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A Di.ensi.nal Reducti.n Approach Based on Essenti.l Constrai.ts i. Li.ear Programmi.g

Ameri.an Journal of Operati.ns Research 2024年第1期14卷 1-31页

作者： eirini i. nikolopoulou George S. Androulaki. Department of Mathemati.s University of Patras Patras Greece Department of Busi.ess Admi.i.trati.n University of Patras Patras Greece

Thi. paper presents a new di.ensi.n reducti.n strategy for medi.m and large-scale li.ear programmi.g problems. The proposed method uses a subset of the ori.i.al constrai.ts and combi.es two algori.hms: the wei.hted average and the cosi.e si.plex algori.hm. The fi.st approach i.enti.i.s bi.di.g constrai.ts by usi.g the wei.hted average of each constrai.t, whereas the second algori.hm i. based on the cosi.e si.i.ari.y between the vector of the objecti.e functi.n and the constrai.ts. These two approaches are complementary, and when used together, they locate the essenti.l subset of i.i.i.l constrai.ts requi.ed for solvi.g medi.m and large-scale li.ear programmi.g problems. After reduci.g the di.ensi.n of the li.ear programmi.g problem usi.g the subset of the essenti.l constrai.ts, the soluti.n method can be chosen from any sui.able method for li.ear programmi.g. The proposed approach was appli.d to a set of well-known benchmarks as well as more than 2000 random medi.m and large-scale li.ear programmi.g problems. The results are promi.i.g, i.di.ati.g that the new approach contri.utes to the reducti.n of both the si.e of the problems and the total number of i.erati.ns requi.ed. A tree-based classi.i.ati.n model also confi.med the need for combi.i.g the two approaches. A detai.ed numeri.al example, the general numeri.al results, and the stati.ti.al analysi. for the deci.i.n tree procedure are presented.

关键词： Li.ear Programmi.g Bi.di.g Constrai.ts Di.ensi.n Reducti.n Cosi.e Si.i.ari.y Deci.i.n Analysi. Deci.i.n Trees

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Locati.g Bi.di.g Constrai.ts i. LP Problems

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Ameri.an Journal of Operati.ns Research 2019年第2期9卷 59-78页

作者： eirini i. nikolopoulou George E. Manoussaki. George S. Androulaki. Department of Busi.ess Admi.i.trati.n University of Patras Patras Greece

i. thi. work, a new method i. presented for determi.i.g the bi.di.g constrai.ts of a general li.ear maxi.i.ati.n problem. The new method uses only objecti.e functi.n values at poi.ts whi.h are determi.ed by si.ple vector operati.ns, so the computati.nal cost i. i.feri.r to the correspondi.g cost of matri. mani.ulati.n and/or i.versi.n. Thi. method uses a recently proposed noti.n for addressi.g such problems: the average of each constrai.t. The i.enti.i.ati.n of bi.di.g constrai.ts decreases the complexi.y and the di.ensi.n of the problem resulti.g to a si.ni.i.ant decrease of the computati.nal cost compari.g to Si.plex-li.e methods. The new method i. hi.hly useful when deali.g wi.h very large li.ear programmi.g (LP) problems, where only a relati.ely small percentage of constrai.ts are bi.di.g at the opti.al soluti.n, as i. many transportati.n, management and economi. problems, si.ce i. reduces the si.e of the problem. The method has been i.plemented and tested i. a large number of LP problems. i. LP problems wi.hout superfluous constrai.ts, the algori.hm was 100% successful i. i.enti.yi.g bi.di.g constrai.ts, whi.e i. a set of large scale LP tested problems that i.cluded superfluous constrai.ts, the power of the algori.hm consi.ered as stati.ti.al tool of bi.di.g constrai.ts i.enti.i.ati.n, was up to 90.4%.

关键词： Li.ear Programmi.g Si.plex Bi.di.g Constrai.ts Wei.hted Average

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