GPU accelerated Hungarian algorithm for traveling salesman problem

In this thesis, we present a model of the Traveling Salesman Problem (TSP) cast in a quadratic assignment problem framework with linearized objective function and constraints. This is referred to as Reformulation Linearization Technique at Level 2 (or RLT2). We apply dual ascent procedure for obtaining lower bounds that employs Linear Assignment Problem (LAP) solver recently developed by Date(2016). The solver is a parallelized Hungarian Algorithm that uses Compute Unified Device Architecture (CUDA) enabled NVIDIA Graphics Processing Units (GPU) as the parallel programming architecture. The aim of this thesis is to make use of a modified version of the Dual Ascent-LAP solver to solve the TSP. Though this procedure is computational expensive, the bounds obtained are tight and our experimental results confirm that the gap is within 2% for most problems. However, due to limitations in computational resources, we could only test problem sizes N < 30. Further work can be directed at theoretical and computational analysis to test the efficiency of our approach for larger problem instances

Branch-and-Refine zur Lösung zeitabhängiger Probleme

Einer der Standardansätze zur Lösung zeitabhängiger diskreter Optimierungsprobleme, wie z.B. das Problem des Handlungsreisenden mit Zeitfenstern oder das Kürzeste Wege Problem mit Zeitfenstern, ist die Herleitung einer sogenannten zeitindizierten Formulierung. Wenn dem Problem eine Struktur zu Grunde liegt, die durch einen Graphen beschrieben werden kann, basiert die zeitindizierte Formulierung normalerweise auf einem anderen, erweiterten Graphen, der in der Literatur als zeitexpandierter Graph bezeichnet wird. Der zeitexpandierte Graph kann oft so generiert werden, dass alle Zeitbeschränkungen bereits aufgrund seiner Topologie erfüllt sind und somit Algorithmen für die entsprechende zeitunabhängige Variante angewendet werden können. Der Nachteil dieses Ansatzes ist, dass die Mengen der Ecken und Bögen des zeitexpandierten Graphen viel größer sind als die des ursprünglichen Graphen. In neueren Arbeiten hat sich jedoch gezeigt, dass für viele praktische Anwendungen eine partielle Expandierung des Graphen, die möglicherweise zeitunmögliche Pfade zulässt, oft ausreicht, um eine beweisbar optimale Lösung zu finden. Diese Ansätze verfeinern iterativ den ursprünglichen Graphen und lösen in jeder Iteration eine Relaxierung der zeitexpandierten Formulierung. Wenn die Lösung der aktuellen Relaxation alle Zeitbeschränkungen erfüllt, kann daraus eine optimale Lösung abgeleitet werden, und der Algorithmus terminiert. In dieser Arbeit stellen wir neue Ideen vor, die das Übertragen von Informationen über die optimale Lösung eines gröberen Graphen zu einem verfeinerten Graphen ermöglichen und zeigen, wie diese in Algorithmen verwendet werden können. Genauer gesagt stellen wir einen neuen Algorithmus zur Lösung von MILP-Formulierungen (Mixed Integer Linear Program) von zeitabhängigen Problemen vor, der es ermöglicht, die Graphenverfeinerung während der Untersuchung des Branch-and-Bound Baums durchzuführen, anstatt jedes Mal neu zu starten, wenn die optimale Lösung sich als nicht zulässig herausgestellt hat. Um die praktische Relevanz dieses Algorithmus zu demonstrieren, präsentieren wir Ergebnisse von numerische Experimenten seiner Anwendung auf das Kürzeste Wege Problem mit Zeitfenstern und das Problem des Handlungsreisenden mit Zeitfenstern.One of the standard approaches for solving time-dependent discrete optimization problems, such as the travelling salesman problem with time-windows or the shortest path problem with time-windows is to derive a so-called time-indexed formulation. If the problem has an underlying structure that can be described by a graph, the time-indexed formulation is usually based on a different, extended graph, commonly referred to as the time-expanded graph. The time-expanded graph can often be derived in such a way that all time constraints are incorporated in its topology, and therefore algorithms for the corresponding time-independent variant become applicable. The downside of this approach is, that the sets of vertices and arcs of the time-expanded graph are much larger than the ones of the original graph. In recent works, however, it has been shown that for many practical applications a partial graph expansion, that might contain time infeasible paths, often suffices to find a proven optimal solution. These approaches, instead, iteratively refine the original graph and solve a relaxation of the time-expanded formulation in each iteration. When the solution of the current relaxation is time feasible an optimal solution can be derived from it and the algorithm terminates. In this work we present new ideas, that allow for the propagation of information about the optimal solution of a coarser graph to a more refined graph and show how these can be used in algorithms, which are based on graph refinement. More precisely we present a new algorithm for solving Mixed Integer Linear Program (MILP) formulations of time-dependent problems that allows for the graph refinement to be carried out during the exploration of the branch-and-bound tree instead of restarting whenever the optimal solution was found to be infeasible. For demonstrating the practical relevance of this algorithm we present numerical results on its application to the shortest path problem with time-windows and the traveling salesman problem with time-windows

A Real-time Crane Service Scheduling Decision Support System (css-dss) For Construction Tower Cranes

The success of construction projects depends on proper use of construction equipment and machinery to a great extent. Thus, appropriate planning and control of the activities that rely on construction equipment could have significant effects on improving the efficiency of project operations. Cranes are the largest and most conspicuous construction equipment, widely used in typical construction sites. They play a major role in relocation of materials in horizontal and vertical directions on construction sites. Given the nature of activities relying on construction cranes in various stages of a project, cranes normally have control over the critical path of the project with the potential to create schedule bottlenecks and delaying the completion of the project. This dissertation intends to improve crane operations efficiency by developing a new framework for optimizing crane service sequence schedule. The crane service sequence problem is mathematically formulated as an NP-complete optimization problem based on the well-known Travel Salesman Problem (TSP) and is solved using different optimization techniques depending on the problem’s size and complexity. The proposed framework sets the basis for developing near-real time decision support tools for on-site optimization of crane operations sequence. To underline the value of the proposed crane sequence optimization methods, these methods are employed to solve several numerical examples. Results show that the proposed method can create a travel time saving of 28% on average in comparison with conventional scheduling methods such as First in First out (FIFO), Shortest Job First (SJF), and Earliest Deadline First (EDF)

Integrated capacitated lot sizing and scheduling problems in a flexible flow line

The lot sizing and scheduling problem in a Flexible Flow Line (FFL) has extensive real-world applications in many industries. An FFL consists of several production stages in series with parallel machines at each stage. The decisions to be taken are the determination of production quantities (lots), machine assignments and production sequences (schedules) on each machine at each stage in an FFL. Lot sizing and scheduling problems are closely interrelated. Solving them separately and then coordinating their interdependencies is often ineffective. However due to their complexity, there is a lack of mathematical modelling and solution procedures in the literature to combine and jointly solve them.Up to now most research has been focused on combining lotsizing and scheduling for the single machine configuration, and research on other configurations like FFL is sparse. This thesis presents several mathematical models with practical assumptions and appropriate algorithms, along with experimental test problems, for simultaneously lotsizing and scheduling in FFL. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL). The objective is to satisfy varying demand over a finite planning horizon with minimal inventory, backorder and production setup costs. The problem is complex as any product can be processed on any machine, but these have different processing rates and sequence-dependent setup times & costs. As a result, even finding a feasible solution of large problems in reasonable time is impossible. Therefore the heuristic solution procedure named Adaptive Simulated Annealing (ASA), with four well-designed initial solutions, is designed to solve GLSP-FFL.A further original contribution of this study is to design linear mixed-integer programming (MILP) formulations for this problem, incorporating all necessary features of setup carryovers, setup overlapping, non-triangular setup while allowing multiple lot production per periods, lot splitting and sequencing through ATSP-adaption based on a variety of subtour elimination

Design of Heuristic Algorithms for Hard Optimization

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

Integrated capacitated lot sizing and scheduling problems in a flexible flow line

The lot sizing and scheduling problem in a Flexible Flow Line (FFL) has extensive real-world applications in many industries. An FFL consists of several production stages in series with parallel machines at each stage. The decisions to be taken are the determination of production quantities (lots), machine assignments and production sequences (schedules) on each machine at each stage in an FFL. Lot sizing and scheduling problems are closely interrelated. Solving them separately and then coordinating their interdependencies is often ineffective. However due to their complexity, there is a lack of mathematical modelling and solution procedures in the literature to combine and jointly solve them. Up to now most research has been focused on combining lotsizing and scheduling for the single machine configuration, and research on other configurations like FFL is sparse. This thesis presents several mathematical models with practical assumptions and appropriate algorithms, along with experimental test problems, for simultaneously lotsizing and scheduling in FFL. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL). The objective is to satisfy varying demand over a finite planning horizon with minimal inventory, backorder and production setup costs. The problem is complex as any product can be processed on any machine, but these have different processing rates and sequence-dependent setup times & costs. As a result, even finding a feasible solution of large problems in reasonable time is impossible. Therefore the heuristic solution procedure named Adaptive Simulated Annealing (ASA), with four well-designed initial solutions, is designed to solve GLSP-FFL. A further original contribution of this study is to design linear mixed-integer programming (MILP) formulations for this problem, incorporating all necessary features of setup carryovers, setup overlapping, non-triangular setup while allowing multiple lot production per periods, lot splitting and sequencing through ATSP-adaption based on a variety of subtour elimination.EThOS - Electronic Theses Online ServiceGBUnited Kingdo