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Asynchronous optimization of part logistics routing problem

JOURNAL OF GLOBAL OPTIMIZATION 2022年第4期82卷 803-834页

作者： Huang, Yaoting Chen, Boyu Lu, Wenlian Jin, Zhong-Xiao Zheng, Ren Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China Fudan Univ Inst Sci & Technol Brain Inspired Intelligence Shanghai Peoples R China Fudan Univ Shanghai Ctr Math Sci Shanghai Peoples R China Fudan Univ Shanghai Key Lab Contemporary Appl Math Shanghai Peoples R China Fudan Univ Lab Math Nonlinear Sci Shanghai Peoples R China Fudan Univ Key Lab Computat Neurosci & Brain Inspired Intell Minist Educ Shanghai Peoples R China SAIC Motor Corp Ltd Artificial Intelligence Lab Shanghai Peoples R China SAIC Intelligent Technol Shanghai Corp Ltd Shanghai Peoples R China

The solution to the capacitated vehicle routing problem (CVRP) is vital for optimizing logistics. However, the transformation of real-world logistics problems into the CVRP involves diverse constraints, interactions between various routes, and a balance between optimization performance and computation load. In this study, we propose a systematic model originating from the part logistic routing problem (PLRP), which is a two-dimensional loading capacitated pickup-and-delivery problem that considers time windows, multiple uses of vehicles, queuing, transit, and heterogeneous vehicles. The newly introduced queuing and transit complicate the problem, and to the best of our knowledge, it cannot be solved using existing methods or the standard commercial optimizer. Hence, this problem has caused the existing research to develop, generalize, and extend into the two-dimensional CVRP (2L-CVRP). To solve this problem, we provide a framework that decouples the combination of 2L-CVRP and global optimization engineering and derives an efficient and realistic solver that integrates diverse types of intelligent algorithms. These algorithms include: (1) a heuristic algorithm for initializing feasible solutions by imitating manual planning, (2) asynchronous simulated annealing (SA) and Tabu search (TS) algorithms to accelerate the optimization of global routes based on novel bundling mechanics, (3) dynamic programming for routing, (4) heuristic algorithms for packing, (5) simulators to review associated time-related constraints, and (6) truck-saving processes to promote the optimal solution and reduce the number of trucks. Moreover, the performances of the SA and TS solver algorithms are compared in terms of various size scales of data to obtain an empirical recommendation for selection. The proposed model successfully established an intelligent management system that can provide systematic solutions for logistics planning, resulting in higher performance and lower costs compared to

关键词： Two-dimensional capacitated vehicle routing Logistics Asynchronous optimization mixed-integer nonlinear programming

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A discretization-based approach for the optimization of the multiperiod blend scheduling problem

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COMPUTERS & CHEMICAL ENGINEERING 2013年 53卷 122-142页

作者： Kolodziej, Scott P. Grossmann, Ignacio E. Furman, Kevin C. Sawaya, Nicolas W. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA ExxonMobil Upstream Res Co Houston TX 77098 USA ExxonMobil Gas & Power Mkt Co Houston TX 77002 USA

In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Pooling problem mixed-integer nonlinear programming Bilinear programming Global optimization Petroleum operations

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Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

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AICHE JOURNAL 2013年第7期59卷 2379-2406页

作者： Chu, Yunfei You, Fengqi Northwestern Univ Dept Chem & Biol Engn Evanston IL 60208 USA

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed-integer dynamic optimization problem or a large-scale mixed-integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed-integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2379-2406, 2013

关键词： integrated scheduling and dynamic optimization decomposition mixed-integer dynamic optimization mixed-integer nonlinear programming multiobjective dynamic optimization

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Solving multistatic sonar location problems with mixed-integer programming

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OPTIMIZATION AND ENGINEERING 2020年第1期21卷 273-303页

作者： Fuegenschuh, Armin R. Craparo, Emily M. Karatas, Mumtaz Buttrey, Samuel E. Brandenburg Tech Univ Cottbus Senftenberg Pl Deutsch Einheit 1 D-03034 Cottbus Germany Naval Postgrad Sch Operat Res Dept 1411 Cunningham Rd Monterey CA 93943 USA Natl Def Univ Naval Acad Ind Engn Dept TR-34940 Istanbul Turkey Bahcesehir Univ Ind Engn Dept TR-34353 Istanbul Turkey

A multistatic sonar system consists of one or more sources that are able to emit underwater sound, and receivers that listen to the reflected sound waves. Knowing the speed of sound in water, the time when the sound was sent from a source, and the arrival time of the sound at one or more receivers, it is possible to determine the location of surrounding objects. The propagation of underwater sound is a complex phenomenon that depends on various attributes of the water (density, pressure, temperature, and salinity) and the emitted sound (pulse length and volume), as well as the reflection properties of the water's surface. These effects can be approximated by nonlinear equations. Furthermore, natural obstacles in the water, such as the coastline, need to be taken into consideration. Given an area of the ocean that should be endowed with a sonar system for surveillance, this paper formulates two natural sensor placement problems. In the first, the goal is to maximize the area covered by a fixed number of sources and receivers. In the second, the goal is to cover the entire area with a minimum-cost set of equipment. For each problem, this paper considers two different sensor models: definite range ("cookie-cutter") and probabilistic. It thus addresses four problem variants using integer nonlinear formulations. Each variant can be reformulated as an integer linear program in one of several ways;this paper discusses these reformulations, then compares them numerically using a test bed from coastlines around the world and a state-of-the-art mixed-integer program solver (IBM ILOG CPLEX).

关键词： mixed-integer nonlinear programming Linearization of quadratic terms Multistatic sonar systems Network design problems Exact methods

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A STRONG DUAL FOR CONIC mixed-integer PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2012年第3期22卷 1136-1150页

作者： Moran R, Diego A. Dey, Santanu S. Vielma, Juan Pablo Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15260 USA

mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [M. Guzelsoy and T. K. Ralphs, Int. J. Oper. Res. (Taichung), 4 (2007), pp. 118-137], [G. L. Nemhauser and L. A. Wolsey, integer and Combinatorial Optimization, Wiley-Interscience, New York, 1988]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we show that strong duality holds.

关键词： mixed-integer nonlinear programming conic programming duality cutting planes

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A Unified Framework for Integrated Energy Systems Optimization With Day-Ahead and Real-Time Coordination

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IEEE ACCESS 2024年 12卷 140628-140642页

作者： Masoumi, Amin Korkali, Mert Marzband, Mousa Univ Missouri Dept Elect Engn & Comp Sci Columbia MO 65211 USA King Abdulaziz Univ Ctr Res Excellence Renewable Energy & Power Syst Jeddah 21589 Saudi Arabia

The operational phase of integrated energy systems (IESs), installed in distribution systems, is increasingly confronted with uncertainties in electrical consumption and output power of variable energy resource (VRE) (e.g., solar photovoltaics). One common approach to mitigate this challenge is to implement day-ahead (DA) scheduling based on cleared prices and purchased power. While this method is effective to some extent, it may not always provide the level of accuracy required. Another viable option is the application of incentive-based demand-response program (I-DRP), where adjustments to energy usage are made in return for a fixed tariff. Nonetheless, this method could result in monopolistic decision-making within an expanding energy industry, albeit assisting in alleviating the barrier. The complexity doubles as the nonlinear formulation of economic objective function is considered in the optimization stage. Hence, the optimality of the solution is a matter of concern. To address these challenges, this research introduces a two-stage coordinated strategy (TSCS) that combines accurate short-term forecasting of uncertainties and I-DRP with regulations of DA and real-time markets to identify the best possible offers and improves the operational efficiency of the IES. By conducting simulations on the IEEE 85-bus test system and comparing the results of the proposed algorithm with those of stochastic programming with fixed reward and penalty rates, our study demonstrates the reliability and accuracy of TSCS, highlighting the flexibility of offers in terms of customer's participation in the optimal operation of the IES.

关键词： Costs Optimization Batteries programming Accuracy Uncertainty Real-time systems Energy management Intserv networks Demand response Machine learning nonlinear systems Integrated energy systems (IESs) incentive-based demand-response programs machine learning mixed-integer nonlinear programming two-stage programming

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SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

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OPTIMIZATION METHODS & SOFTWARE 2018年第3期33卷 563-593页

作者： Vigerske, Stefan Gleixner, Ambros GAMS Software GmbH Zuse Inst Berlin Berlin Germany Zuse Inst Berlin Dept Math Optimizat Berlin Germany

This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.

关键词： mixed-integer nonlinear programming global optimization nonconvex constraints mixed-integer quadratically constrained programming MINLP MIQCP

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Global optimality bounds for the placement of control valves in water supply networks

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OPTIMIZATION AND ENGINEERING 2019年第2期20卷 457-495页

作者： Pecci, Filippo Abraham, Edo Stoianov, Ivan Imperial Coll London Dept Civil & Environm Engn InfraSense Labs London England Delft Univ Technol Fac Civil Engn & Geosci Stevinweg 1 NL-2628 CN Delft Netherlands

This manuscript investigates the problem of optimal placement of control valves in water supply networks, where the objective is to minimize average zone pressure. The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP). Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of the computed valve configurations. In our approach, we implement a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The algorithm relies on the solution of mixed integer linear programs, whose formulations include linear relaxations of the nonconvex hydraulic constraints. We investigate the implementation and performance of different linear relaxation schemes. In addition, a tailored domain reduction procedure is implemented to tighten the relaxations. The developed methods are evaluated using two benchmark water supply networks and an operational water supply network from the UK. The proposed approaches are shown to outperform state-of-the-art global optimization solvers for the considered benchmark water supply networks. The branch and bound algorithm converges to good quality feasible solutions in most instances, with bounds on the optimality gap that are comparable to the level of parameter uncertainty usually experienced in water supply network models.

关键词： Global optimization mixed-integer nonlinear programming Valve placement Pressure management Water supply networks

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Bi-perspective functions for mixed-integer fractional programs with indicator variables

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MATHEMATICAL programming 2021年第1-2期190卷 39-55页

作者： Letchford, Adam N. Ni, Qiang Zhong, Zhaoyu Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England

Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. To obtain a tight relaxation of such problems, one must consider what we call a "bi-perspective" (Bi-P) function. An analysis of Bi-P functions leads to the derivation of a new kind of cutting planes, which we call "Bi-P-cuts". Computational results indicate that Bi-P-cuts typically close a substantial proportion of the integrality gap.

关键词： Fractional programming mixed-integer nonlinear programming Mobile wireless communications OFDMA systems

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Service location grouping and pricing in transportation: Application in air cargo

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第3期267卷 933-943页

作者： Azadian, Farshid Murat, Alper Embry Riddle Aeronaut Univ Coll Business 600 S Clyde Morris Blvd Daytona Beach FL 32114 USA Wayne State Univ Dept Ind & Syst Engn 4815 Fourth St Detroit MI 48202 USA

It is a common practice for transportation firms to group together a set of locations that they serve and price their services based on the group that the origin and destination of a service belong to rather than point-to-point. Proper grouping of service locations and correct pricing under this policy is essential to the financial success of firms. In this research, we develop a novel model for transportation firms to simultaneously group service locations and determine group-to-group pricing by considering the price elasticity of customers' demand. We formulate the problem as a mixed-integer nonlinear programming and propose two exact solution algorithms based on decomposition principles. The performances of our algorithms are evaluated using computational experiments and results show that proposed methods are effective. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Transportation Pricing mixed-integer nonlinear programming Exact solution algorithm

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