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Exact Methods for Multi-Objective integer nonlinear programming

CYBERNETICS AND SYSTEMS 2024年第7期55卷 1668-1701页

作者： Yu, Zixuan Sun, Wei Huang, Min Northeastern Univ Dept Intelligent Data & Syst Engn State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China Liaoning Univ Business Sch Shenyang Peoples R China

Multi-objective integer nonlinear programming (MOINLP) problems are multi-objective integer programming problems with at least one nonlinear objective function or constraint. To date, MOINLP problem has not been exactly solved. Although traditional epsilon-constraint method can be used to solve MOINLP problem, the obtained solution may not be Pareto-optimal. To overcome this shortcoming, a basic epsilon-constraint method (BEM) is proposed to solve MOINLP problem exactly. However, the time complexity of BEM is as high as O((p-1)(MN)-N-2), where p, M, and N are the numbers of objectives, Pareto-optimal solutions, and feasible solutions, respectively. For this reason, an improved BEM (IBEM) is developed whose time complexity is O((MN)-N-2). That is, the time complexity of IBEM for solving MOINLP problem is equal to solving the single-objective one. Finally, to avoid using all the feasible solutions (N) in obtaining each Pareto-optimal solution, three methods to eliminate dominated solutions effectively are used before performing IBEM. The test results illustrate that our method can not only solve MOINLP problem exactly but also has high efficiency.

关键词： Exact method integer nonlinear programming multi-objective reducing solution space

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integer nonlinear programming and optimized weighted-average approach for mobile hotel recommendation by considering travelers' unknown preferences

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OPERATIONAL RESEARCH 2018年第3期18卷 625-643页

作者： Lin, Yu-Cheng Chen, Toly Wang, Li-Chih Overseas Chinese Univ Dept Comp Aided Ind Design Taichung Taiwan Natl Chiao Tung Univ Dept Ind Engn & Management Hsinchu Taiwan Tunghai Univ Dept Ind Engn & Enterprise Informat Taichung Taiwan

The existing mobile hotel recommendation systems are usually subject to a difficult problem-travelers choose dominated hotels. This problem is difficult to resolve because there is no reason to recommend a hotel that is inferior to another in all aspects. To address this problem, an artificial dimension is added to each hotel to model unknown personal preferences. The possible values along the artificial dimension and the weight associated with it are derived by solving an integer nonlinear programming problem. Thus, the proposed methodology hybridizes objective and subjective weights. An illustrative example is provided to show the applicability of the proposed methodology. In addition, a field study was conducted in a small region of Seatwen District, Taichung City, Taiwan to evaluate the possible advantages of the proposed methodology over existing methods. The experimental results showed that the proposed methodology outperformed five existing methods in improving the successful recommendation rate, with the most significant advantage being up to 33 %. Furthermore, the recommendation results generated using the proposed methodology were found to be less risky.

关键词： Hotel Recommendation integer nonlinear programming Dominated solution

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Partial reformulation-linearization based optimization models for the Golomb ruler problem

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RAIRO-OPERATIONS RESEARCH 2024年第4期58卷 3171-3188页

作者： Ouzia, Hacene Sorbonne Univ CNRS 4 Pl Jussieu F-75252 Paris France

In this paper, we provide a straightforward proof of a conjecture proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241-2246.] regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in [B. Kocuk and W.-J. van Hoeve, A Computational Comparison of Optimization Methods for the Golomb Ruler Problem. (2019) 409-425.], utilizing the reformulation-linearization technique. Finally, we provide the correct outputs of the greedy heuristic proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241-2246.] and correct false conclusions stated or implied therein.

关键词： Golomb ruler problem reformulation-linearization techniques mixed integer linear programming integer nonlinear programming quadratic programming

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Enhanced Profit-Driven Optimization for Flexible Server Deployment and Service Placement in Multi-User Mobile Edge Computing Systems

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2024年第6期11卷 6194-6206页

作者： Fang, Juan Wu, Shen Lu, Shuaibing Teng, Ziyi Chen, Huijie Xiong, Neal N. Beijing Univ Technol Coll Comp Sci Beijing 100124 Peoples R China Ross State Univ Dept Comp Math & Phys Sci Alpine TX 79830 USA

Edge computing has emerged as a promising paradigm to meet the increasing demands of latency-sensitive and computationally intensive applications. In this context, efficient server deployment and service placement are crucial for optimizing performance and increasing platform profit. This paper investigates the problem of server deployment and service placement in a multi-user scenario, aiming to enhance the profit of Mobile Network Operators while considering constraints related to distance thresholds, resource limitations, and connectivity requirements. We demonstrate that this problem is NP-hard. To address it, we propose a two-stage method to decouple the problem. In stage I, server deployment is formulated as a combinatorial optimization problem within the framework of a Markov Decision Process (MDP). We introduce the Server Deployment with Q-learning (SDQ) algorithm to establish a relatively stable server deployment strategy. In stage II, service placement is formulated as a constrained integer nonlinear programming (INLP) problem. We present the Service Placement with Interior Barrier Method (SPIB) and Tree-based Branch-and-Bound (TDB) algorithms and theoretically prove their feasibility. For scenarios where the number of users changes dynamically, we propose the Distance-and-Utilization Balance Algorithm (DUBA). Extensive experiments validate the exceptional performance of our proposed algorithms in enhancing the profit.

关键词： Servers Costs Heuristic algorithms Base stations Optimization Clustering algorithms Mobile handsets Telecommunications Symbols programming Mobile edge computing profit-driven optimization reinforcement learning integer nonlinear programming

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Considering greenhouse gas emissions in maintenance optimisation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第3期307卷 1135-1145页

作者： Wu, Shaomin Wu, Di Peng, Rui Univ Kent Kent Business Sch Canterbury CT2 7PE KY England Xi An Jiao Tong Univ Sch Management Xian Peoples R China Beijing Univ Technol Sch Econ & Management Beijing 100124 Peoples R China

Greenhouse gases (GHG) from human activities are the main contributor to climate change since the mid-20th century. Reducing the release of GHG emissions is becoming a thematic research topic in many research disciplines. In the reliability research community, there are research papers relating to reliability and maintenance for systems in power generation farms such as offshore farms. Nevertheless, there is sparse research that aims to optimise maintenance policies for reducing the GHG emissions from sys-tems such as automotive vehicles or building service systems. To fill up this gap, this paper optimises replacement policies for systems that age and degrade and that produce GHG emissions (i.e., exhaust emissions) including the initial manufacturing GHG emissions produced during the manufacturing stage and the emissions generated during the operational stage. Both the exhaust emissions process and the failure process are considered as functions of two time scales (i.e., age and accumulated usage), respec-tively. Other factors that may affect the two processes such as ambient temperature and road conditions are depicted as random effects. Under these settings, the decision problem is a nonlinear programming problem subject to several constraints. Replacement policies are then developed. Numerical examples are provided to illustrate the proposed methods. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Maintenance policy Greenhouse gas emissions Condition-based monitoring Two time scales integer nonlinear programming

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Cost-Optimal Deployment of Millimeter-Wave Base Stations Under Outage Requirement

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第12期21卷 10544-10559页

作者： Dong, Miaomiao Cho, Minsung Lee, Kangeun Yoon, Sungrok Kim, Taejoon City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China Univ Kansas Dept Elect Engn & Comp Sci Lawrence KS USA Samsung Elect Suwon South Korea

Today's growth in the volume of wireless devices coupled with the demand for data-intensive use cases has motivated the deployment of millimeter-wave (mmWave) small-cell networks. Although it is true that mmWave networks can carry a large volume of traffic, highly intermittent connectivity and the challenges related to installing many small-cell base stations (BSs) in urban geometry have impeded its progression into practical networks. To cope with these challenges, we present, in this paper, an approach to the mmWave BS deployment (site planning) problem, based on the minimum-deployment-cost criterion that is subject to user equipment (UE) outage constraints. Unlike the prior works, the proposed model captures the randomness of link blockage and signal-to-interference-plus-noise-ratio (SINR) statistics in mmWave networks. We formulate the minimum-cost deployment problem as large-scale integer nonlinear programming (INP). To deal with the coupled and combinatorial of the problem, the large-scale INP has approached to devise a suboptimal but efficient algorithm by decomposing it into two subproblems: (i) cell coverage optimization and (ii) minimum subset selection. We provide the solutions to each subproblem as well as theoretical justifications of them. Simulation results that illustrate UE outage guarantees of the proposed BS deployment method are presented. The results reveal that the proposed method uniquely distributes the macro-diversity orders that are distinct from other benchmarks.

关键词： Interference Signal to noise ratio Geometry Radio frequency Wireless communication Reliability Quality of service Link blockage outage minimum-cost base station deployment integer nonlinear programming integer linear programming site planning

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Optimization Models for Layout and Pipe Design for Storm Sewer Systems

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WATER RESOURCES MANAGEMENT 2021年第14期35卷 4841-4854页

作者： Alfaisal, Faisal M. Mays, Larry W. King Saud Univ Dept Civil Engn Coll Engn POB 800 Riyadh 11421 Saudi Arabia Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85281 USA

Optimization models are developed for simultaneously determining the pipe layout and the pipe design for storm sewer systems. The pipe design process includes computation of commercial diameters, slopes, and crown elevations for the storm sewer pipes. The optimization models aim to minimize the total costs of the layout and the pipe design for most of system elements. The optimization models are formulated as a 0-1 integer nonlinear programming problem and solved using the General Algebraic Modeling System without the use of heuristic models which were characteristic of all previous models for the simultaneous determine of the pipe layout and pipe design of sewer networks. The models are based upon two different optimization approaches: (1) considers one or more commercial diameters of pipe connecting two manholes and (2) considers only one commercial diameter in a pipe connecting two manholes. The commercial diameters, pipe slopes, crown elevations, and total costs of the storm sewer system were compared for the two approaches using an example that illustrates the savings in cost by allowing multiple pipe sizes. The two new optimization modeling approaches developed herein can simultaneously determine the minimum cost pipe design (commercial diameters, slopes, and crown elevations) and pipe layout of storm sewer systems and satisfy all design constraints.

关键词： Storm sewer systems Optimization Minimum cost design integer nonlinear programming

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Experimental operation of a solar-driven climate system with thermal energy storages using mixed-integer nonlinear model predictive control

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OPTIMAL CONTROL APPLICATIONS & METHODS 2021年第5期42卷 1293-1319页

作者： Buerger, Adrian Bull, Daniel Sawant, Parantapa Bohlayer, Markus Klotz, Andreas Beschuetz, Daniel Altmann-Dieses, Angelika Braun, Marco Diehl, Moritz Karlsruhe Univ Appl Sci Fac Management Sci & Engn Karlsruhe Germany Karlsruhe Univ Appl Sci Inst Refrigerat Air Conditioning & Environm Engn Moltkestr 30 D-76133 Karlsruhe Germany Univ Freiburg Dept Microsyst Engn IMTEK Syst Control & Optimizat Lab Freiburg Germany Offenburg Univ Appl Sci Inst Energy Syst Technol INES Offenburg Germany Friedrich Alexander Univ Erlangen Nurnberg Professorship Econ Ind Org & Energy Markets Nurnberg Germany Univ Freiburg Dept Math Freiburg Germany

This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear model predictive control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as well as a cold water storage. The system and the applied modeling approach is described and a parallelized algorithm for mixed-integer nonlinear MPC and a corresponding implementation for the system are presented. Finally, we show and discuss the results of experimental operation of the system and highlight the advantages of the mixed-integer nonlinear MPC application.

关键词： experimental study mixed‐ integer nonlinear programming model predictive control renewable energy systems solar thermal climate systems

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Continuous monitoring scheduling for moving targets by Earth observation satellites

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AEROSPACE SCIENCE AND TECHNOLOGY 2023年第1期140卷

作者： Han, Xiaofeng Yang, Ming Wang, Songyan Chao, Tao Harbin Inst Technol Control & Simulat Ctr Harbin 150001 Peoples R China

The studies of earth observation satellite (EOS) scheduling for stationary targets have been increasing rapidly in recent years. However, these studies ignore EOS scheduling for moving targets (EOSSMT), which is urgently needed in many situations. EOSSMT is more complicated due to two factors, 1) location prediction of the moving targets and 2) algorithm design of EOSSMT optimization model for highly-nonlinear characteristics. In this article, we present a novel continuous monitoring scheduling methodology for moving targets by EOSs. Firstly, in order to predict the location of moving targets, a prediction-capture method, which can calculate the capture probability (CP) of the targets, is proposed. Then, based on the concept CP, we regard the EOSSMT as a stochastic integer nonlinear programming problem. Aiming to maximize observation times and duration, two objective functions with low complexity are proposed correspondingly. Finally, to solve our highly-nonlinear optimization model more efficiently, a dispersion-based heuristic (DBH) is proposed. In the computational experiments, a number of instances (scenarios), in which moving targets are successfully observed, verify the correctness and efficiency of our novel methodology for EOSSMT. Computational experiments also show that DBH can achieve better results than the Genetic Algorithm and Greedy Algorithm, with significantly less algorithm complexity.

关键词： Earth observation satellites EOS scheduling Moving targets integer nonlinear programming Dispersion-based heuristic

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Capability-based machine layout with a matheuristic-based approach

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期198卷 1页

作者： Baykasoglu, Adil Subulan, Kemal Hamzadayi, Alper Dokuz Eylul Univ Fac Engn Dept Ind Engn Izmir Buca Turkey Van Yuzuncu Yil Univ Dept Ind Engn Van Turkey

Capability-based machine layout (CB-ML) problem is firstly introduced in this paper. In the conventional ma-chine layout problem, part flow matrix is generated from parts' machine routes to minimize total part flows. However, defining part flow matrix based on the machines' routes (instead of processing capability requirements of parts) restricts facility designers to utilize available flexibility in manufacturing systems. In this research, parts' processing requirements are defined in terms of Resource Elements (REs), which describe unique pro-cessing capabilities and the processing capability overlaps of machines. If part flow matrix is defined in terms of REs, it becomes possible to utilize available flexibility in a more effective manner. However, physical part flows cannot be identified directly from the RE-based flow matrices. Because, the processing requirements of manu-factured parts can be satisfied from alternative machines that contain the required REs. Therefore, RE-based part flow matrix must be mapped into the machine flow matrix, which requires defining the machine flow matrix as a decision variable. This makes the proposed CB-ML problem much more complicated than the conventional machine layout problem. We firstly developed an integer non-linear programming model for the proposed CB-ML problem. Because of its NP-completeness and nonlinear structure, a matheuristic-based solution approach is also developed. The extensive computational analysis have shown that the proposed approach is able to provide good quality solutions for the larger problem instances within reasonable computation times.

关键词： Facilities planning and design Capability-based machine layout Matheuristic integer nonlinear programming

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