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An Efficient Modified Particle Swarm Optimization Algorithm for Solving mixed-integer nonlinear programming Problems

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2019年第2期12卷 530-543页

作者： Sun, Ying Gao, Yuelin Hefei Univ Technol Sch Comp Sci & Informat Engn 193 Tunxi Rd Hefei 230009 Anhui Peoples R China North Minzu Univ Ningxia Prov Key Lab Intelligent Informat & Data 204 Wenchang North St Yinchuan 750021 Peoples R China

This paper presents an efficient modified particle swarm optimization (EMPSO) algorithm for solving mixed-integer nonlinear programming problems. In the proposed algorithm, a new evolutionary strategies for the discrete variables is introduced, which can solve the problem that the evolutionary strategy of the classical particle swarm optimization algorithm is invalid for the discrete variables. An update strategy under the constraints is proposed to update the optimal position, which effectively utilizes the available information on infeasible solutions to guide particle search. In order to evaluate and analyze the performance of EMPSO, two hybrid particle swarm optimization algorithms with different strategies are also given. The simulation results indicate that, in terms of robustness and convergence speed, EMPSO is better than the other algorithms in solving 14 test problems. A new performance index (NPI) is introduced to fairly compare the other two algorithms, and in most cases the values of the NPI obtained by EMPSO were superior to the other algorithms. (c) 2019 The Authors. Published by Atlantis Press SARL.

关键词： Particle swarm optimization mixed-integer nonlinear programming Constrained optimization Simulated annealing

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On Solving Nonsmooth mixed-integer nonlinear programming Problems by Outer Approximation and Generalized Benders Decomposition

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第3期181卷 840-863页

作者： Wei, Zhou Ali, M. Montaz Xu, Liang Zeng, Bo Yao, Jen-Chih Yunnan Univ Dept Math Kunming 650091 Yunnan Peoples R China Univ Witwatersrand Sch Comp Sci & Appl Math ZA-2050 Johannesburg South Africa Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Zhejiang Normal Univ Dept Math Jinhua 321004 Peoples R China China Med Univ China Med Univ Hosp Res Ctr Interneural Comp Taichung 40402 Taiwan

In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.

关键词： mixed-integer nonlinear programming Outer approximation Generalized Benders decomposition Subgradient Master program 90C11 90C25 90C30

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A comprehensive multi-objective mixed integer nonlinear programming model for an integrated elderly care service districting problem

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ANNALS OF OPERATIONS RESEARCH 2020年第1-2期291卷 499-529页

作者： Lin, Meiyan Chin, Kwai Sang Ma, Lijun Tsui, Kwok Leung Shenzhen Univ Coll Management Dept Management Sci Shenzhen 518060 Guangdong Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Kowloon Hong Kong Peoples R China City Univ Hong Kong Ctr Syst Informat Engn Kowloon Hong Kong Peoples R China Shenzhen Univ Inst Big Data Intelligent Management & Decis Shenzhen 518060 Guangdong Peoples R China

The integrated care service districting (ICSD) problem is an important logistics decision that the elderly care structures (ECS) face when designing service networks to deliver integrated care to the elderly. The ICSD problem, which aims to prepare enhanced care worker recruitment and training plans for all well-designed service districts, is formulated as a multi-objectives mixed integer nonlinear programming (MOMINLP) model. Several criteria are considered, such as balanced workload of care workers among districts, compactness, indivisibility of elderly locations, and the unknown number of districts to be designed. The model considers three objectives simultaneously, including minimizing the total cost of hiring care workers necessary in all service districts, balancing the workload among districts, and achieving as much compactness of district as possible. Results for analysis were obtained by nondominated sorting genetic algorithm II, a well-known multi-objective evolutionary algorithm for continuous multi-objective optimization, which was modified for our MOMINLP model and tested with actual case. Effects of key parameters, including district- and service-related parameters, on these three objectives were analyzed based on different concerns from decision-makers. Furthermore, different correlations among the deviation of service workload and policies for work encouragement were analyzed for ECS. It informs decision-makers about the performance of key factors of the ICSD problem and improves service quality with proper decisions on related parameters.

关键词： Integrated care service districting problem Multi-objective optimization NSGA-II mixed-integer nonlinear programming Care worker allocation problem Integrated elderly care

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Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2018年 97卷 240-249页

作者： Pourakbari-Kasmaei, Mandi Sanches Mantovani, Jose Roberto State Univ Sao Paulo Dept Elect Engn Ilha Solteira Brazil

There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used to handle the LCOPF problems with logical terms such as conditional statements, logical-and, logical-or, etc., their requirement of several trials and adjustments plagues finding a trustworthy solution. On the other hand, a well-defined solver-based model is of much interest in practice, due to rapidity and precision in finding an optimal solution. To remedy this shortcoming, in this paper we provide a solver-friendly procedure to recast the logical constraints to solver-based mixed-integer nonlinear programming (MINLP) terms. We specifically investigate the recasting of logical constraints into the terms of the objective function, so it facilitates the pre-solving and probing techniques of commercial solvers and consequently results in a higher computational efficiency. By applying this recast method to the problem, two sub-power- and sub-function-based MINLP models, namely SP-MINLP and SF-MINLP, respectively, are proposed. Results not only show the superiority of the proposed models in finding a better optimal solution, compared to the existing approaches in the literature, but also the effectiveness and computational tractability in solving large-scale power systems under different configurations.

关键词： FACTS devices Logical constraint mixed-integer nonlinear programming Optimal power flow Solver-based model Non-smooth terms

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Bi-objective mixed-integer nonlinear programming for multi-commodity tri-echelon supply chain networks

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JOURNAL OF INTELLIGENT MANUFACTURING 2018年第4期29卷 809-826页

作者： Alavidoost, M. H. Tarimoradi, Mosahar Zarandi, M. H. Fazel Amirkabir Univ Technol Dept Ind Engn Computat Intelligent Syst Lab 424 Hafez AvePOB 15875-4413 Tehran Iran Univ Toronto Knowledge Intelligent Syst Lab Toronto ON Canada

The competitive market and declined economy have increased the relevant importance of making supply chain network efficient. Up to now, this has resulted in great motivations to reduce the cost of services, and simultaneously, to improve their quality. A mere network model, as a tri-echelon, consists of Suppliers, Warehouses or Distribution Centers (DCs), and Retailer nodes. To bring it closer to reality, the majority of parameters in this network involve retailer demands, lead-time, warehouses holding and shipment costs, and also suppliers procuring and stocking costs which are all assumed to be stochastic. The aim is to determine the optimum service level so that total cost is minimized. Obtaining such conditions requires determining which supplier nodes, and which DC nodes in network should be active to satisfy the retailers' needs, an issue which is a network optimization problem per se. The proposed supply chain network for this paper is formulated as a mixed-integer nonlinear programming, and to solve this complicated problem, since the literature for the related benchmark is poor, three numbers of genetic algorithm called Non-dominated Sorting Genetic Algorithm (NSGA-II), Non-dominated Ranking Genetic Algorithm (NRGA), and Pareto Envelope-based Selection Algorithm (PESA-II) are applied and compared to validate the obtained results. The Taguchi method is also utilized for calibrating and controlling the parameters of the applied triple algorithms.

关键词： Supply chain management Tri-echelon network mixed-integer nonlinear programming NRGA NSGA-II PESA-II Taguchi method

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Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON

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OPTIMIZATION METHODS & SOFTWARE 2018年第3期33卷 540-562页

作者： Kilinc, Mustafa R. Sahinidis, Nikolaos V. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In this paper, we present recent developments in the global optimization software BARON to address problems with integer variables. A primary development was the addition of mixed-integer linear programming relaxations to BARON's portfolio of linear and nonlinear programming relaxations, aiming to improve dual bounds and offer good starting points for primal heuristics. Since such relaxations necessitate the solution of NP-hard problems, their introduction to a branch-and-bound algorithm raises many practical issues regarding their effective implementation. In addition to describing BARON's dynamic strategy for deciding under what conditions to activate integer programming relaxations in the course of branch-and-bound, the paper also describes cutting plane and probing techniques that originate from the literature of integer linear programming and have been adapted in BARON to solve nonlinear problems. Finally, we describe BARON's primal heuristics for finding good solutions of mixed-integer nonlinear programmes. For all these techniques, we report extensive computational results on a public data set, aiming to analyse the impact of each technique in the solution process and identify techniques that expedite solution the most.

关键词： mixed-integer nonlinear programming global optimization primal heuristics portfolios of relaxations

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mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期260卷 283-290页

作者： Cafieri, Sonia Omheni, Riadh Univ Toulouse ENAC F-31055 Toulouse France Univ Toulouse IMT F-31400 Toulouse France

We consider the problem of aircraft conflict avoidance in Air Traffic Management systems. Given an initial configuration of a number of aircraft sharing the same airspace, the main goal of conflict avoidance is to guarantee that a minimum safety distance between each pair of aircraft is always respected during their flights. We consider aircraft separation achieved by heading angle deviations, and, propose a mixed 0-1 nonlinear optimization model, that is then combined with another one which is based on aircraft speed regulation. A two-step solution approach is proposed, where the two models are sequentially solved using a state-of-the-art mixed-integer nonlinear programming solver. Numerical results validate the proposed approach and clearly show the benefit of combining the two considered separation maneuvers. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Air traffic management Conflict avoidance mixed-integer nonlinear programming Deterministic global optimization Modeling

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Application of mixed-integer nonlinear Optimization programming Based on Ensemble Surrogate Model for Dense Nonaqueous Phase Liquid Source Identification in Groundwater

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ENVIRONMENTAL ENGINEERING SCIENCE 2019年第6期36卷 699-709页

作者： Hou, Zeyu Dai, Zhenxue Lao, Wangmei Wang, Yu Lu, Wenxi Jilin Univ Construct Engn Coll Changchun Jilin Peoples R China Tangshan Polytech Coll Tangshan Peoples R China Jilin Univ Coll New Energy & Environm Changchun 130000 Jilin Peoples R China

Groundwater contamination source identification (GCSI) is critical for taking effective measures to protect groundwater resources, assess risks, mitigate disasters, and design remediation strategies. Simulation-optimization techniques have been effective tools for GCSI. However, previous studies have applied individual surrogate models when replacing simulation models, rather than making efforts to combine various methods to improve the approximation accuracy of the surrogate model over the simulation model. In this study, the kernel extreme learning machine (KELM) model was proposed to enhance the surrogate model, and to approach GCSI problems, especially those of dense nonaqueous phase liquid-contaminated aquifers, more effectively. In addition, a kriging model and a support vector regression (SVR) model were built and compared with the KELM model, and various ensemble surrogate (ES) modeling techniques were applied to establish four ES models. Results showed that the KELM model was more accurate than the kriging and SVR models;however, the ES models performed much better than the three individual surrogate models. The most precise ES model increased the certainty coefficient (R-2) to 0.9837, whereas limiting the maximum relative error to 13.14%. Finally, a mixed-integer nonlinear programming optimization model was established to identify the groundwater contamination source in terms of location and release history, and simultaneously assess aquifer parameters. The ES model developed in this article could reasonably predict the system response under given operation conditions. Replacement of the simulation model by the ES model considerably reduced the computation burden of the simulation-optimization process and simultaneously achieved high computation accuracy.

关键词： dense nonaqueous phase liquids ensemble surrogate model groundwater contamination source identification mixed-integer nonlinear programming simulation-optimization

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mixed-integer nonlinear programming Formulation of a UAV Path Optimization Problem

Mixed-Integer Nonlinear Programming Formulation of a UAV Pat...

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American Control Conference (ACC)

作者： Ragi, Shankarachary Mittelmann, Hans D. Arizona State Univ Sch Math & Stat Sci Tempe AZ 85287 USA

ISBN: (纸本)9781509059928

We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem, and attempt to find the global optimum solution. As objective functions in UAV path optimization problems tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the purpose of this study, we choose a target tracking application, where the goal is to optimize the kinematic controls of UAVs while maximizing the target tracking performance. First, we compare the performance of two traditional solvers numerically - MATLAB's fmincon and knitro. Second, we formulate this UAV path optimization problem as a mixed-integer nonlinear program (MINLP). As this MINLP tends to be computationally expensive, we present two pruning methods to make this MINLP tractable. We also present numerical results to demonstrate the performance of these methods.

关键词： UAV path optimization target tracking mixed-integer nonlinear programming fmincon knitro

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Maximizing the number of conflict-free aircraft using mixed-integer nonlinear programming

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COMPUTERS & OPERATIONS RESEARCH 2017年第Apr.期80卷 147-158页

作者： Cafieri, Sonia Rey, David Univ Toulouse ENAC F-31055 Toulouse France UNSW Univ New South Wales Australia Sch Civil & Environm Engn Sydney NSW 2052 Australia

We address the conflict detection and resolution problem in air traffic control, where an aircraft conflict is a loss of separation between aircraft trajectories. Conflict avoidance is crucial to ensure flight safety and remains a challenging traffic control problem. We focus on speed control to separate aircraft and consider two approaches: (i) maximize the number of conflicts resolved and (ii) identify the largest set of conflict-free aircraft. Both problems are modeled using mixed-integer nonlinear programming and a tailored greedy algorithm is proposed for the latter. Computational efficiency is improved through a preprocessing algorithm which attempts to reduce the size of the conflict resolution models by detecting the existence of pairwise potential conflicts. Numerical results are provided after implementing the proposed models and algorithms on benchmark conflict resolution instances. The results highlight the benefits of using the proposed pre-processing step as well as the versatility and the efficiency of the proposed models. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： mixed-integer nonlinear programming Conflict detection and resolution Air traffic control Deterministic global optimization Modeling

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