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ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2021年第46期 34-52页

作者： Song, Yang Yang, Zhihui East China Univ Technol Sch Sci Nanchang 330013 Jiangxi Peoples R China

The solving methodology of matrix games, with payoffs presented by dual hesitant fuzzy sets, is investigated in this paper. Firstly, the notion of dual hesitant fuzzy sets is given. Next, the concept of solutions for the matrix games is defined on the basis of dual hesitant fuzzy sets, which thereby prove the solutions of the matrix games can be obtained through solving a pair of linear programming models. Lastly, a numerical example is given to illustrate the effectiveness of the proposed method.

关键词： matrix games dual hesitant fuzzy set multi-objective programming linear programming

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Strategic vegetable crop distribution in Himachal Pradesh for sustainable economic and environmental outcomes

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Scientific reports 2025年第1期15卷 19437页

作者： Nikhil Chandel S A Wani Mushtaq A Lone Ohud A Alqasem Aafaq A Rather S A Mir Danish Qayoom M Nagy Getachew Tekle Mekiso Oluwafemi Samson Balogun School of Agricultural Economics and Horti-Business Management SKUAST Kashmir Srinagar 190025 India. Directorate of Planning & Monitoring SKUAST Kashmir Srinagar 190025 India. Department of Mathematical Sciences College of Science Princess Nourah bint Abdulrahman University P.O. Box 84428 Riyadh 11671 Saudi Arabia. Symbiosis Statistical Institute Symbiosis International (Deemed University) Pune 411004 India. Department of Statistics and Operations Research King Saud University P.O. Box 2455 11451 Riyadh Saudi Arabia. Wachemo University Hosaina Ethiopia. getachewtekle@wcu.edu.et. Department of Computing University of Eastern Finland 70211 Kuopio Finland.

India, the second-largest global producer of fruits and vegetables, faces challenges in translating productivity into profitability, particularly in vegetable farming. This study examined resource use efficiency in Himachal Pradesh, focusing on optimizing land allocation using multi-objective programming (MOP) to maximize income and employment while minimizing fertilizer and pesticide use. Primary data were gathered from Solan and Sirmaur districts through structured questionnaires employing a multi-stage sampling design. Optimization models were developed annually for marginal, small, and medium farmers over three cropping seasons. The study demonstrated significant productivity, profitability, and sustainability improvements through optimization techniques. For marginal farmers, income increased from Rs 229,359 to Rs 280,058 per hectare, employment peaked at 252 man-days from 190, and fertilizer costs reduced from Rs 6180 to Rs 4420 per hectare, with the MOP approach allocating Chinese cabbage (March-May), cauliflower (August-November), and peas (November-March). Small farmers saw income rise from Rs 238,095 to Rs 296,214 per hectare, employment reaches 263 man-days from 217, and fertilizer costs decrease from Rs 6686 to Rs 3977 per hectare, with the MOP approacgh allocating Chinese cabbage (March-May), beans (August-November), and peas (November-March). For medium farmers, income maximized from Rs 256,071 to Rs 374,673 per hectare, employment at 253 man-days from 219, and fertilizer costs minimized from Rs 7092 to Rs 4428 per hectare, with the MOP approach allocating Chinese cabbage (March-May), beans (August-November), and peas (November-March). The study highlighted the need for efficient resource use and strategic crop selection for sustainable agriculture. Key policy recommendations include targeted support programs, resource efficiency initiatives, customized training, improved access to credit, and infrastructure development. These measures can boost produc

关键词： Agricultural productivity multi-objective programming Optimization Resource use efficiency Vegetable farming

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multi-objective multi-item fixed-charge solid transportation problem under twofold uncertainty

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NEURAL COMPUTING & APPLICATIONS 2019年第12期31卷 8593-8613页

作者： Roy, Sankar Kumar Midya, Sudipta Weber, Gerhard-Wilhelm Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India Middle East Tech Univ Inst Appl Math Ankara Turkey

In this paper, we investigate a multi-objective multi-item fixed-charge solid transportation problem (MOMIFCSTP) with fuzzy-rough variables as coefficients of the objective functions and of the constraints. The main focus of the paper is to analyze MOMIFCSTP under a fuzzy-rough environment for a transporting system. In practical situations, the parameters of a MOMIFCSTP are imprecise in nature, due to several uncontrollable factors. For these reasons, we introduce the fuzzy-rough variables in MOMIFCSTP to tackle vague data which are different from fuzziness and roughness. Fuzzy-rough expected-value operator is employed to convert fuzzy-rough MOMIFCSTP into deterministic MOMIFCSTP. Thereafter, we develop a methodology to solve the deterministic MOMIFCSTP by technique for order preference by similarity to ideal solution (TOPSIS). Three distinct approaches, namely extended TOPSIS, weighted goal programming (WGP) and fuzzy programming, are used to derive Pareto-optimal solution from the suggested model. A comparison is drawn among the optimal solutions which are derived from different approaches. It is observed from the extracted results that TOPSIS provides a better optimal solution than WGP and fuzzy programming. TOPSIS also overcomes some difficulties which arise in WGP. Finally, a real-world (industrial) problem is incorporated to show the applicability and feasibility of the proposed problem.

关键词： Fixed-charge solid transportation problem multi-objective programming Fuzzy-rough variable Twofold uncertainty TOPSIS Fuzzy programming Weighted goal programming

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Monte-Carlo simulation based multi-objective optimum allocation of renewable distributed generation using OpenCL

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ELECTRIC POWER SYSTEMS RESEARCH 2019年第May期170卷 81-91页

作者： Abdelaziz, Morad Moradzadeh, Majid Univ British Columbia Sch Engn Fac Appl Sci Kelowna BC Canada

Monte-Carlo simulation (MCS) is the most accurate technique for considering the stochastic nature of renewable energy resources in power system analysis and planning. However, due to its heavy computational burden, MCS is rarely utilized when solving the multi-objective renewable distributed generation (DG) allocation problem. In order to address this problem, this paper proposes a novel methodology to exploit the massively parallel architecture of graphics processing units (GPU) in a way that enables the use of MCS when solving the multi-objective renewable DG allocation problem. First, the renewable DG allocation problem is formulated as a multi-objective optimization problem to minimize the lines losses and the costs pertaining to installing renewable DG units in the distribution network. Then, a parallelized implementation of NSGA-II using OpenCL is described in details to solve the formulated multi-objective renewable DG planning problem. The feasibility and effectiveness of the proposed methodology are validated using the IEEE 32-bus test system and two real distribution test systems. The results show that the proposed parallelized implementation can enable the use of MCS for modelling the generation and demand uncertainties when solving the multi-objective renewable DG allocation problem using a metaheuristic approach.

关键词： Distribution system High performance computing (HPC) multi-objective programming Renewable energy resources Parallel algorithms Uncertainties modeling

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Optimality of E-pseudoconvex multi-objective programming problems without constraint qualifications

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OPTIMIZATION LETTERS 2012年第8期6卷 1603-1611页

作者： Yu, GuoLin Lu, Yangyang Jiang, Yan Beifang Univ Nationalities Res Inst Informat & Syst Computat Sci Yinchuan 750021 Peoples R China

In this note, we consider the optimality criteria of multi-objective programming problems without constraint qualifications involving generalized convexity. Under the E-pseudoconvexity assumptions, the unified necessary and sufficient optimality conditions are established for weakly efficient and efficient solutions, respectively, in multi-objective programming problems.

关键词： multi-objective programming E-Convexity E-Pseudoconvex function Efficient solution

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Smooth tool path generation for five-axis flank milling using multi-objective programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2012年第B2期226卷 247-254页

作者： Zheng, G. Bi, Q-Z Zhu, L-M Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

Flank milling provides an efficient way to machine turbo-machinery components. However, the trajectory smoothness is seldom considered in the existing tool positioning strategies. In this paper, the tool trajectory is smoothed with a constraint on the resulting geometric error for five-axis flank milling. Unlike existing methods, this new method simultaneously considers the geometric smoothness and geometric deviation. The geometric smoothness is characterized by the strain energy of the cutter axis trajectory surface (S-A). The geometric deviation is measured by the signed maximal orthogonal distance between the design surface (S-D) and the tool envelope surface (S-E). For finish and semi-finish flank millings, smooth tool path optimizations are then modelled as multi-objective programming (MOP) problems. Given a prescribed geometric tolerance, the MOP problems are reformulated as constrained nonlinear programming (NLP) problems. Based on the Taylor expansions of the strain energy and the signed distance on the differential deformation of S-A, the constrained NLP problems are solved efficiently by the sequential quadratic programming (SQP) method. The existence of the optimal solutions is also discussed. The validity of the approach is confirmed by two numerical examples that generate five-axis flank milling tool paths with cylindrical and conical cutters, respectively.

关键词： flank milling tool trajectory smoothness tool orientation machining error multi-objective programming

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A data-driven sustainable scheduling model for dispatch-steerable last-mile delivery systems with negotiable time windows

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Engineering Applications of Artificial Intelligence 2025年 156卷

作者： Keivan Tafakkori Reza Tavakkoli-Moghaddam Ali Siadat School of Industrial Engineering College of Engineering University of Tehran Tehran Iran Research Center of Performance and Productivity Analysis Istinye University Istanbul Turkey Arts et Métiers Institute of Technology Université de Lorraine LCFC F-57070 Metz France

With the surge in e-commerce, last-mile delivery (LMD) faces challenges in meeting the dynamic arrival of large-scale customer demand. Existing research considers traditional, static, single or two-echelon, and inflexible vehicle routing-based dispatch strategies, yielding inefficiencies while the sustainability impacts remain unclear. This paper proposes a novel tri-objective mathematical model for dispatch-steerability in sustainable LMD systems by integrating insourced and crowdsourced transport modes with heterogeneous capacities. Deliveries originate from main dispatch points (MDPs) or dynamically generated alternative dispatch points (ADPs), adapting to stakeholder, driver, and customer preferences via negotiable timing through temporary rejections or incentives. The model optimizes economic efficiency (minimizing routing, rejection, and negotiation costs), environmental impact (reducing underutilization of transport modes), and social responsibility (balancing driver workload and just-in-time deliveries). A data-driven density-based spatial clustering of applications with noise (DBSCAN) algorithm identifies ADP locations, enhancing the adaptability of the decisions. Scalability is achieved via a rolling horizon strategy, an improved augmented epsilon-constraint method, and multi-objective meta-heuristics, including a genetic algorithm (GA) and simulated annealing (SA) featuring an archive and grid mechanism with a tailored representation scheme. Results show a 200 % increase in Pareto-optimal solutions as demand rises, and that a dispatch steerable LMD system with ADPs offers 150 % more diverse delivery options than MDP-only systems. Pareto surface analysis underscores LMD adaptation trends and the need for multi-criteria decision-making in sustainable LMD systems.

关键词： Last-mile delivery Sustainability multi-objective programming Order acceptance scheduling Meta-heuristics Machine learning

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Construction of a Clinical Path Discrimination Model for Stroke Patients Based on the XGBoost Integrated Learning Algorithm and Its Application Analysis in the MOP under the DIP Payment Model

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Journal of Clinical and Nursing Research 2025年第4期9卷 291-298页

作者： Huisi Hong Yiming Yuan Jianlong Huang Liqun Zheng Wentao Guo Bingteng Sun Xiaoxing Huang Zhongshan Hospital of Traditional Chinese Medicine Affiliated to Guangzhou University of Chinese Medicine Zhongshan 528401GuangdongChina

objective:Aiming at the problems of clinical pathway optimization and medical cost control for stroke patients,this study proposes a clinical pathway discrimination model based on the XGBoost integrated learning *** with the multi-objective programming(MOP)method,this study explores its application value under the Diagnosis-Intervention Packet(DIP)payment ***:The data of stroke patients(ICD codes I60-I63)from 2018 to 2024 were obtained through the medical record statistical management system of medical institutions in Guangdong *** indicators(average length of hospital stay),health economics indicators(total cost),effectiveness indicators(mortality rate),and specific indicators(NIHSS score)were *** XGBoost algorithm was used to construct the clinical pathway discrimination model,and the hyperparameters were optimized through grid *** on the DIP payment rules,the prediction results of the model were used as inputs to establish a dynamic programming model,aiming to minimize costs and maximize curative effects to obtain the optimal clinical pathway ***:The goodness-of-fit(R 2)of the XGBoost model on the test set reached 0.768,which was significantly better than that of the random forest(0.691)and the BP neural network(0.343).The total cost of the clinical pathway optimized by the dynamic programming model decreased by 12.7%(95%CI:10.2-15.1%),the average length of hospital stay was shortened by 1.8 days,and the NIHSS improvement rate increased by 8.3%.Conclusion:The integrated model proposed in this study has high accuracy and robustness in clinical pathway *** with the MOP method,it can provide a scientific basis for the optimization of medical resources under the DIP model,helping medical institutions achieve the dual goals of precise cost control and curative effect improvement.

关键词： XGBoost multi-objective programming Clinical pathway DIP payment Stroke

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Reformulation of Network Data Envelopment Analysis models using a common modelling framework

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期278卷 472-480页

作者： Koronakos, Gregory Sotiros, Dimitris Despotis, Dimitris K. Univ Piraeus Dept Informat 80 Karaoli & Dimitriou Piraeus 18534 Greece Univ Catolica Portuguesa Catolica Porto Business Sch Rua Diogo Botelho 1327 P-4169005 Porto Portugal Univ Catolica Portuguesa CEGE Rua Diogo Botelho 1327 P-4169005 Porto Portugal

Network Data Envelopment Analysis (network DEA) is an extension of the conventional Data Envelopment Analysis (DEA) developed to take into account the internal structure of the Decision Making Units (DMUs). In network DEA, the DMU is considered as a network of interconnected sub-processes, where the connections indicate the flow of the intermediate measures. In this paper, we reformulate some of the basic network DEA methodologies in a common modelling framework. We show that the leader-follower approach, the multiplicative and the additive decomposition methods as well as the recently introduced min-max method and the "weak-link" approach, can all be modelled in a multi-objective programming framework, differentiating only in the definition of the overall system efficiency and the solution procedure adopted. Such a common modelling framework makes the direct comparison of the different methodologies possible and enables us to spot and underline their similarities and dissimilarities effectively. We illustrate graphically how the aforementioned methodologies locate their optimal efficiency scores on the Pareto front in the objective functions space, with an example taken from the literature. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Data Envelopment Analysis Network DEA multi-objective programming

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A novel approach for distant wind farm interconnection: Iran South-West wind farms integration

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RENEWABLE ENERGY 2019年 140卷 737-750页

作者： Javadi, Mohammad Sadegh Razavi, Seyed-Ehsan Ahmadi, Abdollah Siano, Pierluigi Islamic Azad Univ Shiraz Branch Young Researchers & Elite Club Shiraz Iran Univ Birjand Dept Elect & Comp Engn Birjand Iran Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Univ Salerno Dept Ind Engn Fisciano Italy

A multi-objective wind farm integration framework is proposed in this paper which considers the composite generation and reliability assessment and annualized operating and investment cost evaluation. An emission-controlled policy is adopted such that the amount of SOx and NOx decreases in line with renewable resource planning. Since the incorporation of large-scale distant wind farms is a problem of the multi-objective mixed-integer type with nonlinearities and non-convexities, this paper utilizes a fast elicit multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA II) by probabilistic indices. It is noted that the impacts of the unavailability of the transmission system are modeled employing DC Optimal Power Flow (OPF) based on the incidence matrix together with the static security evaluation. Furthermore, in order to assess the performance of the suggested approach, the model is implemented on the Roy Billinton Test System (RBTS). Afterwards, distant wind farms integration into Iran's South-West Regional Grid (ISWRG) is studied. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Distant wind farm incorporation Combined generation and transmission reliability assessment Iran's South-West Regional grid multi-objective programming

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