Approximation algorithms for process systems engineering

Letsios, Dimitrios; Baltean-Lugojan, Radu; Ceccon, Francesco; Mistry, Miten; Wiebe, Johannes; Misener, Ruth

doi:10.1016/j.compchemeng.2019.106599

“…as arising in Royal Mail deliveries. This project is part of our larger aims toward approximation algorithms for process systems engineering (Letsios et al 2019). The main contributions are (i) better than 2-approximation algorithms for various cases of the problem and (ii) a two-stage robust optimization approach for BJSP under uncertainty based on machine augmentation and lexicographic optimization, whose performance is substantiated empirically.…”

Section: Resultsmentioning

confidence: 99%

Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Letsios

¹

,

Bradley²,

Suraj

³

et al. 2021

J Sched

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Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling $$P||C_{\max }$$ P | | C max problem which we call the bounded job start scheduling problem. Given a set of jobs, each specified by an integer processing time $$p_j$$ p j , that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound $$g\le m$$ g ≤ m on the number of jobs that may simultaneously begin per unit of time. With perfect input knowledge, we show that Longest Processing Time First (LPT) algorithm is tightly 2-approximate. After proving that the problem is strongly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard even when $$g=1$$ g = 1 , we elaborate on improving the 2-approximation ratio for this case. We distinguish the classes of long and short instances satisfying $$p_j\ge m$$ p j ≥ m and $$p_j<m$$ p j < m , respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. In the presence of uncertain job processing times, we exploit machine augmentation and lexicographic optimization, which is useful for $$P||C_{\max }$$ P | | C max under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines. Given a collection of schedules of makespan $$\le D$$ ≤ D , this approach allows distinguishing which are the more robust. We substantiate both the heuristics and our recovery approach numerically using Royal Mail data. We show that for the Royal Mail application, machine augmentation, i.e., short-term van rental, is especially relevant.

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“…is true. As a first step we determine the regular component T(t) in the composition (1) using known approximation algorithms [8].…”

Section: Mathematics In Analysis and Forecasting Of Covid-19 Dynamicsmentioning

confidence: 99%

“…Understanding the worldwide COVID-19 dynamics enable to assess its epidemiological characteristics and develop effective public health plans and responses within admissible resource base. The purpose of this work is to create a mathematical model [8] of the epidemic process, which makes it possible to explain the observed dynamics and to predict its development reliably. To reach this goal the following steps are necessary:…”

Section: Introductionmentioning

confidence: 99%

Statistical assessment of biogenic risk for the human population caused by COVID-19

Azimova

¹

,

Kholodova

²

,

Bedoidze

³

et al. 2023

E3S Web Conf.

0

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In the paper an appreciable hierarchy of mathematical models is proposed. It describes the actual dynamics of COVID-19 thickness during 02/12/2020 – 09/22/2021. The incidence sub-model reflects reliably regular (aperiodic and periodic), as well as random components. It is established that the dynamics of the epidemy is essentially seasonal thrice a year. Model elaborated enables to clarify and explain weak weekly fluctuations in the death rate dynamics. It turned out that the maximum risk of death is at 15 and 22 days of disease duration. It means that this virus will presumably be a "satellite" of the human population with corresponded mortality at 1.75%. Calculations performed enable to estimate the level of stochastics in disease and death dynamics. It is near to the amplitude of periodic variation. Computer experiments with developed model predict the global dynamics of the incidence of COVID-19. New epidemic data can show the prospect of improving our model to regard the competitiveness between new sporadically emerging virus strains.

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“…We focus on the pooling problem because of its many industrial applications, including (Misener and Floudas, 2009): crude-oil scheduling (Lee et al, 1996;Li et al, 2007Li et al, , 2012a, water networks (Galan and Grossmann, 1998;Castro et al, 2007), natural gas production (Selot et al, 2008;Li et al, 2011), fixedcharge transportation with product blending (Papageorgiou et al, 2012), hybrid energy systems (Baliban et al, 2012), multi-period blend scheduling (Kolodziej et al, 2013), and mining (Boland et al, 2015). Solving the pooling problem is NP-hard (Alfaki and Haugland, 2013b;Baltean-Lugojan and Misener, 2018;Letsios et al, 2020), so deterministic global optimization solvers use algorithms such as branch & bound to solve the problem. Our goal with explicitly using special structure information is practically solving larger problem sizes.…”

Section: Introductionmentioning

confidence: 99%

Solving the pooling problem at scale with extensible solver GALINI

Ceccon¹,

Martin-Misener²

2021

Preprint

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This paper presents a Python library to model pooling problems, a class of network flow problems with many engineering applications. The library automatically generates a mixed-integer quadratically-constrained quadratic optimization problem from a given network structure. The library additionally uses the network structure to build 1) a convex linear relaxation of the non-convex quadratic program and 2) a mixed-integer linear restriction of the problem. We integrate the pooling network library with GALINI, an open-source extensible global solver for quadratic optimization. We demonstrate GALINI's extensible characteristics by using the pooling library to develop two GALINI plug-ins: 1) a cut generator plug-in that adds valid inequalities in the GALINI cut loop and 2) a primal heuristic plug-in that uses the mixed-integer linear restriction.We test GALINI on large scale pooling problems and show that, thanks to the good upper bound provided by the mixed-integer linear restriction and the good lower bounds provided by the convex relaxation, we obtain optimality gaps that are competitive with Gurobi 9.1 on the largest problem instances.

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Approximation algorithms for process systems engineering

Cited by 6 publications

References 191 publications

Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Statistical assessment of biogenic risk for the human population caused by COVID-19

Solving the pooling problem at scale with extensible solver GALINI

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