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INFORMS JOURNAL ON COMPUTING 2021年第2期33卷 421-435页

作者： Berthold, Timo Witzig, Jakob Fair Isaac Germany GmbH D-64625 Bensheim Germany Zuse Inst Berlin D-14195 Berlin Germany

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.

关键词： mixed integer nonlinear programming infeasibility analysis conflict analysis branch-and-bound

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A new efficient GA-Benders' decomposition method: For power generation expansion planning with emission controls

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IEEE TRANSACTIONS ON POWER SYSTEMS 2007年第3期22卷 1092-1100页

作者： Sirikum, Jiraporn Techanitisawad, Anulark Kachitvichyanukul, Voratas Elect Generating Author Thailand Syst Planning Div Bang Krui 11130 Nonthaburi Thailand Asian Inst Technol Sch Engn Technol Ind Syst Engn Program Ind Engn & Management Dept Klongluang 12120 Pathumthani Thailand

The power generation expansion planning (PGEP) problem is a large-scale mixed integer nonlinear programming (MINLP) problem cited as one of the most complex optimization problems. In this paper, an application of a new efficient methodology for solving the power generation expansion planning problem is presented, A comprehensive planning production simulation model is introduced toward formulating into an MINLP model. The model evaluates the most economical investment planning for additional thermal power generating units of the optimal mix for long-term power generation expansion planning with emission controls, regarding to the incorporated environmental costs, subject to the integrated requirements of powers demands, power capacities, loss of load probability (LOLP) levels, locations, and environmental limitations for emission controls. A. GA-heuristic-based method called GA-Benders' decomposition (GA-BD) is proposed for solving this complex problem. Finally, an application of the proposed GA-BD method is discussed and concluded.

关键词： Benders' decomposition emission modeling GA-Benders' decomposition genetic algorithms mixed integer nonlinear programming power generation expansion planning

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Resource allocation in uplink wireless multi-cell OFDMA networks

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COMPUTER STANDARDS & INTERFACES 2016年 44卷 274-289页

作者： Adasme, Pablo Leung, Janny Lisser, Abdel Univ Santiago Chile Dept Ingn Elect Santiago Chile Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Univ Paris 11 Lab Rech Informat F-91190 Orsay France

We propose resource allocation models for wireless multi-cell orthogonal frequency division multiple access (OFDMA) networks. The models-maximize signal to interference noise ratio (SINR) and capacity with SINR produced in an OFDMA network subject to user power and subcarrier assignment constraints. We derive mixed integer programming formulations for the case when maximizing SINR and piecewise linear approximations for the capacity objective. A variable neighborhood search (VNS) metaheuristic is proposed to compute near optimal solutions. Our numerical results indicate that VNS provides near optimal solutions and better feasible solutions than CPLEX and DICOPT solvers in significantly less computational cost. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Wireless multi-cell OFDMA networks mixed integer linear programming mixed integer nonlinear programming Resource allocation Variable neighborhood search

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Development of a Diversity-Preserving Strategy for the Pareto Optimization in Chemical Process Design

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CHEMIE INGENIEUR TECHNIK 2017年第10期89卷 1297-1305页

作者： Zimmermann, Kristina Fieg, Georg Hamburg Univ Technol Inst Proc & Plant Engn Schwarzenberg Campus 4 D-21073 Hamburg Germany

The simulation-based design of chemical processes with an overlaid multi-objective optimization is of growing importance. The quality of the determined optimization results, referred to as the Pareto front, influences directly the variety of solutions given to the decision maker. In case of the frequently used genetic algorithms, a lot of studies have been done for a precise approximation of the Pareto front. However, most of the developed methods are inconvenient and/or time-consuming and, thus, inappropriate for industrial applications. A novel approach, the two-step optimization, was successfully tested in order to overcome these challenges.

关键词： Computer-aided process engineering Diversity Genetic algorithm mixed integer nonlinear programming Multi-objective optimization

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Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第2-3期59卷 277-306页

作者： Castro, Pedro M. Grossmann, Ignacio E. Lab Nacl Energia & Geol P-1649038 Lisbon Portugal Univ Lisbon Fac Ciencias Ctr Invest Operac P-1749016 Lisbon Portugal Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).

关键词： Global optimization mixed integer nonlinear programming mixed integer linear programming Scheduling Hydroelectric system

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FiberSCIP-A Shared Memory Parallelization of SCIP

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INFORMS JOURNAL ON COMPUTING 2018年第1期30卷 11-30页

作者： Shinano, Yuji Heinz, Stefan Vigerske, Stefan Winkler, Michael Zuse Inst Berlin D-14195 Berlin Germany Fair Isaac Germany GmbH D-14195 Berlin Germany GAMS Software GmbH D-14195 Berlin Germany Gurobi GmbH D-14195 Berlin Germany

Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint integer Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present away to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel.

关键词： parallel branch-and-bound deterministic parallelism constraint integer programming mixed integer programming mixed integer nonlinear programming SCIP MIP MINLP

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Optimal processing route for the utilization and conversion of municipal solid waste into energy and valuable products

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JOURNAL OF CLEANER PRODUCTION 2018年 174卷 857-867页

作者： Rizwan, Muhammad Saif, Yousef Almansoori, Ali Elkamel, Ali Khalifa Univ Sci & Technol Dept Chem Engn Petr Inst POB 2533 Abu Dhabi U Arab Emirates Univ Waterloo Dept Chem Engn Waterloo ON N2L 3G1 Canada

A systematic design of municipal solid waste (MSW) management system can lead to identify a promising and/or sustainable way of handling MSW by processing it into energy and valuable products. In this study, a systematic framework is developed for the superstructure-based optimization of MSW processing routes. The proposed superstructure includes the potential technological alternatives (such as recycling, composting, anaerobic digestion with electricity generation, gasification followed by catalytic transformation, gasification with electricity generation, plasma arc gasification with electricity generation, pyrolysis with electricity generation, incineration with electricity generation, and landfill with electricity generation) for producing valuable products from MSW. Based on the developed superstructure, a mixed integer nonlinear programming (MINLP) model is developed to identify the optimal MSW processing pathways considering two different MSW handling scenarios. For ease of the solution, the MINLP model is linearized to its equivalent MILP form, and solved in GAMS. The solution to the optimization problem provides the optimal/promising route for the synthesis of useful products from MSW under chosen economic objective function. The developed framework is applied on a case study of Abu Dhabi Emirate to find the optimal processing pathway for handling and processing of MSW into energy and value-added products. The optimization results show that an integrated pathway comprising of recycling the recyclable components of MSW along with the production of bioethanol from the rest of the waste via gasification followed by catalytic transformation can provide potential economic benefits. A sensitivity analysis is also executed to investigate the effect of key economic and technical parameters on the optimization results. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Municipal solid waste Superstructure-based optimization Sustainable management Waste-to-energy mixed integer nonlinear programming

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Production/Distribution System Design with Inventory Considerations

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NAVAL RESEARCH LOGISTICS 2012年第2期59卷 172-195页

作者： Keskin, Burcu B. Uester, Halit Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA Univ Alabama Dept Informat Syst Stat & Management Sci Tuscaloosa AL 35487 USA

This study addresses the design of a three-stage production/distribution system where the first stage includes the set of established retailers and the second and third stages include the sets of potential distribution centers (DCs) and potential capacitated suppliers, respectively. In this problem, in addition to the fixed location/operating costs associated with locating DCs and suppliers, we consider the coordinated inventory replenishment decisions at the located DCs and retailers along with the appropriate inventory costs explicitly. In particular, we account for the replenishment and holding costs at the retailers and selected DCs, and the fixed plus distance-based transportation costs between the selected plants and their assigned DCs, and between the selected DCs and their respective retailers, explicitly. The resulting formulation is a challenging mixed-integer nonlinear programming model for which we propose efficient heuristic solution approaches. Our computational results demonstrate the performance of the heuristic approaches as well as the value of integrated decision-making by verifying that significant cost savings are realizable when the inventory decisions and costs are incorporated in the production distribution system design. (C) 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 172-195, 2012

关键词： production/distribution inventory mixed integer nonlinear programming heuristics

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mixed integer programming with kriging surrogate model technique for dispersion control of photonic crystal fibers

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OPTICAL AND QUANTUM ELECTRONICS 2024年第1期56卷 1-16页

作者： Hammad, Ahmed E. Hameed, Mohamed Farhat O. Obayya, S. S. A. Etman, Ahmed S. Cairo Univ Fac Engn Dept Engn Math & Phys Giza 12613 Egypt Zewail City Sci Technol & Innovat Ctr Photon & Smart Mat October Gardens 6th Of October City 12578 Giza Egypt Ctr Nanotechnol Zewail City Sci Technol & Innovat October Gardens 6th October City 12578 Giza Egypt Univ Mansoura Fac Engn Dept Math & Engn Phys Mansoura 35516 Egypt Univ Mansoura Fac Engn Dept Elect & Commun Engn Mansoura 35516 Egypt

In this paper, mixed integer nonlinear programming (MINLP) optimization algorithm integrated with kriging surrogate-model is newly formulated to optimize the dispersion characteristics of photonic crystal fibers (PCFs). The MINLP is linked with full vectorial finite difference method (FVFDM) to optimize the modal properties of the PCFs. Through the optimization process, the design parameters can take real and/or integer values. The integer values can be used to selectively fill the PCF air holes to control its dispersion characteristics. However, the other optimization techniques deal with real design parameters where the PCF can be optimized using none or predefined infiltrated air holes. The MINLP algorithm is used to obtain an ultra-flat zero dispersion over a broadband of wavelength range from 1.25 to 1.6 mu m using silica PCF selectively infiltrated with Ethanol material. To show the superiority of the proposed algorithm, nematic liquid crystal selectively infiltrated PCFs are also designed with high negative flat dispersion over wide range of wavelengths from 1.25 to 1.6 mu m for the quasi transverse magnetic (TM) and the quasi transverse electric (TE) modes. Such designs have negative flat dispersions of - 163 +/- 0.9 and - 170 +/- 1.2 ps/Km nm, respectively over the studied wavelength range. Therefore, the MINLP algorithms could be used efficiently for the design and optimization of selectively filled photonic devices.

关键词： Photonic crystal fibers mixed integer nonlinear programming Branch and bound Dispersion Nematic liquid crystal Dispersion compensating photonic crystal fibers Selective infiltration Kriging models

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Optimal processing pathway for the production of biodiesel from microalgal biomass: A superstructure based approach

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COMPUTERS & CHEMICAL ENGINEERING 2013年 58卷 305-314页

作者： Rizwan, Muhammad Lee, Jay H. Gani, Rafiqul Korea Adv Inst Sci & Technol Dept Chem & Biomol Engn Taejon 305701 South Korea Tech Univ Denmark Dept Chem & Biochem Engn CAPEC DK-2800 Lyngby Denmark

In this study, we propose a mixed integer nonlinear programming (MINLP) model for superstructure based optimization of biodiesel production from microalgal biomass. The proposed superstructure includes a number of major processing steps for the production of biodiesel from microalgal biomass, such as the harvesting of microalgal biomass, pretreatments including drying and cell disruption of harvested biomass, lipid extraction, transesterification, and post-transesterfication purification. The proposed model is used to find the optimal processing pathway among the large number of potential pathways that exist for the production of biodiesel from microalgae. The proposed methodology is tested by implementing on a specific case with different choices of objective functions. The MINLP model is implemented and solved in GAMS using a database built in Excel. The results from the optimization are analyzed and their significances are discussed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Superstructure optimization Biodiesel Microalgae mixed integer nonlinear programming Biorefinery

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