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Global optimization of mixed-integer nonlinear programs with SCIP 8

JOURNAL OF GLOBAL OPTIMIZATION 2025年第2期91卷 287-310页

作者： Bestuzheva, Ksenia Chmiela, Antonia Mueller, Benjamin Serrano, Felipe Vigerske, Stefan Wegscheider, Fabian Zuse Inst Berlin Dept AIS2T Berlin Germany GAMS Software GmbH Zuse Inst Berlin Berlin Germany

For over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

关键词： Global optimization mixed-integer nonlinear programming SCIP Branch-and-cut Optimization software Benchmark

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Multi-objective surrogate optimization of mixed-variable IPM motor design problem with ADMM-based approach

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OPTIMIZATION AND ENGINEERING 2025年 1-26页

作者： Asanuma, Tatsuya Kanno, Yoshihiro Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Hongo 7-3-1 Tokyo 1138656 Japan JMAG Business Co JSOL Corp Kudan Kaikan TerraceKudan Minami 1-6-5 Tokyo 1020074 Japan

Designing electric motors boils down to solving multi-objective optimization problems where we look for design variables satisfying multiple requirements on, e.g., torque and electromagnetic losses. To design high-performance motors without restriction by existing design ideas, it is necessary to take the design space as wide as possible at the initial design stage. When dealing with the extensive design space, it is required to treat the basic structure parameters of motors and the detailed dimensions as design variables. For an interior permanent magnet (IPM) motor, which is one of the typical motor types, we need to handle discrete integer design variables such as the number of slots and the coil pitch in addition to the continuous ones. However, it is difficult to obtain the discrete design variable values without rounding off to the nearest allowed values in the framework of the existing continuous surrogate optimization such as sequential approximation optimization (SAO) with the response surface created from the electromagnetic finite element analysis results. We solve this mixed-variable optimization problem by the heuristic approach based on the alternating direction method of multipliers (ADMM) and show with example design problems that the better results are obtained more efficiently in terms of the number of expensive objective function evaluations compared to taking rounding-off measures.

关键词： Electric motor Multi-objective optimization mixed-integer nonlinear programming Sequential approximation optimization Surrogate-based optimization Radial basis function network

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Optimization of container ship sailing speed considering carbon emissions policies and cargo time value

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ENGINEERING OPTIMIZATION 2025年

作者： Xing, Yuwei Wu, Zerong Yang, Hualong Zheng, Jianfeng Liu, Baoli Dalian Maritime Univ Transportat Engn Coll Dalian Peoples R China

This article addresses the container ship sailing speed optimization problem considering carbon emissions policies and cargo time value. A mixed-integer nonlinear programming model is formulated to minimize total cost. For consistent sailing speeds across different legs of the voyage, a novel analytical solution is introduced. For scenarios where sailing speeds vary, a discretization method is proposed to transform the nonlinear model into an integer linear one, which can be solved by CPLEX. The proposed model is validated via a numerical experiment. The findings indicate that fluctuations in the unit time value of container cargo exert a more significant influence on the average container ship sailing speed than factors associated with carbon emissions policies. Sensitivity analysis reveals that the cap-and-trade policy is more effective than the carbon tax policy in reducing carbon dioxide emissions. These insights are valuable for liner shipping companies to achieve a balance between environmental sustainability and customer satisfaction.

关键词： Container ship sailing speed cap-and-trade policy carbon tax policy cargo time value mixed-integer nonlinear programming

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On the use of overlapping convex hull relaxations to solve nonconvex MINLPs

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JOURNAL OF GLOBAL OPTIMIZATION 2025年第2期91卷 415-436页

作者： Wu, Ouyang Muts, Pavlo Nowak, Ivo Hendrix, Eligius M. T. HAW Hamburg D-20099 Hamburg Germany Univ Malaga Malaga 29016 Spain

We present a novel relaxation for general nonconvex sparse MINLP problems, called overlapping convex hull relaxation (CHR). It is defined by replacing all nonlinear constraint sets by their convex hulls. If the convex hulls are disjunctive, e.g. if the MINLP is block-separable, the CHR is equivalent to the convex hull relaxation obtained by (standard) column generation (CG). The CHR can be used for computing an initial lower bound in the root node of a branch-and-bound algorithm, or for computing a start vector for a local-search-based MINLP heuristic. We describe a dynamic block and column generation (DBCG) MINLP algorithm to generate the CHR by dynamically adding aggregated blocks. The idea of adding aggregated blocks in the CHR is similar to the well-known cutting plane approach. Numerical experiments on nonconvex MINLP instances show that the duality gap can be significantly reduced with the results of CHRs. DBCG is implemented as part of the CG-MINLP framework Decogo, see https://***/en/latest/***.

关键词： Decomposition method Parallel computing Column generation Nonconvex optimization mixed-integer nonlinear programming

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Benefit Maximizing Network Design in the public sector

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COMPUTERS & OPERATIONS RESEARCH 2025年 178卷

作者： Aboolian, Robert Karimi, Majid Calif State Univ San Marcos Coll Business Adm Dept Operat & Supply Chain Management 333 S Twin Oaks Valley Rd San Marcos CA 92096 USA

This paper introduces the Benefit Maximization Network Design Problem (BNDP), an innovative framework aimed at optimizing public service systems. By integrating consumer choice models with a focus on minimizing consumer disutility, the BNDP strategically maximizes societal welfare by optimizing the net benefits derived from service utilization, carefully weighing the costs of service capacity against the value delivered to the public. An essential aspect of this study is the development of an epsilon-optimal solution approach, which effectively addresses the intricate optimization challenges inherent in public service system design, including nonlinear equilibrium conditions. This approach efficiently identifies the optimal number, locations, and capacities for service facilities, ensuring practical and effective solutions despite the model's complexity. A practical application of the BNDP is demonstrated through a detailed case study on preventive healthcare in San Diego, showcasing the model's ability to refine operational solutions and significantly enhance societal benefits. The results underscore the importance of prioritizing benefit maximization over simplistic capacity thresholds and participation maximization, leading to either higher levels of consumer participation while using optimal levels of resources or comparable levels of customer participation with significantly fewer resources and reasonable utilization rates. Furthermore, the paper explores the model's applicability in the private sector to maximize corporate profits, highlighting its versatility. The study concludes by advocating for policymakers to prioritize the use of BNDP in establishing optimal budgets for public agencies rather than allocating resources based on exogenous capacities.

关键词： Location models Service system design Elastic demand Congestion Stochastic demand User-choice mixed-integer nonlinear programming Public sector

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Disaggregated and Distributed Near-Real-Time RIC for Large Scale User-Centric RAN

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2025年 6卷 1591-1609页

作者： Amrallah, Amr Tsukamoto, Yu Murakami, Takahide Ikami, Akio Shinbo, Hiroyuki Amano, Yoshiaki KDDI Res Inc Wireless Technol Div Saitama 3568502 Japan

The evolution toward user-centric radio access networks (RANs) necessitates innovative management strategies to handle growing network demands efficiently. This study presents a novel framework for the disaggregated and distributed deployment of near-real-time RAN intelligent controllers (near-RT RICs) tailored for large-scale user-centric networks. By leveraging a mixed-integer nonlinear programming (MINLP) approach, we aim to optimize both control latency and deployment costs, which are critical considerations in next-generation network management. Our proposed divide-and-conquer (D&C) and heuristic-greedy (HG)-based algorithms significantly reduce computational complexity while maintaining near-optimal performance. Simulation results indicated that the distributed framework achieved a 78% reduction in control latency with only 7% increase in deployment cost compared with the traditional centralized approach. Additionally, it achieved 99% reduction in runtime performance with an objective function value that was just 2% lower than the optimal value. These findings confirm the framework's scalability and effectiveness, validating its suitability for operational telecom environments.

关键词： Open RAN Optimization Costs Heuristic algorithms Computer architecture programming Delays 6G mobile communication 3GPP Time factors Cell-free massive MIMO large-scale network mixed-integer nonlinear programming near-real-time RIC O-RAN RAN optimization user-centric RAN

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Optimum Operation of Microgrid Considering the Effects of Energy Storage and Load Response Program to Increase Resilience

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INTERNATIONAL JOURNAL OF ENGINEERING 2025年第5期38卷 1147-1163页

作者： Valizadeh, M. Mansoor, S. Siyah Sarvenoee, A. Khosravi Kohzadipour, M. Ilam Univ Dept Elect Engn Ilam Iran

Resilience is one of the important issues in power networks. This article analyzes resilience during severe incidents and in normal and critical situations. A mixed-integer nonlinear programming (MINLP) model is presented to investigate the issue. The optimization is done in two levels. In the first level, the optimal size of the energy storage system and its optimal discharge depth are determined for the optimal planning of the microgrid under normal operating conditions. In the second level, after a fault occurs and the microgrid is disconnected from the upstream network and operates in island mode, an energy storage system (ESS) and load response program reduces the system's vulnerability and minimizes the cost of load shedding. This model aims to observe the impact of ESS and demand response programs (DRP) on system performance in numerical conditions and during extreme weather events as a strategy to increase grid resilience. Under normal operating conditions, the return on investment for ESS occurs within one year, and the economic profit of the microgrid with the addition of DRP is about $160,000. Additionally, in critical conditions, the ESS supplies 40% of the loads shut down during the fault, which increases to 66% with the addition of the load response program.

关键词： Resiliency Microgrid Optimal Operation Load Response Program Energy Storage System mixed-integer nonlinear programming Demand Response Program

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Classifier surrogates to ensure phase stability in optimisation-based design of solvent mixtures

DIGITAL CHEMICAL ENGINEERING

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DIGITAL CHEMICAL ENGINEERING 2025年 14卷

作者： Karia, Tanuj Chaparro, Gustavo Chachuat, Benoit Adjiman, Claire S. Imperial Coll London Inst Mol Sci & Engn Sargent Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England

The ability to guarantee a single homogeneous liquid phase is a key consideration in computer-aided mixture/blend design (CAMbD). In this article, we investigate the use of a classifier surrogate of the phase stability condition within a CAMbD optimisation model for designing solvent mixtures with guaranteed phase stability properties. We show how to develop such classifiers for describing multiple candidate mixtures over range of compositions and temperatures based on the generation of phase stability data using thermodynamic models such as UNIFAC. We test the approach on two solvent design case studies and illustrate its effectiveness in enabling the in silico design of stable mixtures, simultaneously providing a probability of phase stability as an interpretable metric.

关键词： Computer-aided mixture/blend design Phase stability mixed-integer nonlinear programming Surrogate-based optimisation Classifier Artificial neural network

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Bi-level data-driven enterprise-wide optimization with mixed-integer nonlinear scheduling problems

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DIGITAL CHEMICAL ENGINEERING 2025年 14卷 100218页

作者： Nikkhah, Hasan Aghayev, Zahir Shahbazi, Amir Charitopoulos, Vassilis M. Avraamidou, Styliani Beykal, Burcu Univ Connecticut Dept Chem & Biomol Engn Storrs CT 06269 USA Univ Connecticut Ctr Clean Energy Engn Storrs CT 06269 USA UCL Sargent Ctr Proc Syst Engn Dept Chem Engn Torrington Pl London WC1E 7JE England Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

Planning and scheduling are crucial components of enterprise-wide optimization (EWO). For the successful execution of EWO, it is vital to view the enterprise operations as a holistic decision-making problem, composed of different interconnected elements or layers, to make the most efficient use of resources in process industries. Among different layers of the operating decisions, planning and scheduling are often treated sequentially, leading to impractical solutions. To tackle this problem, integrated approaches, such as bi-level programming are utilized to optimize these two layers simultaneously. Nonetheless, the bi-level optimization of such interdependent and holistic formulations is still difficult, particularly when dealing with mixed-integer nonlinear programming (MINLP) problems, due to a lack of effective algorithms. In this study, we employ the Data-driven Optimization of bi-level mixed-integer nonlinear problems (DOMINO) framework, a data- driven algorithm developed to handle single-leader single-follower bi-level mixed-integer problems, to solve single-leader multi-follower planning and scheduling problems subject to MINLP scheduling formulations. We apply DOMINO to the continuous production of multi-product methyl methacrylate polymerization process formulated as a Traveling Salesman Problem and demonstrate its capability in achieving near-optimal guaranteed feasible solutions. Building on this foundation, we extend this strategy to solve a high-dimensional and highly constrained nonlinear crude oil refinery operation problem that has not been previously tackled in this context. Our study further evaluates the efficacy of using local, NOMAD (nonlinear Optimization by Mesh Adaptive Direct Search), and a global data-driven optimizer, ARGONAUT (AlgoRithms for Global Optimization of coNstrAined grey-box compUTational), within the DOMINO framework and characterize their performance both in terms of solution quality and computational expense. The results ind

关键词： Data-driven optimization Integrated planning and scheduling Bi-level programming mixed-integer nonlinear programming

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Integrating lot-sizing and pricing decisions in multi-channel markets with discrete menus of prices

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Computers & Operations Research 2025年 182卷

作者： Mourad Terzi Yassine Ouazene Alice Yalaoui Farouk Yalaoui Mines Saint-Etienne Univ. Clermont Auvergne CNRS UMR 6158 LIMOS CMP Department of Manufacturing Sciences and Logistics F-13541 Gardanne France Computer Science and Digital Society Laboratory (LIST3N) Université de Technologie de Troyes 12 rue Marie Curie CS 42060 10004 Troyes CEDEX France Chaire Connected Innovation Université de Technologie de Troyes 12 rue Marie Curie CS 42060 10004 Troyes CEDEX France

This paper presents a model for coordinating lot-sizing and pricing decisions for manufacturers operating in multichannel markets with limited production capacity. Integrating these decisions is a significant challenge for manufacturers because it allows them to align their marketing and operational strategies effectively. This study addresses the application of attraction models to characterize consumers’ preferences and switching behavior between sales channels. Initially, the problem is formulated as a non-convex mixed-integer nonlinear programming ( MINLP ) model that incorporates production capacity constraints and a discrete menu of prices for each channel. To overcome the challenges of nonlinearity and nonconvexity, the problem is reformulated as an exact mixed-integer linear programming ( MILP ) model. Then, two MILP -based heuristics, the Fix-and-Relax and Double-Fix-and-Relax methods, are designed to solve the problem efficiently. An illustrative example demonstrates the model’s practical application and offers valuable insights for decision-makers in real-life scenarios. Furthermore, a comprehensive experimental study on 120 benchmark instances shows that the proposed solution methods achieve near-optimal solutions in less than one minute of computational time.

关键词： Lot-sizing Pricing Multi-channel market Attraction demand models mixed-integer nonlinear programming mixed-integer linear programming Heuristics

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