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A mixed-coding scheme of evolutionary algorithms to solve mixed-integer nonlinear programming problems

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2004年第8-9期47卷 1295-1307页

作者： Lin, YC Hwang, KS Wang, FS Natl Chung Cheng Univ Dept Chem Engn Chiayi 62102 Taiwan Natl Chung Cheng Univ Dept Elect Engn Chiayi 62102 Taiwan

In this paper, mixed-integer hybrid differential evolution (MIHDE) is developed to deal with the mixed-integer optimization problems. This hybrid algorithm contains the migration operation to avoid candidate individuals clustering together. We introduce the population diversity measure to inspect when the migration operation should be performed so that the user can use a smaller population size to obtain a global solution. A mixed coding representation and a rounding operation are introduced in MIHDE so that the hybrid algorithm is not only used to solve the mixed-integer nonlinear optimization problems, but also used to solve the real and integer nonlinear optimization problems. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional genetic algorithms. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： hybrid method differential evolution genetic algorithms mixed-integer nonlinear programming evolutionary algorithms

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Optimal design of electronic components by mixed-integer nonlinear programming

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OPTIMIZATION AND ENGINEERING 2004年第3期5卷 271-294页

作者： Van De Braak, G Bünner, MJ Schittkowski, K Univ Bayreuth Dept Math D-95440 Bayreuth Germany Univ Munster Dept Math D-48149 Munster Germany EPCOS AG D-81617 Munich Germany

Cornputer-aided design optimization of electronic components is a powerful tool to reduce development costs on one hand and to improve the performance of (lie components on the other. In this paper, a mathematical model of an electronic filter is outlined. It depends oil certain parameters, some of then) of being continuous, others of integer type. The purpose of the paper is to introduce an extension of the well-known sequential quadratic programming (SQP) method to solve the mixed-integer programming problem (MINLP). It is assumed that the integer variables cannot be relaxed to real ones, that the integer range is sufficiently large, and that they possess some physical meaning so that they basically behave like continuous ones. The general idea is to combine all SQP step with a direct search cycle in the integer space, Hessian information is updated based on difference formulae at neighbored grid points. Numerical results are included to show the feasibility of the mixed-integer nonlinear programming code for academic test examples and in addition for the optimal design of an electronic filter.

关键词： electronic components mixed-integer nonlinear programming discrete optimization categorial variables sequential quadratic programming direct search method

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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

作者： Shankarachary Ragi Hans D. Mittelmann School of Mathematical and Statistical Sciences Arizona State University Tempe 85287-1804 USA

ISBN: (纸本)9781509045839

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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Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2021年 147卷 102240-102240页

作者： Pei, Mingyang Lin, Peiqun Du, Jun Li, Xiaopeng Chen, Zhiwei South China Univ Technol Dept Civil & Transportat Engn Guangzhou 510641 Guangdong Peoples R China Beijing Jiaotong Univ MOE Key Lab Urban Transportat Complex Syst Theory Beijing 100044 Peoples R China Univ S Florida Dept Civil & Environm Engn Tampa FL 33620 USA

Modular vehicle (MV) technology offers the possibility of flexibly adjusting the vehicle capacity by docking/undocking modular pods into vehicles of different sizes en route to satisfy passenger demand. Based on the MV technology, a modular transit network system (MTNS) concept is proposed to overcome the mismatch between fixed vehicle capacity and spatially varying travel demand in traditional public transportation systems. To achieve the optimal MTNS design, a mixed-integer nonlinear programming model is developed to balance the tradeoff between the vehicle operation cost and the passenger trip time cost. The nonlinear model is reformulated into a computationally tractable linear model. The linear model solves the lower and upper bounds of the original nonlinear model to produce a near-optimal solution to the MTNS design. This reformulated linear model can be solved with off-the-shelf commercial solvers (e.g., Gurobi). Two numerical examples are used to demonstrate the applicability of the proposed model and its effectiveness in reducing system costs.

关键词： Public transit Modular vehicle Operation design mixed-integer nonlinear programming

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Optimal design and operation of a multi-energy microgrid using mixed-integer nonlinear programming: Impact of carbon cap and trade system and taxing on equipment selections

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APPLIED ENERGY 2023年第PartA期330卷

作者： Akulker, Handan Aydin, Erdal Bogazici Univ Dept Chem Engn TR-34342 Istanbul Turkiye Ondokuz Mayis Univ Dept Chem Engn TR-55139 Samsun Turkiye Koc Univ Dept Chem & Biol Engn TR-34457 Istanbul Turkiye Koc Univ Koc Univ TUPRAS Energy Ctr KUTEM TR-34450 Istanbul Turkiye

Multi-energy microgrids comprise various energy sources such as solar, wind, hydro, biomass, oil, gas, and coal. Optimal configuration and scheduling of multi-energy microgrids enhance energy efficiency and reduce carbon dioxide emissions. In this work, a novel and detailed mixed-integer nonlinear programming (MINLP) model is proposed to compare the effects of carbon emission taxing and cap and trade system on the optimal equipment selection and scheduling under the regulatory effects of the Paris Agreement. The candidate equipment to be selected by the MINLP model includes two solar panel arrays, two wind turbine farms, two integrated gasification combined cycles, two combined heat and power units, two conventional generators, one biogenerator, one battery, two bio-gasifiers, and one power-to-gas system. The impact of carbon dioxide price, taken as 50, 75, and 100 $/ton, is investigated for both emission taxing and carbon dioxide cap and trade system. Equipment se-lections with the multi-period seasonal data and the carbon dioxide prices of 50 $/ton and 75 $/ton in stand-alone mode are the same for both cases without selecting renewable sourced generators. For the same condi-tions and with a carbon dioxide price of 100 $/ton, the MINLP model selects one wind turbine farm, one bio-generator, and one bio-gasifier. Moreover, the power-to-gas system is chosen in electricity grid-connected mode under emission taxing with the carbon dioxide price of 100 $/ton. For both emission taxing and cap and trade system, the trials using the seasonal data and the yearly average data with carbon dioxide price of 75 $/ton in stand-alone mode contributes to different equipment selections. Results show that carbon dioxide price may be a crucial parameter for equipment selection and must be taken into account in the design phase for optimal design and management. Finally, the MINLP solvers SCIP, BARON, and DICOPT, are compared in terms of CPU times and equipment selections.

关键词： Cap and trade system Carbon taxing mixed-integer nonlinear programming Multi-energy microgrid Optimal design Optimal scheduling

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Sample average approximation for stochastic nonconvex mixed integer nonlinear programming via outer-approximation

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OPTIMIZATION AND ENGINEERING 2021年第3期22卷 1245-1273页

作者： Li, Can Bernal, David E. Furman, Kevin C. Duran, Marco A. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA ExxonMobil Upstream Res Co 22777 Springwoods Village Pkwy Spring TX 77389 USA

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333-346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation algorithm where we iterate between a mixed-integer linear programming (MILP) master problem and a nonconvex nonlinear programming (NLP) subproblem. We prove that the optimal solutions and optimal value obtained by the SAAOA algorithm converge to the optimal solutions and the optimal value of the true SP problem as the sample size goes to infinity. The convergence rate is also given to estimate the sample size. Since the theoretical sample size estimate is too conservative in practice, we propose an SAAOA algorithm with confidence intervals for the upper bound and the lower bound at each iteration of the SAAOA algorithm. Two policies are proposed to update the sample sizes dynamically within the SAAOA algorithm with confidence intervals. The proposed algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently. The proposed algorithm is tested with a stochastic pooling problem and is shown to outperform the external sampling approach where large scale MINLPs need to be solved.

关键词： Stochastic programming Sample average approximation mixed-integer nonlinear programming Outer-approximation

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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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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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Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach

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COMPUTING 2012年第2-4期94卷 325-343页

作者： Patil, Bhagyesh V. Nataraj, P. S. V. Bhartiya, Sharad Indian Inst Technol Syst & Control Engn Grp Bombay 400076 Maharashtra India Indian Inst Technol Dept Chem Engn Bombay 400076 Maharashtra India

In this paper, we propose an algorithm for constrained global optimization of mixed-integer nonlinear programming (MINLP) problems. The proposed algorithm uses the Bernstein polynomial form in a branch-and-bound framework. Ingredients such as continuous relaxation, branching for integer decision variables, and fathoming for each subproblem in the branch-and-bound tree are used. The performance of the proposed algorithm is tested and compared with several state-of-the-art MINLP solvers, on two sets of test problems. The results of the tests show the superiority of the proposed algorithm over the state-of-the-art solvers in terms of the chosen performance metrics.

关键词： Bernstein polynomials Branch-and-bound Global optimization mixed-integer nonlinear programming

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A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

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AERONAUTICAL JOURNAL 2024年第1320期128卷 340-370页

作者： Kaplan, Z. Cetek, C. Sarac, T. Eskisehir Tech Univ Air Traff Control Dept TR-26555 Iki Eylul Eskisehir Turkiye Eskisehir Osmangazi Univ Ind Engn Dept TR-26480 Meselik Eskisehir Turkiye

Global air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the epsilon-constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gokcen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

关键词： Multi-objective programming Air traffic management Aircraft sequencing and scheduling problem mixed-integer nonlinear programming

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