Generating Multiple Solutions for Mixed Integer Programming Problems

Danna, Emilie; Fenelon, Mary; Gu, Zonghao; Wunderling, Roland

doi:10.1007/978-3-540-72792-7_22

Cited by 67 publications

(54 citation statements)

References 10 publications

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“…For example, the algorithm can be used only when the solutions are integer valued. Hence, the new algorithm is somewhat simpler than the one presented in Danna et al (2007).…”

Section: Estimation Of Elevator Trip Origin-destination Matricesmentioning

confidence: 98%

“…The new algorithm resembles the second phase of the one-tree algorithm presented in Danna et al (2007), which can be used to find multiple solutions to a mixed integer programming problem. The new algorithm exploits the properties of the LP formulation for the elevator trip OD matrix estimation problem.…”

Section: Estimation Of Elevator Trip Origin-destination Matricesmentioning

confidence: 99%

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The Elevator Trip Origin-Destination Matrix Estimation Problem

Kuusinen¹,

Sorsa²,

Siikonen³

2015

Transportation Science

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This dissertation studies people flow in buildings, especially the process of how passengers arrive at elevator lobbies, estimation of elevator passenger traffic, and human behaviour and decision making in evacuations. The arrival process is studied by taking into account, for the first time, that passengers do not always arrive and use elevators individually but rather in batches. The results suggest that the common assumption that individual arrivals follow a Poisson distribution may not hold when the proportion of batch arrivals is large.To estimate the elevator passenger traffic in a building, new mathematical models and algorithms are developed. The new methods are based on mathematical optimization, namely, linear programming, integer least squares and constraint programming. The results from numerical experiments show that the new approaches satisfy real-time elevator control requirements. In addition, randomized algorithms result in better quality passenger traffic statistics than traditional deterministic algorithms. The dissertation presents also an experimental evacuation study. The results show that people may not be able to select the fastest exit route and that cooperation may slow down the evacuation.The new estimation models and algorithms presented in this dissertation enable better elevator control and some of them are already being implemented by KONE Corporation. The results also give new insights into the process of how passengers arrive at the elevator lobbies and use elevators and into human behaviour in evacuation situations, which affect elevator and building safety planning. Tiivistelmä Tässä väitöskirjassa tutkitaan rakennusten henkilöliikennettä, erityisesti henkilöiden saapumisprosessia hissiauloihin, hisseillä tapahtuvan henkilöliikenteen estimointia sekä henkilöiden käyttäytymistä ja päätöksentekoa rakennuksen evakuoinnissa. Saapumisprosessia tutkitaan ottaen ensimmäistä kertaa huomioon, että henkilöt eivät aina saavu ja käytä hissiä yksin vaan isommissa joukoissa. Tulokset osoittavat, että yleinen olettamus yksittäisten saapumisten Poisson jakautuneisuudesta ei välttämättä päde, kun joukkosaapumisten osuus on suuri.Rakennuksen henkilöliikenteen estimoimiseksi väitöskirjassa kehitetään matemaattisia malleja ja algoritmeja, jotka perustuvat lineaariseen optimointiin, pienimmän neliösumman kokonaislukuoptimointiin ja rajoiteoptimointiin. Numeeristen testien tulokset osoittavat, että menetelmät toteuttavat todellisen hissiohjauksen reaaliaikavaatimukset. Lisäksi satunnaistetut algoritmit tuottavat laadultaan parempia henkilöliikennetilastoja kuin perinteiset deterministiset algoritmit. Väitöskirjassa esitetään myös kokeellinen evakuointitutkimus, jonka tulokset osoittavat, että ihmiset eivät välttämättä kykene valitsemaan nopeinta poistumisreittiä ja että evakuoitavien pyrkimys yhteistyöhön voi hidastaa poistumista.Väitöskirjassa kehitetyt henkilöliikenteen estimointimallit ja -algoritmit mahdollistavat hissien tehokkaamman ohjaamisen ja osa menetelmistä on jo tuotannossa KONE...

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“…For example, the algorithm can be used only when the solutions are integer valued. Hence, the new algorithm is somewhat simpler than the one presented in Danna et al (2007).…”

Section: Estimation Of Elevator Trip Origin-destination Matricesmentioning

confidence: 98%

Section: Estimation Of Elevator Trip Origin-destination Matricesmentioning

confidence: 99%

The Elevator Trip Origin-Destination Matrix Estimation Problem

Kuusinen¹,

Sorsa²,

Siikonen³

2015

Transportation Science

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“…A description of a possible implementation is found in [DFGW07]. We remark that standard Integer Programming algorithms usually find only a single optimal solution.…”

Section: Algorithm 1 Intprogmentioning

confidence: 99%

Pisot unit generators in number fields

Vávra

Veneziano

2018

Journal of Symbolic Computation

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Pisot numbers are real algebraic integers bigger than 1, whose other conjugates have all modulus smaller than 1. In this paper we deal with the algorithmic problem of finding the smallest Pisot unit generating a given number field. We first solve this problem in all real fields, then we consider the analogous problem involving the so called complex Pisot numbers and we solve it in all number fields that admit such a generator, in particular all fields without CM, but not only those.

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“…As defined in section 2, the BLP model is only able to find the optimal solution. There are multiple ways to search for many solutions [3]. In the context of our study, we have chosen to call iteratively the model and to discard the successive optimal solutions after each call.…”

Section: Search For Multiple Solutionsmentioning

confidence: 99%

GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism

Lerouge

Bodic

Héroux

et al. 2015

Graph-Based Representations in Pattern Recognition

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Abstract. The substitution-tolerant subgraph isomorphism is a particular error-tolerant subgraph matching that allows label substitutions for both vertices and edges. Such a matching is often required in pattern recognition applications since graphs extracted from images are generally labeled with features vectors computed from raw data which are naturally subject to noise. This paper describes an extended version of a Binary Linear Program (BLP) for solving this class of graph matching problem. The paper also presents GEM++, a software framework that implements the BLP and that we have made available for the research community. GEM++ allows the processing of different sub-problems (induced isomorphism or not, directed graphs or not) with complex labelling of vertices and edges. We also present some datasets available for evaluating future contributions in this field.

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Generating Multiple Solutions for Mixed Integer Programming Problems

Cited by 67 publications

References 10 publications

The Elevator Trip Origin-Destination Matrix Estimation Problem

The Elevator Trip Origin-Destination Matrix Estimation Problem

Pisot unit generators in number fields

GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism

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