9 research outputs found
Time-constrained project scheduling with adjacent resources
We develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Adjacent Resources. For adjacent resources the resource units are ordered and the units assigned to a job have to be adjacent. On top of that, adjacent resources are not required by single jobs, but by job groups. As soon as a job of such a group starts, the adjacent resource units are occupied, and they are not released before all jobs of that group are completed. The developed decomposition method separates the adjacent resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with adjacent resources and may form a good basis to develop more elaborated methods
Evolutionary algorithms and hyper-heuristics for orthogonal packing problems
This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems.
The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area
Vehicle routing with multi-dimensional loading constraints
Zwei der wichtigsten Problemstellungen in der Transportlogistik behandeln einerseits das
Verladen von Produkten auf LKWs und andererseits die ressourceneffiziente Belieferung
der Kunden auf dem gegebenen Straßennetz.
Bis dato wurden diese zwei Probleme mit Hilfe von kombinatorischer Optimierung getrennt
von einander behandelt und es existieren zahlreiche Publikationen zu beiden Themen in
den einschlägigen Fachzeitschriften. Erst in den letzten drei Jahren wurde einem integrierten
Ansatz, der beide Problemstellungen zu einem Optimierungsproblem vereint betrachtet.
Somit werden die Bestellungen einzelner Kunden nicht bloß über ihre Gewichte,
sondern auch über ihre Abmessungen definiert. Der klare Vorteil dieses Ansatzes liegt
darin, dass die einzelnen LKW Routen auch tatsächlich so gefahren werden können, da
die tatsächliche Beladung auch berücksichtigt wurde. Andererseits steigt die kombinatorische
Komplexität drastisch, weil das kapazitierte Vehicle Routing Problem (CVRP)
mit Bin Packing Problemen (BPP) kombiniert wird und beide Probleme für sich alleine
NP schwer sind.
Diese Dissertation präsentiert drei verschiedene Probleme, die sich neben der Frage welches
Fahrzeug beliefert welchen Kunden auch der Frage widmet, wie die bestellten Produkte
auf den LKW geladen werden können.
- Das Multi-Pile Vehicle Routing Problem (MP-VRP) bindet in das klassische CVRP
eine Beladekomponente ein, die zwischen eindimensionalem und zweidimensionalem
Bin Packing Problem angesiedelt ist. Die Problemstellungen wurden durch einen
österreichischen Holzzulieferer motiviert.
- Beim kapazitierten Vehicle Routing Problem mit zweidimensionalen Beladenebenbedingungen
(2L-CVRP) bestellt jeder Kunden rechteckige Objekte, welche auf der
rechteckigen Beladefläche des LKWs untergebracht werden müssen.
- Das allgemeinste Beladeproblem stellt das dreidimensionale Bin Packing Problem
dar. Hier bestellt jeder Kunde dreidimensionale Objekte, welche auf dem dreidimensionalen
Laderaum des LKWs untergebracht werden müssen. Das klassische dreidimensionale Bin Packing
Problem wird durch zusätzliche Beladenebenbedingungen
erweitert.
Momentan gibt es zu diesen kombinierten Problemen nur wenige Publikationen. Exakte
Ansätze gibt es momentan nur zwei, einen für das MP-VRP (hier können Probleme bis
zu 50 Kunden gelöst werden) und für das 2L-CVRP (hier können Probleme bis zu 30
Kunden exakt gelöst werden). Für Realweltanwendungen müssen jedoch Heuristiken gefunden
werden, welche größere Probleminstanzen lösen können. In dieser Arbeit wird
für alle drei Problemstellungen ein Ameisenalgorithmus verwendet und mit bestehenden
Lösungsansätzen aus dem Bereich der Tabu-Suche (TS) verglichen. Es wird gezeigt, dass
der präsentierte Ameisenansatz für die zur Verfügung stehenden Benchmarkinstanzen die
besten Ergebnisse liefert. Darüber hinaus wird der Einfluss verschiedener Beladenebenbedingungen
auf die Lösungsgüte untersucht, was eine wichtige Entscheidungsgrundlage für
Unternehmen darstellt.Two of the most important problems in distribution logistics concern the loading of the
freight into the vehicles, and the successive routing of the vehicles along the road network,
with the aim of satisfying the demands of the clients.
In the combinatorial optimization field, these two loading and routing problems have been
studied intensively but separately yielding a large number of publications either for routing
or packing problems. Only in recent years some attention has been brought to their
combined optimization. The obvious advantage is that, by considering the information on
the freight to be loaded, one can construct more appropriate routes for the vehicles. The
counterpart is that the combinatorial difficulty of the problem increases consistently. One
must not forget that both the vehicle routing problem and the bin packing problem are
NP hard problems!
This thesis presents three different problems concerning the combination of routing and
loading (packing) problems.
- The Multi-Pile Vehicle Routing Problem (MP-VRP) incorporates an interesting
loading problem situated between one dimensional and two dimensional bin packing.
This problem has been inspired by a real world application of an Austrian wood
distributing company.
- The Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints
(2L-CVRP) augments the classical Capacitated Vehicle Routing Problem
by requiring the satisfaction of general two dimensional loading constraints. This
means that customers order items represented by rectangles that have to be feasibly
placed on the rectangular shaped loading surface of the used vehicles.
- The most general packing problem to be integrated is the Three Dimensional Bin
Packing Problem (3DBPP) resulting in the Capacitated Vehicle Routing Problem
with Three-Dimensional Loading Constraints (3L-CVRP). Here the order of each
customer consists of cuboid shaped items that have to be feasibly placed on the loading space of the vehicle. A feasible placement is influenced by additional constraints
that extend the classical 3DBPP.
Concerning the literature solving these problems with exact methods it becomes clear that
this is only possible to some very limited extent (e.g.: the MP-VRP can be solved up to
50, the 2L-CVRP can be solved exact up to 30 customers, for the 3L-CVRP no exact
approach exists). Nevertheless for real world applications the problem instances are much
larger which justifies the use of (meta-)heuristics.
The rank-based Ant System was modified and extended to solve the combined problem
by integrating different packing routines. The designed methods outperform the existing
techniques for the three different problem classes.
The influence of different loading constraints on the objective value is investigated/is
intensively studied to support the decision makers of companies facing similar problems
Evolutionary algorithms and hyper-heuristics for orthogonal packing problems
This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems.
The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area