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mixed-integer nonlinear programming for Energy-Efficient Container Handling: Formulation and Customized Genetic Algorithm

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第8期23卷 10542-10555页

作者： Xin, Jianbin Meng, Chuang D'Ariano, Andrea Wang, Dongshu Negenborn, Rudy R. Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Roma Tre Univ Dept Engn I-00146 Rome Italy Delft Univ Technol Dept Marine & Transport Technol NL-2628 Delft Netherlands

Energy consumption is expected to be reduced while maintaining high productivity for container handling. This paper investigates a new energy-efficient scheduling problem of automated container terminals, in which quay cranes (QCs) and lift automated guided vehicles (AGVs) cooperate to handle inbound and outbound containers. In our scheduling problem, operation times and task sequences are both to be determined. The underlying optimization problem is mixed-integer nonlinear programming (MINLP). To deal with its computational intractability, a customized and efficient genetic algorithm (GA) is developed to solve the studied MINLP problem, and lexicographic and weighted-sum strategies are further considered. An epsilon-constraint algorithm is also developed to analyze the Pareto frontiers. Comprehensive experiments are tested on a container handling benchmark system, and the results show the effectiveness of the proposed lexicographic GA, compared to results obtained with two commonly-used metaheuristics, a commercial MINLP solver, and two state-of-the-art methods.

关键词： Containers Task analysis Energy consumption Genetic algorithms Cranes Optimization Job shop scheduling Automated container terminals energy efficiency mixed-integer nonlinear programming genetic algorithm

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Hybrid improved sine cosine algorithm for mixed-integer nonlinear programming problems

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SOFT COMPUTING 2023年第20期27卷 14909-14933页

作者： Song, Haohao Wang, Jiquan Cheng, Zhiwen Chang, Tiezhu Northeast Agr Univ Coll Engn Harbin 150030 Peoples R China Tianjin Univ Coll Management & Econ Tianjin 300072 Peoples R China Anhui Jianghuai Automobile Grp Co Ltd Hefei 230000 Peoples R China

Aiming at the shortcomings of existing algorithms in solving mixed-integer programming problems, such as local convergence and poor solution accuracy, this paper presents a hybrid improved sine and cosine algorithm. The improved position update formula is introduced to enhance the global and local search abilities of the algorithm, and combined mutation is further given to avoid local convergence. The performance of proposed algorithm is validated by the high-dimensional modified CEC 2017 COPs and two complex engineering optimization problems. The experimental findings indicate that the hybrid mechanism of improved sine and cosine algorithm and combined mutation is demonstrably effective, and the proposed algorithm provides a satisfactory solution for addressing high-dimensional complicated mixed-integer programming problems.

关键词： Improved sine cosine algorithm Combined mutation mixed-integer nonlinear programming

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A Branch and Bound Algorithm for Transmission Network Expansion Planning Using Nonconvex mixed-integer nonlinear programming Models

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IEEE ACCESS 2022年 10卷 39875-39888页

作者： Zoppei, Reinaldo T. Delgado, Marcos A. J. Macedo, Leonardo H. Rider, Marcos J. Romero, Ruben Fed Univ Rondonopolis Inst Exact & Nat Sci BR-78736900 Rondonopolis Mato Grosso Brazil Sao Paulo State Univ Dept Elect Engn BR-15385000 Ilha Solteira SP Brazil Univ Estadual Campinas Dept Syst & Energy BR-13083852 Campinas SP Brazil

The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective, mainly due to the nonlinearity and nonconvexity of the feasible region of the problem. This article presents the difficulties and ineffectiveness of the direct use of the traditional BB algorithm for solving nonconvex MINLP problems and proposes the formulation of an efficient BB algorithm for solving this category of problems. The algorithm is formulated taking into account particular aspects of nonconvex MINLP problems, including (i) how to deal with the nonlinear programming (NLP) subproblems, (ii) how to detect the infeasibility of an NLP subproblem, (iii) how to treat the nonconvexity of the problem, and (iv) how to define the fathoming rules. The proposed BB algorithm is used to solve the transmission network expansion planning (TNEP) problem, a classical problem in power systems optimization, and its performance is compared with the performances of off-the-shelf optimization solvers for MINLP problems. The results obtained for four test systems, with different degrees of complexity, indicate that the proposed BB algorithm is effective for solving the TNEP problem with and without considering losses, showing equal or better performance than off-the-shelf optimization solvers.

关键词： Search problems Propagation losses Planning Metaheuristics Linear programming Biological system modeling programming profession Branch and bound algorithm mixed-integer nonlinear programming optimization transmission network expansion planning

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Model updating based on mixed-integer nonlinear programming under model-form uncertainty in finite element model

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ENGINEERING WITH COMPUTERS 2021年第4期37卷 3699-3725页

作者： Jin, Seung-Seop Park, Young-Soo Kim, SungTae Park, Young-Hwan KICT Sustainable Infrastruct Res Ctr Goyang South Korea KICT Dept Infrastruct Safety Res Goyang South Korea

In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers' preference and experience, various FE models can be constructed for a specific structure in practice. However, no one can guarantee that a specific model representation is always best (Model-form uncertainty). Conventional method should perform model updating for each FE model independently and select a best one among them, so that it becomes computationally intensive with many candidate FE models. To handle model-form uncertainty, this study formulates FEMU as the MINLP problem. The proposed method assigns an integer variable for model choice, while continuous real variables are used for the updating parameters. With this formulation, the optimization algorithm can explore both model and parameter space simultaneously to deal with the model-form uncertainty in FE models. Firstly, three numerical experiments were explored to evaluate the performance of the proposed method by considering possible situations in reality as follows: (1) a true FE model exists in model space with an admissible FE model;(2) only admissible FE model exists in model space;and (3) no true and admissible FE models exist in model space. Then, the proposed method was experimentally validated through a real bridge. The results show that the proposed method can find a best FE model with optimal estimates of the updating parameters with much less computational efforts against the conventional FEMU.

关键词： Finite element model updating Model-form uncertainty mixed-integer nonlinear programming Genetic algorithm

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mixed-integer nonlinear programming model for layout design of subsea satellite well system in deep water oil field

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AUTOMATION IN CONSTRUCTION 2021年 123卷 103524-103524页

作者： Hong, Cheng Estefen, Segen F. Wang, Yuxi Lourenco, Marcelo Igor Ningbo Univ Fac Maritime & Transportat Ningbo 315211 Peoples R China Univ Fed Rio de Janeiro Ocean Engn Dept COPPE BR-21941972 Rio De Janeiro Brazil State Key Lab Petr Pollut Control Beijing 102206 Peoples R China CNPC Res Inst Safety & Environm Technol Beijing 102206 Peoples R China

This paper focuses on the concept of a subsea satellite well system in deep water oil field, and a mixed-integer nonlinear programming model (MINLP) is proposed to help design the layout to minimize the payback period. The proposed model has two key aspects. First, the objective function, payback period, reflects the link between the total cost and production. And second, the Floating Production Storage and Offloading units (FPSOs), subsea wells, flowlines, and subsea obstacles are integrated for the modeling, presenting the interaction of the components from underground to the sea level. A decomposition strategy based on gradient descent algorithm is proposed to solve the model. The case studies indicate the model's feasibility. Besides, two different applications of the model are presented, one is to optimize the layout under given horizontal displacements and the other is the cost comparison between drilling horizontal well and vertical well, indicating the model's flexibility.

关键词： Subsea production system Satellite well system concept Layout design mixed-integer nonlinear programming Gradient descent algorithm

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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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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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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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Index fund optimization using a hybrid model: genetic algorithm and mixed-integer nonlinear programming

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ENGINEERING ECONOMIST 2019年第3期64卷 298-309页

作者： Diaz, Juan Cortes, Maria Hernandez, Juan Clavijo, Oscar Ardila, Carlos Cabrales, Sergio Univ Los Andes COPA Dept Ind Engn Bogota Colombia

Index funds consist of a subset of stocks, an index tracking portfolio, included in the market index. The index tracking portfolio aims to match the performance of the benchmark index. In this paper, we propose a hybrid model for solving the multiperiod index tracking problem, which includes rebalancing concerns, transaction costs, limits on the number of stocks, and diversification by sector, market capitalization, and stock weight. Our hybrid model combines the genetic algorithm (GA) to select stocks of the index tracking portfolio and mixed-integer nonlinear programming (MINLP) to estimate its weights. Finally, we apply our proposed hybrid model to the S&P500 to find an index tracking portfolio that includes those constraints. The results show that our hybrid model is able to create an index fund whose return rate is similar to the market index with significantly lower risk.

关键词： Index fund Portfolio optimization Genetic algorithm mixed-integer nonlinear programming

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mixed-integer nonlinear programming framework for combined heat and power units with nonconvex feasible operating region: Feasibility, optimality, and flexibility evaluation

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2019年第3期29卷

作者： Razavi, Seyed-Ehsan Javadi, Mohammad Sadegh Nezhad, Ali Esmaeel Univ Birjand Fac Elect & Comp Engn Birjand Iran Islamic Azad Univ Shiraz Branch Dept Elect Engn Shiraz Iran Univ Bologna Dept Elect Elect & Informat Engn Bologna Italy

This paper presents an optimization framework to determine the optimal operating points of combined heat and power (CHP) units with nonlinear, nonconvex feasible operating region (FOR). The mentioned problem is the economic dispatch (ED) of heat-only units, thermal units, and CHP units. Also, the electric units are of thermal technology while their valve-point impact is taken into consideration. Also, the heat power curve of heat-only units is nonlinear. It is noted that the FOR of CHP units has been defined both as convex and nonconvex regions. For those with nonconvex characteristic, a method is proposed to convert it into a convex characteristic. Accordingly, a separate binary variable must be defined to determine the optimal operating point in each convex region. Thus, the presented problem in this paper is of mixed-integer nonlinear programming (MINLP) type modeled in General Algebraic Modeling System (GAMS) software. In this respect, different case studies have been presented to assess the optimality, feasibility, and the flexibility of the model. It is noteworthy that the valve-point effect of thermal units and different FORs of CHP units as well as the electrical power losses have been considered.

关键词： economic heat and power dispatch mixed-integer nonlinear programming nonconvex feasible operating region

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