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Global Solution of Semi-infinite Programs with Existence Constraints

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2021年第3期188卷 863-881页

作者： Djelassi, Hatim Mitsos, Alexander Rhein Westfal TH Aachen Proc Syst Engn AVT SVT Aachen Germany

We consider what we term existence-constrained semi-infinite programs. They contain a finite number of (upper-level) variables, a regular objective, and semi-infinite existence constraints. These constraints assert that for all (medial-level) variable values from a set of infinite cardinality, there must exist (lower-level) variable values from a second set that satisfy an inequality. Existence-constrained semi-infinite programs are a generalization of regular semi-infinite programs, possess three rather than two levels, and are found in a number of applications. Building on our previous work on the global solution of semi-infinite programs (Djelassi and Mitsos in J Glob Optim 68(2):227-253, 2017), we propose (for the first time) an algorithm for the global solution of existence-constrained semi-infinite programs absent any convexity or concavity assumptions. The algorithm is guaranteed to terminate with a globally optimal solution with guaranteed feasibility under assumptions that are similar to the ones made in the regular semi-infinite case. In particular, it is assumed that host sets are compact, defining functions are continuous, an appropriate global nonlinear programming subsolver is used, and that there exists a Slater point with respect to the semi-infinite existence constraints. A proof of finite termination is provided. Numerical results are provided for the solution of an adjustable robust design problem from the chemical engineering literature.

关键词： Semi-infinite programming multi-level programming Nonlinear programming Nonconvex Global optimization

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A hierarchical multi-level model for compromise allocation in multivariate stratified sample surveys with non-response problem

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KNOWLEDGE-BASED SYSTEMS 2023年第1期278卷

作者： Jalil, Syed Aqib Haq, Ahteshamul Al Owad, Ali Hashmi, Nausheen Adichwal, Nitesh Kumar Sohar Univ Fac Business Sohar Oman Aligarh Muslim Univ Dept Stat & OR Aligarh India Integral Univ Dept Math & Stat Lucknow India Jazan Univ Fac Engn Dept Ind Engn Jazan Saudi Arabia Rajagiri Business Sch Kochi Kerala India Univ Petr & Energy Studies UPES Sch Business Misraspatti India

Stratified sampling, a widely-applicable probabilistic technique, is especially suited for large and heterogeneously distributed populations. This paper studies optimal allocation of sampling units to minimize variances and cost. Given that not all strata hold equal importance in survey projects, we propose a hierarchical multi-level programming model for compromise allocation in stratified sampling. The model considers multiple objectives across hierarchical levels and addresses the issue of non-response by dividing strata into respondent and non-respondent groups. The survey budget restriction is considered as a constraint in our model. We employ a fuzzy concept-based solution methodology to solve the multi-level allocation problem. A literature-based numerical example describes the model's applicability and efficiency. Comparative analysis shows our model's superior efficiency over existing models due to its optimization of allocation across varied strata, non-response consideration, and budget constraint integration. The proposed model promotes flexibility, enhancing representativeness and cost-effectiveness of large-scale surveys, thereby improving decision-making in research and industry settings.(c) 2023 Elsevier B.V. All rights reserved.

关键词： multivariate stratified sample survey multi-level programming Compromise allocation

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Solving multi-level multi-objective Fractional programming Problems with Fuzzy Demands via FGP Approach

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International Journal of Applied and Computational Mathematics 2018年第1期4卷 1-24页

作者： Osman, M.S. Emam, O.E. El Sayed, M.A. Mathematics and Operations Research El Asher University El Asher City Egypt Department of Information Systems Faculty of Computers and Information Helwan University P.O. Box 11795 Greater Cairo Egypt Department of Basic Engineering Sciences Faculty of Engineering Benha University Benha ElQalyoubia Egypt

This paper presents a fuzzy goal programming approach for solving multi-level multi-objective fractional programming problem with fuzzy demands. It makes an extension work of Pal et al. (Fuzzy Sets Syst 139(2):395–405, 2003). Firstly, the concept of α-cut is applied to transform the fuzzy mathematical problem into a common deterministic one. Then, the membership functions for the defined fuzzy goals are developed. Also, in the proposed approach, linearization of membership goals of the objective functions is presented. Secondly, the highest degree of each of these membership goals is achieved by minimizing the sum of the negative deviational variables. Moreover, the final model is simplified by eliminating solution preferences by the decision makers at each level, thereby avoiding decision deadlock situations. Finally, an illustrative numerical examples and comparisons with the existing methods are used to demonstrate the applicability and performance of the proposed approach. © 2017, Springer (India) Private Ltd., part of Springer Nature.

关键词： Fractional programming Fuzzy goal programming Fuzzy sets multi-level programming multi-objective programming

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Non-deterministic multi-level model for planning water-ecology nexus system under climate change

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Cell Reports Sustainability 2024年第3期1卷

作者： Ma, Yuan Li, Yongping Wang, Hao Zhang, Yufei Zhou, Yanxiao Huang, Guohe State Key Joint Laboratory of Environmental Simulation and Pollution Control School of Environment Beijing Normal University Beijing 100875 China Institute for Energy Environment and Sustainable Communities University of Regina Regina S4S 7H9 SK Canada

Water scarcity and ecological degradation impede sustainable development in Central Asia, which urgently calls for synergistic planning of water-ecology (WE) nexus system. However, existing management models may have large uncertainties, restricting their effectiveness. Here, we develop a copula-based flexible fuzzy multi-level programming (CFMP) method, which tackles uncertainties, such as water demands, and balances trade-offs among competing managers in top-down decision-making processes. Next, we formulate a CFMP-WE model for Central Asia (2021–2050), considering objectives of economic development, food security, and ecological restoration, and design 243 planning scenarios. We found that ecological water allocation would account for 5.9%–12.2% to support sustainable development;however, policymakers need to reduce agricultural water allocation, forgoing 7.8%–20.1% of the system benefit (i.e., economic benefit for WE nexus system). Agricultural water use would still be the largest (with 25.6%–29.4% for cereal crops to ensure food security), but its share would decline to conserve water for users like industry. © 2024 The Authors

关键词： Central Asia climate change copula-based programming multi-level programming multi-uncertainty sustainability water-ecology

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Hierarchical tri-level optimization model for effective use of by-products in a sugarcane supply chain network

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APPLIED SOFT COMPUTING 2022年第0期128卷

作者： Chouhan, Vivek Kumar Khan, Shahul Hamid Hajiaghaei-Keshteli, Mostafa Indian Inst Informat Technol Dept Mech Engn Design & Mfg Chennai India Tecnol Monterrey Escuela Ingn & Ciencias Puebla Campus Monterrey Mexico

Developing a solution algorithm for tri-level facility location-allocation problem is always challenging due to the inherent complexity of these problems. The proposed sugarcane supply chain network is a tri-level modeling approach formulated based on the static Stackelberg game between producer, distribution center, sugarcane industry, compost unit, biorefinery unit and market in the framework. The network emphasizes the use of massive amount of the by-products generated in the sugarcane industry. These by-products are excellent raw materials for compost unit and biorefinery units. In such cases decisions are made in the hierarchy. By reviewing the proposed algorithms in the past, it has been realized that the shortcomings of the algorithm could be improved by introducing some efficient search mechanism in the algorithms. In this context, a strong local search mechanism based on social engineering optimizer is developed to intensify search space more carefully. Two-hybrid algorithms, GASEO based on Genetic algorithm and social engineering optimizer, and KASEO based on Keshtel algorithm and social engineering optimizer is proposed. To appraise the performance of the proposed algorithm, we pervasively discussed the parameter tuning using Taguchi approach. The ANOVA and Tukey post-hoc test ensures that the performance of the proposed GASEO is appreciable over other algorithms. (C) 2022 Elsevier B.V. All rights reserved.

关键词： multi-level programming Facility location-allocation Agricultural by-products Metaheuristics Hybrid algorithms

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A soft robust methodology to devise hedging strategies in renewable energy trading based on electricity options

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ELECTRIC POWER SYSTEMS RESEARCH 2022年第0期207卷 107852-107852页

作者： Brigatto, Arthur Fanzeres, Bruno Pontifical Catholic Univ Rio de Janeiro PUC Rio Ind Engn Dept Rio De Janeiro RJ Brazil Pontifical Catholic Univ Rio de Janeiro PUC Rio Elect Engn Dept Rio De Janeiro RJ Brazil

Supply contracts play an important role in competitive electricity markets. They help ensure supply adequacy and hedge against market power, among other benefits. However, when variable renewable energy is involved, the mixture of uncertainty in energy production with a high volatile spot market poses a risk difficult to manage. Within this context, call/put options are suitable hedging instruments to cover production imbalance with respect to supply contracts. To efficiently balance the cost/benefit of a set of energy options in a portfolio composed by renewable sources short in supply contracts, a precise definition of the probabilistic nature of the spot market price should be available. However, it is recognized that in practice agents only have an imprecise approximation of the "true" underlying process. Thus, decisions are made under ambiguity, which challenges the practical application of standard pure stochastic-programming methods for the optimal composition of electricity contracts. In this work, we propose a risk-and ambiguity-constrained portfolio allocation model that defines the optimal composition of call/put options and renewable sources to back a supply contract. A case study with realistic data from the Brazilian electricity market is presented to illustrate the applicability of the proposed portfolio allocation methodology. Comparing with two benchmark, we found an increase of roughly 20% and 42% on the average revenue and at least 40% on the average of the 5% worst-case revenue scenarios for different spot price probability distributions.

关键词： Ambiguity constraints Call Put options multi-level programming Power system economics Renewable energy sources Supply contracts

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Urban hazmat transportation with multi-factor

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SOFT COMPUTING 2020年第9期24卷 6307-6328页

作者： Du, Jiaoman Li, Xiang Li, Lei Shang, Changjing Beijing Univ Chem Technol Sch Econ & Management Beijing Peoples R China Hosei Univ Fac Sci & Engn Tokyo Japan Aberystwyth Univ Dept Comp Sci Aberystwyth Dyfed Wales Beijing Univ Chem Technol Beijing Adv Innovat Ctr Soft Matter Sci & Engn Beijing 100029 Peoples R China

In this paper, an urban hazmat transportation problem considering multiple factors that tangle with real-world applications (i.e., weather conditions, traffic conditions, population density, time window, link closure and half link closure) is investigated. Based on multiple depot capacitated vehicle routing problem, we provide a multi-level programming formulation for urban hazmat transportation. To obtain the Pareto optimal solution, an improved biogeography-based optimization (improved BBO) algorithm is designed, comparing with the original BBO and genetic algorithm, with both simulated numerical examples and a real-world case study, demonstrating the effectiveness of the proposed approach.

关键词： Urban hazmat transportation multiple factors multi-level programming Biogeography-based optimization Pareto optimization

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Competitive location and pricing on a line with metric transportation costs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第1期282卷 188-200页

作者： Arbib, Claudio Pinar, Mustafa C. Tonelli, Matteo Univ Aquila Dipartimento Sci Ingn Informaz & Matemat Via Vetoio I-67010 Laquila Italy Bilkent Univ Dept Ind Engn Ankara Turkey Gran Sasso Sci Inst Via Francesco Crispi 7 I-67100 Laquila Italy

Consider a three-level non-capacitated location/pricing problem: a firm first decides which facilities to open, out of a finite set of candidate sites, and sets service prices with the aim of revenue maximization;then a second firm makes the same decisions after checking competing offers;finally, customers make individual decisions trying to minimize costs that include both purchase and transportation. A restricted two-level problem can be defined to model an optimal reaction of the second firm to known decision of the first. For non-metric costs, the two-level problem corresponds to ENVY-FREE PRICING or to a special NETWORK PRICING problem, and is APX-complete even if facilities can be opened at no fixed cost. Our focus is on the metric 1-dimensional case, a model where customers are distributed on a main communication road and transportation cost is proportional to distance. We describe polynomial-time algorithms that solve two- and three-level problems with opening costs and single 1st level facility. Quite surprisingly, however, even the two-level problem with no opening costs becomes NP-hard when two 1st level facilities are considered. (C) 2019 Published by Elsevier B.V.

关键词： Pricing Location Sequential games multi-level programming Computational complexity

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Interactive Approach for multi-level multi-Objective Fractional programming Problems with Fuzzy Parameters

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Beni-Suef University Journal of Basic and Applied Sciences 2018年第1期7卷 139-149页

作者： M.S. Osman O.E. Emam M.A. Elsayed Professor of Mathematics and Operations Research Vicepresedent of ElAsher University Egypt Department of Information Systems Faculty of Computers and Information Helwan University P.O.Box 11795 Egypt Department of Basic Engineering Sciences Faculty of Engineering Benha University ElQalyoubia Egypt

In this paper, an interactive approach for solving multi-level multi-objective fractional programming (ML-MOFP) problems with fuzzy parameters is presented. The proposed interactive approach makes an extended work of Shi and Xia (1997). In the first phase, the numerical crisp model of the ML-MOFP problem has been developed at a confidence level without changing the fuzzy gist of the problem. Then, the linear model for the ML-MOFP problem is formulated. In the second phase, the interactive approach simplifies the linear multi-level multi-objective model by converting it into separate multi-objective programming problems. Also, each separate multi-objective programming problem of the linear model is solved by the ∊ -constraint method and the concept of satisfactoriness. Finally, illustrative examples and comparisons with the previous approaches are utilized to evince the feasibility of the proposed approach.

关键词： multi-level programming multi-objective programming Fractional programming Fuzzy parameters

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Contribution to multi-level multi-objective linear optimization

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2021年第6期42卷 1383-1395页

作者： Delhoum, Zohra Sabrina Oran Higher Sch Econ BP 65 CH2 Achaba Hnifi Technopole Usto Bir El Djir Oran 31000 Algeria Univ Oran 1 Lab Math & Its Applicat LAMAP BP 1524 El MNaouer Ahmed Ben Bella 31000 Oran Algeria

In this paper, we present a new method for the resolution of a multi-level multi-objective linear programming problem with bounded variables based on the adaptive method for solving multi-level multi-objective linear programming with bounded variables. The peculiarity of this method is that it has the suboptimality criterion that allows us to find epsilon - efficient solutions, and unlike to other methods, the method we are going to present has the advantage of solving exactly these kind of problems and manipulating the constraints as they are without any transformation. We will present the detailed algorithm of the method and give a numerical example to demonstrate its applicability.

关键词： multi-level programming multi-objective Linear programming Bounded variables Adaptive method Pareto optimal solution Slater optimal solution epsilon-efficiency

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