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Optimization heuristic solutions, how good can they be?: With empirical applications in location problems
Dalarna University, School of Technology and Business Studies, Statistics.ORCID iD: 0000-0003-2970-9622
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

Abstract [sv]

Kombinatoriska optimeringsproblem, är en av de viktigaste typerna av problem i operationsanalys (OR). Heuristiska och metaheuristiska algoritmer tillämpas allmänt för att hitta lösningar med hög kvalitet. Ett vanligt problem är dock att dessa algoritmer inte garanterar optimala lösningar och sålunda kan det finnas osäkerhet i kvaliteten på lösningar på tillämpade operationsanalytiska problem. Huvudsyftet med denna avhandling är att undersöka användbarheten av statistiska konfidensintervall för att utvärdera kvaliteten på heuristiska lösningar då de tillämpas på stora kombinatoriska optimeringsproblem. Bidragen från denna avhandling är både metodologiska och empiriska. Ur metodologisk synvinkel har nyttan av statistiska konfidensintervall för ett lokaliseringsproblem (p-median problemet) undersökts. Statistiska konfidensintervall fungerar väl för att tillhandahålla information om lösningens kvalitet vid rätt implementering av problemen. Statistiska konfidensintervall överträffar även intervallen som erhålls vid den vanligen använda Lagrange-relaxation. I avhandlingen visas även på att metoden med statistiska konfidensintervall är fungerar väl jämfört med många andra deterministiska intervall i ett mer komplexa optimeringsproblem som det kvadratiska tilldelningsproblemet. P-median problemet och de statistiska konfidensintervallen har implementerats empiriskt för att beräkna och jämföra e-handelns och traditionell handels CO2-utsläpp från transporter, vilken visar att ehandel medför betydligt mindre CO2-utsläpp. Ett annat lokaliseringsproblem som analyserats empiriskt är hur förändringar av den regionala administrativa indelningen av Sverige, vilket är en aktuell och pågående samhällsdiskussion, påverkar medborgarnas tillgänglighet till offentlig service. Analysen visar att regionala administrativa iv gränserna lett till en suboptimal placering av offentliga tjänster. Därmed finns en risk att den samhällsekonomiska nyttan av dessa tjänster är suboptimerad.

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2015. , 200 p.
Series
Dalarna Doctoral Dissertations, 2
National Category
Computational Mathematics
Research subject
Komplexa system - mikrodataanalys
Identifiers
URN: urn:nbn:se:du-17353ISBN: 978-91-89020-94-8 (print)OAI: oai:DiVA.org:du-17353DiVA: diva2:810112
Public defence
2015-04-23, Clas Ohlson, Borlänge, 10:00 (English)
Opponent
Available from: 2015-05-07 Created: 2015-05-06 Last updated: 2015-05-18Bibliographically approved
List of papers
1. On statistical bounds of heuristic solutions to location problems
Open this publication in new window or tab >>On statistical bounds of heuristic solutions to location problems
2016 (English)In: Journal of combinatorial optimization, ISSN 1382-6905, E-ISSN 1573-2886, Vol. 31, no 4, 1518-1549 p.Article in journal (Refereed) Published
Abstract [en]

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region.

Keyword
p-median problem;simulated annealing; jack-knife; discrete optimization; extreme value theory
National Category
Probability Theory and Statistics
Research subject
Complex Systems – Microdata Analysis, General Microdata Analysis - methods
Identifiers
urn:nbn:se:du-16828 (URN)10.1007/s10878-015-9839-0 (DOI)000373574300012 ()
Available from: 2015-02-09 Created: 2015-02-09 Last updated: 2017-12-04Bibliographically approved
2. Confidence in heuristic solutions?
Open this publication in new window or tab >>Confidence in heuristic solutions?
2015 (English)In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 63, no 2, 381-399 p.Article in journal (Refereed) Published
Abstract [en]

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Keyword
p-median problem, deterministic bounds, statistical bounds, jackknife, discrete optimization, extreme value theory
National Category
Probability Theory and Statistics Computational Mathematics
Research subject
Komplexa system - mikrodataanalys, General Microdata Analysis - methods
Identifiers
urn:nbn:se:du-17153 (URN)10.1007/s10898-015-0293-4 (DOI)000361485700009 ()
Available from: 2015-03-17 Created: 2015-03-17 Last updated: 2017-12-04Bibliographically approved
3. Statistical bound of genetic solutions to quadratic assignment problems
Open this publication in new window or tab >>Statistical bound of genetic solutions to quadratic assignment problems
2015 (English)Report (Other academic)
Abstract [en]

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2015. 20 p.
Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2015:02
Keyword
quadratic assignment problem, genetic algorithm, Jack-knife, discrete optimization, extreme value theory
National Category
Computer Engineering
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-17034 (URN)
Available from: 2015-03-02 Created: 2015-03-02 Last updated: 2015-05-07Bibliographically approved
4. On transforming a road network database to a graph for localization purpose
Open this publication in new window or tab >>On transforming a road network database to a graph for localization purpose
2016 (English)In: International Journal of Web Services Research, ISSN 1545-7362, E-ISSN 1546-5004, Vol. 13, no 2, 46-55 p.Article in journal (Refereed) Published
Abstract [en]

The problems of finding best facility locations require complete and accurate road networks with the corresponding population data in a specific area. However the data obtained from road network databases usually do not fit in this usage. In this paper we propose a procedure of converting the road network database to a road graph which could be used for localization problems. Several challenging problems exist in the transformation process which are commonly met also in other data bases. The procedure of dealing with those challenges are proposed. The data come from the National road data base in Sweden. The graph derived is cleaned, and reduced to a suitable level for localization problems. The residential points are also processed in ordered to match the graph. The reduction of the graph is done maintaining the accuracy of distance measures in the network.

Keyword
road network, graph, population, GIS
National Category
Economic Geography
Research subject
Complex Systems – Microdata Analysis
Identifiers
urn:nbn:se:du-17361 (URN)10.4018/IJWSR.2016040103 (DOI)000384810100004 ()
Available from: 2015-05-07 Created: 2015-05-07 Last updated: 2017-12-04Bibliographically approved
5. Measuring CO2 emissions induced by online and brick-and-mortar retailing
Open this publication in new window or tab >>Measuring CO2 emissions induced by online and brick-and-mortar retailing
Show others...
2014 (English)Report (Other academic)
Abstract [en]

We develop a method for empirically measuring the difference in carbon footprint between traditional and online retailing (“e-tailing”) from entry point to a geographical area to consumer residence. The method only requires data on the locations of brick-and-mortar stores, online delivery points, and residences of the region’s population, and on the goods transportation networks in the studied region. Such data are readily available in most countries, so the method is not country or region specific. The method has been evaluated using data from the Dalecarlia region in Sweden, and is shown to be robust to all assumptions made. In our empirical example, the results indicate that the average distance from consumer residence to a brick-and-mortar retailer is 48.54 km in the studied region, while the average distance to an online delivery point is 6.7 km. The results also indicate that e-tailing increases the average distance traveled from the regional entry point to the delivery point from 47.15 km for a brick-and-mortar store to 122.75 km for the online delivery points. However, as professional carriers transport the products in bulk to stores or online delivery points, which is more efficient than consumers’ transporting the products to their residences, the results indicate that consumers switching from traditional to e-tailing on average reduce their CO2 footprints by 84% when buying standard consumer electronics products. 

Place, publisher, year, edition, pages
Stockholm: HUI Research, 2014. 30 p.
Series
HUI Working Papers, 106
Keyword
E-tailing; Spatial distribution of firms and consumers; p-median model; Emission measurement; Emission reduction
National Category
Economic Geography Economics Computer and Information Science
Research subject
Complex Systems – Microdata Analysis, General Microdata Analysis - methods; Complex Systems – Microdata Analysis, General Microdata Analysis - retail; Complex Systems – Microdata Analysis, General Microdata Analysis - transports
Identifiers
urn:nbn:se:du-17360 (URN)
Available from: 2015-05-07 Created: 2015-05-07 Last updated: 2015-12-11Bibliographically approved
6. On administrative borders and accessibility to public services:: The case of hospitals in Sweden.
Open this publication in new window or tab >>On administrative borders and accessibility to public services:: The case of hospitals in Sweden.
2014 (English)Report (Other academic)
Abstract [en]

An administrative border might hinder the optimal allocation of a given set of resources by restricting the flow of goods, services, and people. In this paper we address the question: Do administrative borders lead to poor accessibility to public service such as hospitals? In answering the question, we have examined the case of Sweden and its regional borders. We have used detailed data on the Swedish road network, its hospitals, and its geo-coded population. We have assessed the population’s spatial accessibility to Swedish hospitals by computing the inhabitants’ distance to the nearest hospital. We have also elaborated several scenarios ranging from strongly confining regional borders to no confinements of borders and recomputed the accessibility. Our findings imply that administrative borders are only marginally worsening the accessibility.

Place, publisher, year, edition, pages
Borlänge: Högskolan Dalarna, 2014
Series
Working papers in transport, tourism, information technology and microdata analysis, ISSN 1650-5581 ; 2014:15
Keyword
hospitals, optimal location, network distance, travel time, location model, Spatial planning, Regional planning, public sevice
National Category
Economic Geography Computer and Information Science
Research subject
Complex Systems – Microdata Analysis, General Microdata Analysis - methods
Identifiers
urn:nbn:se:du-15969 (URN)
Available from: 2014-09-29 Created: 2014-09-29 Last updated: 2016-09-08Bibliographically approved

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