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A cutting-plane algorithm for an orienteering problem with mandatory visits and simultaneous production

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年

作者： Wang, Shijin Zhang, Hanyu Chu, Feng Fang, Kan Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Univ Paris Saclay Univ Evry Lab IBISC Evry France Tianjin Univ Coll Management & Econ Tianjin Peoples R China

This work investigates an orienteering problem with mandatory visits and simultaneous production (denoted by OPMV-SP) in additive manufacturing, where some nodes must be visited and others are optional, and the objective is to maximise the total collected scores. The problem is firstly formulated as a mixed-integer linear programming (MILP) model. Four sets of valid inequalities are then introduced to enhance the MILP. Based on the MILP, an exact method namely cutting-plane algorithm (CPA) is developed and evaluated on both benchmark and simulated instances. The results of benchmarks demonstrate that CPA is competitive, proving the optimality for 191 out of 202 feasible instances. Additionally, the performance of different combinations of valid inequalities are evaluated. Sensitivity analysis on the effects of mandatory visits and waiting times offers managerial insights for production and delivery strategies. The results of simulated instances of real-world cases further demonstrate CPA's efficiency and effectiveness.

关键词： Orienteering problem cutting-plane algorithm additive manufacturing simultaneous production and transportation mixed-integer linear programming

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Hop-to-Hug algorithm: Novel strategy to stable cutting-plane algorithm based on convexification of yield functions

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JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING 2025年第4期17卷 2041-2058页

作者： Chen, Yanbin Lai, Yuanming Liu, Enlong Sichuan Univ Hong Kong Polytech Univ Inst Disaster Management & Reconstruct IDMR Chengdu 610041 Peoples R China Chinese Acad Sci Northwest Inst Eco Environm & Resources State Key Lab Frozen Soil Engn Lanzhou 730000 Peoples R China Sichuan Univ Coll Water Resources & Hydropower State Key Lab Hydraul & Mt River Engn Chengdu 610041 Peoples R China

Numerical challenges, incorporating non-uniqueness, non-convexity, undefined gradients, and high curvature, of the positive level sets of yield function F > 0 are encountered in stress integration when utilizing the return-mapping algorithm family. These phenomena are illustrated by an assessment of four typical yield functions: modified spatially mobilized plane criterion, Lade criterion, Bigoni-Piccolroaz criterion, and micromechanics-based upscaled Drucker-Prager criterion. One remedy to these issues, named the "Hop-to-Hug" (H2H) algorithm, is proposed via a convexification enhancement upon the classical cutting-plane algorithm (CPA). The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point. Furthermore, a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform. Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence. All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation, in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/ 4.0/).

关键词： Elastoplastic model Constitutive model integration cutting-plane algorithm Geotechnical analysis Finite element method (FEM)

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cutting-plane algorithm for estimation of sparse Cox proportional hazards models

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TOP 2024年第1期32卷 57-82页

作者： Saishu, Hiroki Kudo, Kota Takano, Yuichi Univ Tsukuba Grad Sch Sci & Technol 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan Univ Tsukuba Inst Syst & Informat Engn 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan

Survival analysis is a family of statistical methods for analyzing event occurrence times. We adopt a mixed-integer optimization approach to estimation of sparse Cox proportional hazards (PH) models for survival analysis. Specifically, we propose a high-performance cutting-plane algorithm based on a reformulation of our sparse estimation problem into a bilevel optimization problem. This algorithm solves the upper-level problem using cutting planes that are generated from the dual lower-level problem to approximate an upper-level nonlinear objective function. To solve the dual lower-level problem efficiently, we devise a quadratic approximation of the Fenchel conjugate of the loss function. We also develop a computationally efficient least-squares method for adjusting quadratic approximations to fit each dataset. Computational results demonstrate that our method outperforms regularized estimation methods in terms of accuracy for both prediction and subset selection especially for low-dimensional datasets. Moreover, our quadratic approximation of the Fenchel conjugate function accelerates the cutting-plane algorithm and maintains high generalization performance of sparse Cox PH models.

关键词： Cox model Sparse estimation cutting-plane algorithm Mixed-integer optimization Fenchel conjugate Survival analysis

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Interactive stability cutting-plane algorithm for multiobjective nonlinear programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期192卷 446-456页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called "interactive stability cutting-plane compromise programming (ISCPCP)". The cutting-planes which I am going to derive, are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker (DM) at each iterate generated by the algorithm. This algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. Also, we investigate the stability of its efficient solutions which are obtained by using this algorithm. An illustrating example is presented to clarify this algorithm. (C) 2007 Elsevier Inc. All rights reserved.

关键词： cutting-plane algorithm multiobjective nonlinear programming trade-off method best-compromise solution stability

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Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2021年第2期81卷 493-528页

作者： Kobayashi, Ken Takano, Yuichi Nakata, Kazuhide Fujitsu Ltd Artificial Intelligence Lab Nakahara Ku 4-1-1 Kamikodanaka Kawasaki Kanagawa 2118588 Japan Univ Tsukuba Fac Engn Informat & Syst 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan Tokyo Inst Technol Sch Engn Meguro Ku 2-12-1 Ookayama Tokyo 1528552 Japan

This paper studies mean-risk portfolio optimization models using the conditional value-at-risk (CVaR) as a risk measure. We also employ a cardinality constraint for limiting the number of invested assets. Solving such a cardinality-constrained mean-CVaR model is computationally challenging for two main reasons. First, this model is formulated as a mixed-integer optimization (MIO) problem because of the cardinality constraint, so solving it exactly is very hard when the number of investable assets is large. Second, the problem size depends on the number of asset return scenarios, and the computational efficiency decreases when the number of scenarios is large. To overcome these challenges, we propose a high-performance algorithm named the bilevel cutting-plane algorithm for exactly solving the cardinality-constrained mean-CVaR portfolio optimization problem. We begin by reformulating the problem as a bilevel optimization problem and then develop a cutting-plane algorithm for solving the upper-level problem. To speed up computations for cut generation, we apply to the lower-level problem another cutting-plane algorithm for efficiently minimizing CVaR with a large number of scenarios. Moreover, we prove the convergence properties of our bilevel cutting-plane algorithm. Numerical experiments demonstrate that, compared with other MIO approaches, our algorithm can provide optimal solutions to large problem instances faster.

关键词： Mixed-integer optimization Portfolio optimization Cardinality constraint Conditional value-at-risk cutting-plane algorithm

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Consistent tangent operator for cutting-plane algorithm of elasto-plasticity

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2014年第0期272卷 214-232页

作者： Starman, Bojan Halilovic, Miroslav Vrh, Marko Stok, Boris Univ Ljubljana Fac Mech Engn Lab Numer Modelling & Simulat SI-1000 Ljubljana Slovenia

The paper presents a derivation of the consistent tangent operator (CTO) for the cuttingplane algorithm (CPA). For a class of plasticity models that are suitable to be integrated using CPA, an explicit recursive expression is analytically derived and is updated in each iteration of the CPA integration procedure to yield the final value of the CTO when the CPA is converged. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Constitutive equations Numerical integration Consistent tangent operator cutting-plane algorithm YLD2004 UMAT

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An effective hybrid meta-heuristic method for the simultaneous batch production and transportation problem in additive manufacturing

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年第5期63卷 1607-1623页

作者： Wang, Shijin Zhang, Hanyu Chu, Feng Tongji Univ Sch Econ & Management Shanghai Peoples R China Univ Evry Univ Paris Saclay Lab IBISC Evry France

One notable advancement in additive manufacturing (AM) is the mobile mini-factory, which uses a truck equipped with an AM machine to produce orders while en-route to customers' locations. This offers potential benefits such as reduced delivery times and storage expenses for companies. This study investigates a simultaneous batch production and transportation problem (denoted by SBPTP) in additive manufacturing. To solve this problem, a mixed integer linear programming (MILP) model is first formulated. Then, to solve large-scale problems, a meta-heuristic method (denoted by SA-CP) combining a simulated annealing (SA) algorithm, an ant colony optimisation algorithm (ACO) and a cutting-plane algorithm is developed, in which the assignment subproblem is dealt with the SA, the simultaneous production and transportation subproblem is dealt with the ACO, and finally the current solution is further improved by the cutting-plane algorithm. Computational experiments are conducted on both randomly generated instances and modified benchmark instances. The results demonstrate that the SA-CP is very effective since it can obtain the solutions with an average relative percentage gap 0.16% on randomly generated instances and -0.09% on modified benchmark instances within less than 180 CPU seconds, compared to those obtained by solving the MILP model directly with CPLEX within 1 h.

关键词： Additive manufacturing simultaneous production and transportation batch production simulated annealing ant colony optimisation cutting-plane algorithm

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An exact solution approach for the mobile multi-agent sensing problem

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2023年第17期33卷 10405-10424页

作者： Kim, Gwang Lee, Jongmin Moon, Ilkyeong Chosun Univ Div Business Adm Gwangju South Korea Seoul Natl Univ Dept Ind Engn Seoul South Korea Seoul Natl Univ Inst Engn Res Seoul South Korea

Multi-agent systems are generally applicable in various fields and aim to coordinate the decisions from agents, each of which makes a local decision. In particular, research on operations management with mobile multi-agents such as drones has gained prominence in recent years. In this article, we present a mobile multi-agent sensing problem, which is formulated as a submodular maximization problem under a partition matroid constraint. When events detected by agents lead to severe and catastrophic consequences, obtaining (near)-optimal solutions by using exact algorithms is crucial to reducing the probability of harmful situations. Therefore, in this article we propose an exact solution approach, using two valid inequalities for our problem to find a (near)-optimal solution. Moreover, we deal with the risk-averse decision and its cutting-plane algorithm for our problem, which is to maximize conditional value-at-risk (CVaR). Finally, we show the performance of our algorithms through numerical experiments, including a case study on forest fires.

关键词： conditional value-at-risk cutting-plane algorithm mobile multi-agent systems submodular functions valid inequality

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Probabilistic N-k failure-identification for power systems

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NETWORKS 2018年第3期71卷 302-321页

作者： Sundar, Kaarthik Coffrin, Carleton Nagarajan, Harsha Bent, Russell Los Alamos Natl Lab Ctr Nonlinear Studies Los Alamos NM 87545 USA

This article considers a probabilistic generalization of the N-k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N-k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances;the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.

关键词： AC power flow convex relaxation cutting-plane algorithm DC power flow N-k vulnerability network flow network interdiction nonlinear optimization power network resilience

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Network design in scarce data environment using moment-based distributionally robust optimization

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COMPUTERS & OPERATIONS RESEARCH 2017年 88卷 44-57页

作者： Nakao, Hideaki Shen, Siqian Chen, Zhihao Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

We consider a network design problem (NDP) under random demand with unknown distribution for which only a small number of observations are known. We design arc capacities in the first stage and optimize single-commodity network flows after realizing the demand in the second stage. The objective is to minimize the total cost of allocating arc capacities, flowing commodities, and penalty for unmet demand. We formulate a distributionally robust NDP (DR-NDP) by constructing an ambiguity set of the unknown demand distribution based on marginal moment information, to minimize the worst-case total cost over all possible distributions. Approximating polynomials with piecewise-linear functions, we reformulate DR-NDP as a mixed-integer linear program optimized via a cutting-plane algorithm. We test diverse network instances to compare DR-NDP with a stochastic programming approach, a deterministic benchmark model, and a robust NDP formulation. Our results demonstrate adequate robustness of optimal DR-NDP solutions and how they perform under varying demand, modeling parameter, network, and cost settings. The results highlight potential niche uses of DR-NDP in data-scarce contexts. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Stochastic/robust network design Distributionally robust optimization Mixed-integer linear programming Polynomial linearization cutting-plane algorithm

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