-multiobjective interval optimization problem and of a φ-multiobjective fuzzy interval optimization problems, respectively. Some optimality conditions for both these two families of optimization problems are provided and the methods, concepts and results presented herein are illustrated by several examples.

Integrated energy system scheduling model based on non-complete interval multi-objective fuzzy optimization

Integrated energy system scheduling model based on non-complete interval multi-objective fuzzy optimization

Robust optimization of multi-objective multi-cycle remanufacturing supply chain network considering incentive compatibility theory under improved algorithm

In recent years, industrial production and transportation have generated a significant amount of carbon emissions, leading to a heightened focus on environmental resource conservation. Concurrently, with the development of internet technologies, an increasing number of enterprises are leveraging big data and artificial intelligence for production and logistics. Within this context, the challenge of how enterprises can utilize big data services to reduce costs while minimizing carbon emissions has become a pressing concern. Meanwhile, remanufacturing, as a sustainable solution, has garnered substantial attention. However, remanufacturing supply chain networks become exceptionally complex and challenging when faced with uncertainties in demand and recovery quantities, necessitating government intervention. Thus, to examine the impact of government intervention on the optimization of green remanufacturing supply chain networks, this paper, based on incentive compatibility theory, establishes an optimization function with objectives of minimizing total cost, reducing carbon emissions, and maximizing return on data investment in scenarios marked by uncertain market demand and recovery quantities. It constructs multi-objective fuzzy optimization models for various scenarios. The paper employs improved robust optimization to address uncertainties related to demand and recovery quantities. It also utilizes the Improved Multi-Objective Genetic Algorithm (IMOGA) to address multi-objective optimization, addressing the limitations of Genetic Algorithms (GA) and Multi-Community particle swarm optimization (MPSO). Case study results indicate that robust optimization effectively handles uncertainties in the model, aligning better with real-world conditions. High-tech enterprises often prioritize economic objectives, and government intervention measures can compensate for their limited carbon reduction capabilities. In most cases, the improved multi-objective genetic algorithm (IMOGA) outperforms MPSO and GA in terms of performance. In the context of the evolving internet landscape, high-tech enterprises should harness big data and artificial intelligence to establish green remanufacturing supply chain networks. Simultaneously, government guidance to reduce carbon emissions is instrumental in enhancing corporate competitiveness and industrial upgrading.

Streamlining extracellular polymeric substance removal: Fuzzy multi-objective optimization of ultrasonic-Fenton treatment

Managing high water content sludge in wastewater treatment is crucial for sustainability. This involves a complex challenge of maximizing the removal of loosely bound extracellular polymeric substances (LB-EPS) while minimizing ultrasonic-Fenton process costs. This study introduces a novel approach to address these conflicting objectives by adopting fuzzy multi-objective optimization. This method reconciles the conflicting objectives by identifying the optimal conditions for ferrous ion (Fe2+) dosage, hydrogen peroxide (H2O2) dosage, and ultrasonication time. The optimization model incorporates empirical equations that define the effects of Fenton’s reagent and ultrasonication on LB-EPS removal, as well as considerations for material and electricity usage costs and the cumulative uncertainties associated with experimental runs. To effectively capture the trade-offs between EPS removal and process costs, the ɛ -constraint method was utilized to delineate the Pareto front. This approach significantly enhances LB-EPS removal from anaerobically digested sludge and establishes boundary limits within the Pareto front for practical application within the context of fuzzy optimization. The optimized solution derived from this innovative approach resulted in the conditions of 10 mM Fe2+ dosage, 100 mM H2O2 dosage, and 10 min of ultrasonication. This configuration achieves an impressive 60.7% ± 3.7% LB-EPS removal while maintaining a cost of 26.6 USD/L and ensuring 100% overall satisfaction. This research represents a significant advancement in sludge dewatering strategies. It underscores the pivotal role of innovative decision-making approaches in advancing the field of sludge dewatering methodologies for more sustainable wastewater treatment practices.

A fuzzy multi-objective optimization model for sustainable healthcare supply chain network design

Healthcare supply chains play a crucial role, which enables the implementation of optimization strategies that have rapidly emerged as highly effective means for improving the overall structure of pharmaceutical and healthcare supply chains.. In the healthcare industry, parameters such as increasing the quality of service, as well as optimizing costs, environmental, and social factors play a unique role in supply chain management. To improve the healthcare supply chain network, this study proposed a novel optimization model to optimize multiple objectives, including minimizing the total costs and environmental impacts, while maximizing the social factors by creating jobs simultaneously. To address the effects of uncertain parameters, a fuzzy optimization method alongside the multi-objective gray wolf optimizer (MOGWO), non-dominated sorting genetic algorithm II (NSGA-II), multi-objective differential evolution algorithm (MODEA), and ε-constraint are applied to optimize the model. Also, a case study of the pharmaceutical industry demonstrates the model's efficacy in a real-life context. The numerical results show the MOGWO manages to create high-quality Pareto solutions with a good spread at the Pareto boundary within a short time compared to the ε-constraint approach. Further, it has shown a more robust performance compared to MODEA and NSGA-II, indicating the efficiency of MOGWO, among other solution methods and other objective indicators.