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Bi-perspective functions for mixed-integer fractional programs with indicator variables

MATHEMATICAL programming 2021年第1-2期190卷 39-55页

作者： Letchford, Adam N. Ni, Qiang Zhong, Zhaoyu Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England

Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. To obtain a tight relaxation of such problems, one must consider what we call a "bi-perspective" (Bi-P) function. An analysis of Bi-P functions leads to the derivation of a new kind of cutting planes, which we call "Bi-P-cuts". Computational results indicate that Bi-P-cuts typically close a substantial proportion of the integrality gap.

关键词： Fractional programming mixed-integer nonlinear programming Mobile wireless communications OFDMA systems

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Optimising the configuration of food supply chains

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第12期59卷 3722-3746页

作者： Li, Haitao Li, De Jiang, Dali Univ Missouri Coll Business Adm Supply Chain & Analyt Dept St Louis MO 63121 USA Army Logist Univ PLA Dept Mil Logist Chongqing Peoples R China

We study the food supply chain configuration problem (FSCCP) to optimise the tactical-level mode selection and inventory positioning decisions for a general multi-echelon food supply chain. A mixed-integer nonlinear programming (MINLP) model is developed for the FSCCP, with new building blocks to address the perishability issue in terms of both food loss and quality deterioration. Our model minimises the system-wide total supply chain costs and balances multiple supply chain performance metrics: cost, time and quality. Computational studies show that the optimal FSCCP solutions significantly outperform two heuristic solutions that focus solely on cost or quality. Additional insights are obtained on the impacts of key input parameters on the optimal configuration and performance metrics.

关键词： supply chain configuration food supply chain perishability inventory positioning safety stock placement mixed-integer nonlinear programming

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Optimal charging scheduling for Indoor Autonomous Vehicles in manufacturing operations

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ADVANCED ENGINEERING INFORMATICS 2024年 62卷

作者： Mohammadpour, Mohammad Allani, Bilel Kelouwani, Sousso Ouameur, Messaoud Ahmed Zeghmi, Lotfi Amamou, Ali Bahmanabadi, Hossein Univ Quebec Trois Rivieres Dept Mech Engn Trois Rivieres PQ G8Z 4M3 Canada Univ Quebec Trois Rivieres Dept Elect & Comp Engn Trois Rivieres PQ G8Z 4M3 Canada Sharif Univ Technol Dept Mech Engn Tehran Iran

Indoor Autonomous Vehicles (IAVs) have become instrumental in modern logistics, particularly in dynamic operational environments. Their consistent availability is crucial for both timely task execution and energy efficiency in smart factories. Therefore, an inefficient charging schedule can waste energy, compromising production and warehousing efficiency. In addition, formulating an effective charging schedule is challenging due to the nonlinearity of its design and the uncertainties inherent in smart factory settings. In contrast to previous studies that either simplify the problem using linearization-based methods or approach it with computationally demanding algorithms, this paper efficiently addresses the nonlinear challenge, ensuring a closer alignment with real-world conditions. Hence, a simulation environment is first designed to replicate a smart factory, including validated models of IAVs, Charging Stations (CSs), and a variety of unpredictable static and dynamic obstacles. A comprehensive dataset is then provided from this simulation setup. Utilizing this dataset, a model tailored to ascertain the travel time of IAVs, accounting for inherent uncertainties, is trained using Deep Neural Networks (DNNs). Subsequently, a mixed-integer nonlinear programming (MINLP) problem is formulated to design the optimization task. Finally, integration of the DNNs' model with the Branch-and-Bound (BnB) approach, forming the BnBD method, streamlines the determination of the optimal charging schedule. Experimental results highlight significant improvements in charging scheduling, establishing this approach as a viable and promising solution for manufacturing operations.

关键词： Industry 4.0 Energy efficiency Indoor Autonomous Vehicles Charging scheduling mixed-integer nonlinear programming Branch-and-Bound Deep neural networks

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mixed integer programming with a class of nonlinear convex constraints

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DISCRETE OPTIMIZATION 2017年 24卷 66-86页

作者： Vinel, Alexander Krokhmal, Pavlo A. Auburn Univ Dept Ind & Syst Engn Shelby Ctr 3301 Auburn AL 36849 USA Univ Arizona Dept Syst & Ind Engn 1127 E James E Rogers Way Tucson AZ 85721 USA

We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be generalized to the problems under consideration. Particularly, we consider a branch-and-bound method based on outer polyhedral approximations, lifted nonlinear cuts, and linear disjunctive cuts. Results of numerical experiments with discrete portfolio optimization models are presented. (C) 2016 Elsevier B.V. All rights reserved.

关键词： mixed-integer nonlinear programming Measures of risk Quasi-arithmetic average Valid inequalities Conic programming

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Branch-and-price for a class of nonconvex mixed-integer nonlinear programs

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JOURNAL OF GLOBAL OPTIMIZATION 2021年第4期81卷 861-880页

作者： Allman, Andrew Zhang, Qi Univ Minnesota Dept Chem Engn & Mat Sci Minneapolis MN 55455 USA

This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer nonlinear programs (MINLPs) with linear complicating constraints and integer linking variables. If the complicating constraints are removed, the problem becomes easy to solve, e.g. due to decomposable structure. Integrality of the linking variables allows us to apply a discretization approach to derive a Dantzig-Wolfe reformulation and solve the problem to global optimality using branch-andprice. It is a remarkably simple idea;but to our surprise, it has barely found any application in the literature. In this work, we show that many relevant problems directly fall or can be reformulated into this class of MINLPs. We present the branch-and-price algorithm and demonstrate its effectiveness (and sometimes ineffectiveness) in an extensive computational study considering multiple large-scale problems of practical relevance, showing that, in many cases, orders-of-magnitude reductions in solution time can be achieved.

关键词： mixed-integer nonlinear programming Branch-and-price Decomposition Nonconvex optimization

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On decomposition and multiobjective-based column and disjunctive cut generation for MINLP

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OPTIMIZATION AND ENGINEERING 2021年第3期22卷 1389-1418页

作者： Muts, Pavlo Nowak, Ivo Hendrix, Eligius M. T. Hamburg Univ Appl Sci Hamburg Germany Univ Malaga Malaga Spain

Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. This paper investigates the potential of using decomposition and a novel multiobjective-based column and cut generation approach for solving nonconvex block-separable MINLPs, based on the so-called resource-constrained reformulation. Based on this approach, two decomposition-based inner- and outer-refinement algorithms are presented and preliminary numerical results with nonconvex MINLP instances are reported.

关键词： Decomposition method Parallel computing Column generation Nonconvex optimization Global optimization mixed-integer nonlinear programming

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Integrated UAV Trajectory Control and Resource Allocation for UAV-Based Wireless Networks With Co-Channel Interference Management

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IEEE INTERNET OF THINGS JOURNAL 2021年第14期9卷 12754-12769页

作者： Minh Dat Nguyen Long Bao Le Girard, Andre Univ Quebec Inst Natl Rech Sci Energie Mat & Telecommun Montreal PQ H5A 1K6 Canada

In this article, we study the trajectory control, subchannel assignment, and user association design for unmanned aerial vehicles (UAVs)-based wireless networks. We propose a method to optimize the max-min average rate subject to data demand constraints of ground users (GUs) where spectrum reuse and co-channel interference management are considered. The mathematical model is a mixed-integer nonlinear optimization problem which we solve by using the alternating optimization approach where we iteratively optimize the user association, subchannel assignment, and UAV trajectory control until convergence. For the subchannel assignment subproblem, we propose an iterative subchannel assignment (ISA) algorithm to obtain an efficient solution. Moreover, the successive convex approximation (SCA) is used to convexify and solve the nonconvex UAV trajectory control subproblem. Via extensive numerical studies, we illustrate the effectiveness of our proposed design considering different UAV flight periods and number of subchannels and GUs as compared with a simple heuristic.

关键词： Trajectory Autonomous aerial vehicles Optimization Channel allocation Wireless networks Internet of Things Bandwidth mixed-integer nonlinear programming subchannel assignment unmanned aerial vehicle (UAV) trajectory user association

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OUTER APPROXIMATION FOR PSEUDO-CONVEX mixed-integer nonlinear PROGRAM PROBLEMS

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF nonlinear AND VARIATIONAL ANALYSIS 2024年第2期8卷 181-197页

作者： Wei, Zhou Chen, Liang Yao, Jen-Chih Hebei Univ Hebei Key Lab Machine Learning & Computat Intellig Baoding 071002 Peoples R China Hebei Univ Coll Math & Informat Sci Baoding 071002 Peoples R China Chinese Acad Sci LSEC Acad Math & Syst Sci Beijing 100190 Peoples R China China Med Univ China Med Univ Hosp Res Ctr Interneural Comp Taichung 40402 Taiwan

Outer approximation (OA) for solving convex mixed-integer nonlinear programming (MINLP) problems is heavily dependent on the convexity of functions and a natural issue is to relax the convexity assumption. This paper is devoted to OA for dealing with a pseudo-convex MINLP problem. By solving a sequence of nonlinear subproblems, we use Lagrange multiplier rules via Clarke subdifferentials of subproblems to introduce a parameter and then equivalently reformulate such MINLP as the mixed-integer linear program (MILP) master problem. Then, an OA algorithm is constructed to find the optimal solution to the MNILP by solving a sequence of MILP relaxations. The OA algorithm is proved to terminate after a finite number of steps. Numerical examples are illustrated to test the constructed OA algorithm.

关键词： . Clarke Subdifferential mixed-integer nonlinear programming MILP master program Outer Approximation Pseudo-convexity

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Decentralized AC Optimal Power Flow Problem Considering Prohibited Operating Zones

Decentralized AC Optimal Power Flow Problem Considering Proh...

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IEEE International Conference on Environment and Electrical Engineering (EEEIC) / IEEE Industrial and Commercial Power Systems Europe (I and CPS Europe) Conference

作者： Do Carmo Yamaguti, Lucas Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mahdi Sanches Mantovani, Jose Roberto Sao Paulo State Univ Dept Elect Engn Ilha Solteira Brazil Aalto Univ Dept Elect Engn & Automat Espoo Finland

ISBN: (纸本)9781665485371

The Optimal Power Flow (OPF) problem is commonly formulated considering one central operator manager (centralized approach). However, in practice, the power system is structured by interconnected areas, controlled by several system operators, which are dependent on their neighbors and must exchange sensitive data with each other. In addition, some generation units must be restricted in some zones of operation to avoid negative operational effects. This paper proposes a mixed-integer nonlinear programming model to solve the decentralized AC-OPF considering prohibited operation zones (POZ). A matheuristic algorithm based on the variable neighborhood descent heuristic method is used to deal with the integer variables of the problem, while a non-linear optimization solver is used to solve the optimal power flow with continuous variables. The proposed model and solution technique are validated using the IEEE 118-bus system, ensuring that the decentralized model determines solutions close to the centralized model without and with POZ constraints.

关键词： Decentralized optimization matheuristic optimization mixed-integer nonlinear programming optimal power flow prohibited operating zones

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Promoting ship sewage recycling in China's inland waterways: A balanced funding approach for advanced disposal fees and subsidies

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OCEAN & COASTAL MANAGEMENT 2025年 267卷

作者： Zhong, Huiling Gao, Jiajue Gu, Yimiao South China Univ Technol Inst Digital Business & Intelligent Logist Dept Elect Business Guangzhou Peoples R China

Ship-generated sewage presents significant environmental challenges in maritime transport, particularly in inland waterways. In China, the existing fee-free delivery policies fall short of providing sufficient incentives for ports and ships, while heavily relying on unsustainable government subsidies. To tackle these challenges, this paper introduces a financially sustainable Advance Disposal Fee (ADF) system paired with a subsidy recycling policy. The proposed approach is built on a tri-level Stackelberg game framework that involves the government, two ports, and a fleet of ships, aiming to optimize recycling policies and stakeholder decision-making. This framework is further formalized into a mixed-integer nonlinear tri-level programming model, where four stakeholders strategically maximize their respective profits. Using two ports along the Pearl River in China as a case study, the findings reveal that the proposed recycling policy substantially improves engagement from both ports and ships, achieving a sewage delivery rate of 89 %. These results provide practical guidance for the development of government recycling policies, the selection of port reception strategies, and the formulation of ship sewage management plans.

关键词： Ship wastes Advanced disposal fees Sewage recycling Tri-level programming mixed-integer nonlinear programming

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