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A Multi-Reference Relaxation Enforced Neighborhood Search Heuristic in SCIP

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arXiv 2024年

作者： Bolusani, Suresh Mexi, Gioni Besançon, Mathieu Turner, Mark Zuse Institute Berlin Germany Grenoble Alpes University Inria LIG France

This paper proposes and evaluates a Multi-Reference Relaxation Enforced Neighborhood Search (MRENS) heuristic within the SCIP solver. This study marks the first integration and evaluation of MRENS in a full-fledged MILP solver, specifically coupled with the recently-introduced Lagromory separator for generating multiple reference solutions. Computational experiments on the MIPLIB 2017 benchmark set show that MRENS, with multiple reference solutions, improves the solver's ability to find higher-quality feasible solutions compared to single-reference approaches. This study highlights the potential of multi-reference heuristics in enhancing primal heuristics in MILP *** Codes 90-08, 90C11, 90C57, 90C59, © 2024, CC BY.

关键词： mixed-integer linear programming

2-Distance Coloring of Planar Graphs Without 4,6-Cycles

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SSRN

SSRN 2024年

作者： Bu, Yuehua Bao, Zhimin Zhu, Hongguo Department of Mathematics Zhejiang Normal University Zhejiang321004 China Department of Basics Zhejiang Guangsha Vocational and Technical University of Construction Zhejiang322100 China

For a graph G and a positive integer k, a 2-distance k-coloring of G is a proper k-coloring such that any two vertices at distance 2 cannot share the same color. In this paper, we prove that every planar graph without 4,6-cycles and ∆ ≥ 20 admits a 2-distance (∆ + 3)-coloring, which improves the result of Cranston ***(2017). © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Energy Management for Prepaid Customers: A linear Optimization Approach

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arXiv 2024年

作者： Marathe, Maitreyee Roald, Line A. Dept. of Electrical and Computer Engineering University of Wisconsin-Madison Madison United States

With increasing energy prices, low income households are known to forego or minimize the use of electricity to save on energy costs. If a household is on a prepaid electricity program, it can be automatically and immediately disconnected from service if there is no balance in its prepaid account. Such households need to actively ration the amount of energy they use by deciding which appliances to use and for how long. We present a tool that helps households extend the availability of their critical appliances by limiting the use of discretionary ones, and prevent disconnections. The proposed method is based on a linear optimization problem that only uses average power demand as an input and can be solved to optimality using a simple greedy approach. We compare the model with two mixed-integer linear programming models that require more detailed demand forecasts and optimization solvers for implementation. In a numerical case study based on real household data, we assess the performance of the different models under different accuracy and granularity of demand forecasts. Our results show that our proposed linear model is much simpler to implement, while providing similar performance under realistic circumstances. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Reducing the Large Set Threshold for Oertel’s Conjecture on the mixed-integer Volume

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arXiv 2024年

作者： Cristi, Andrés Salas, David EPFL Lausanne Switzerland Instituto de ciencias de la Ingeniería Universidad de O’Higgins Rancagua Chile

In 1960, Grünbaum proved that for any convex body C ⊂ d and every halfspace H containing the centroid of C, one has that the volume of H ∩ C is at least a 1e-fraction of the volume of C. Recently, in 2014, Oertel conjectured that a similar result holds for mixed-integer convex sets. Concretely, he proposed that for any convex body C ⊂ n+d, there should exist a point x ∈ S = C ∩ (n × d) such that for every halfspace H containing x, one has that (Formula Presented), where Hd denotes the d-dimensional Hausdorff measure. While the conjecture remains open, Basu and Oertel proved in 2017 that the above inequality holds true for sufficiently large sets, in terms of a measure known as the lattice width of a set. In this work, by following a geometric approach, we improve this result by substantially reducing the threshold at which a set can be considered large. We reduce this threshold from an exponential to a polynomial dependency on the dimension, therefore significantly enlarging the family of mixed-integer convex sets over which Oertel’s conjecture holds true. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Gracefulness of two nested cycles: a first approach

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arXiv 2024年

作者： Licona, Miguel Tey, Joaquín Universidad Autónoma Metropolitana Iztapalapa Av. San Rafael Atlixco 186 col. Vicentina Iztapalapa09340 Mexico

It is known that if a plane graph admits a graceful (resp. near-graceful) labeling, then its semidual admits a conservative (resp. near-conservative) labeling. In this work we prove that the semidual of a plane graph of size M consisting of two nested cycles is conservative if M ≡ 0, 3 (mod 4), and it is near-conservative otherwise. We also show that for a given integer m1 ≥ 3, there exists m∗ > m1 such that for m2 ≥ m∗, if m1 + m2 ≡ 0, 3 (mod 4) (resp. m1 + m2 ≡ 1, 2 (mod 4)), then there exists a graceful (resp. near-graceful) plane graph consisting of two nested cycles with sizes m1 and m2, *** Codes 05C78, 05C05, 05C21 © 2024, CC BY-NC-ND.

关键词： mixed-integer linear programming

Flow Shop Scheduling with Inter-Stage Flexibility and Blocking Constraints

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arXiv 2024年

作者： Nicosia, Gaia Pacifici, Andrea Pferschy, Ulrich Russo, Anna Russo Salvatore, Cecilia Dipartimento di Ingegneria Civile Informatica e delle Tecnologie Aeronautiche Università degli Studi "Roma Tre" via della Vasca Navale 79 Rome00146 Italy Dipartimento di Ingegneria Civile e Ingegneria Informatica Università degli Studi di Roma "Tor Vergata" Via del Politecnico 1 Rome00133 Italy Department of Operations and Information Systems University of Graz Universitaetsstrasse 15 Graz8010 Austria

We investigate a scheduling problem arising from a material handling and processing problem in a production line of an Austrian company building prefabricated house walls. The addressed problem is a permutation flow shop with blocking constraints in which the machine of at least one stage can process a number operations of two other stages in the system. This situation is usually referred to as multitask or inter-stage flexibility. The problem is in general NP-hard, but we derive a number of special cases that can be solved in polynomial time. For the general case, we present a variety of heuristic algorithms, with a focus on matheuristics that are grounded in two different mixed-integer linear programming (MIP) formulations of the problem. These matheuristics leverage the strengths of exact optimization techniques while introducing flexibility to address limits on computation time. To assess the performance of the proposed approaches, we conduct an extensive computational study on randomly generated test cases based on real-world *** Codes 90B35 (Primary) 90C59, 65Y20 (Secondary) © 2024, CC BY-NC-ND.

关键词： mixed-integer linear programming

Regularized MIP Model for Integrating Energy Storage Systems and its Application for Solving a Trilevel Interdiction Problem

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arXiv 2024年

作者： Han, Dahye Jiang, Nan Dey, Santanu S. Xie, Weijun School of Industrial and Systems Engineering Georgia Institute of Technology United States School of Operations Research and Information Engineering Cornell Tech United States

Incorporating energy storage systems (ESS) into power systems has been studied in many recent works, where binary variables are often introduced to model the complementary nature of battery charging and discharging. A conventional approach for these ESS optimization problems is to relax binary variables and convert the problem into a linear program. However, such linear programming relaxation models can yield unrealistic fractional solutions, such as simultaneous charging and discharging. In this paper, we develop a regularized mixed-integer programming (MIP) model for the ESS optimal power flow (OPF) problem. We prove that under mild conditions, the proposed regularized model admits a zero integrality gap with its linear programming relaxation;hence, it can be solved efficiently. By studying the properties of the regularized MIP model, we show that its optimal solution is also near-optimal to the original ESS OPF problem, thereby providing a valid and tight upper bound for the ESS OPF problem. The use of the regularized MIP model allows us to solve a trilevel min-max-min network contingency problem which is otherwise intractable to solve. © 2024, CC BY.

关键词： mixed-integer linear programming

Positioned and primary positioned C-semigroups

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arXiv 2024年

作者： Cisto, Carmelo Tapia-Ramos, Raquel

Let C be a positive integer cone and k ∈ C. A C-semigroup S is kpositioned if for every h ∈ C \ S we have that k − h belongs to S. In this work, we focus on this family of semigroups and introduce primary positioned C-semigroups, characterizing a subfamily of them through the perspective of irreducibility. Furthermore, we provide some procedures to compute all such semigroups, describing a family of graphs containing all the primary positioned C-semigroups for a fixed k ∈ *** Codes 20M14, 06F05, 05C05, 11D07 © 2024, CC BY-SA.

关键词： mixed-integer linear programming

Tight MIP Formulations for Optimal Operation and Investment of Storage Including Reserves

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arXiv 2024年

作者： Elgersma, Maaike B. Morales-España, Germán Aardal, Karen I. Helistö, Niina Kiviluoma, Juha de Weerdt, Mathijs M.

Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, the standard mixed-integer programming (MIP) models that describe optimal investment and operation of these storage units, including the optional capacity to provide up/down reserves, do not scale well. To improve scalability, the integrality constraints are often relaxed, resulting in linear programming (LP) relaxations that allow simultaneous charging and discharging, while this is not feasible in practice. To address this, we derive the convex hull of the solutions for the optimal operation of storage for one time period, as well as for problems including investments and reserves, guaranteeing that no tighter MIP formulation or better LP approximation exists for one time period. When included in multi-period large-scale energy system models, these improved LP relaxations can better prevent simultaneous charging and discharging. We demonstrate this with illustrative case studies of a unit commitment problem and a transmission expansion planning problem. © 2024, CC BY.

关键词： mixed-integer linear programming