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A Hybrid Quantum-Classical Approach for Multimodal Container Planning

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A Hybrid Quantum-Classical Approach for Multimodal Container Planning Erasmus University Rotterdam 1 Erasmus School of Economics Master Thesis Operations Research and Quantitative Logistics A hybrid quantum-classical approach for multimodal container planning Author: S.L. Huizinga (Simone) (Student ID number: 446850) Supervisor Erasmus University Rotterdam: dr. R. Spliet (Remy) Second assessor Erasmus University Rotterdam: prof.dr.ir. R. Dekker (Rommert) Supervisors TNO: dr. F. Phillipson (Frank) I. Chiscop (Irina) Thesis Coordinator: dr. W. van den Heuvel (Wilco) Abstract In the years 2011-2020 the commercial quantum annealer of D-Wave Systems grew from 128 to over 5000 qubits. This rapid growth creates new oppor- tunities within the quantum computing area. In this thesis, the quantum annealer is used within a genetic algorithm to solve the multimodal container planning problem. The multimodal container planning problem determines which route every container takes to arrive at its destination before its due date. For every container there is an option to be transported from its origin to its destination by truck. The quantum annealer can only solve Quadratic Unconstrained Binary Optimization problems. Such a formulation is known for the multimodal container planning problem. This formulation only considers two transportation options per container. The first option is the transportation by truck. The second option is a single given multimodal route. The quantum annealer determines for every container whether the first or the second option is used. Which multimodal route is used as option still needs to be determined. This thesis focuses on determining the given multi- modal route option for every container. A genetic algorithm is used as the solution approach to determine the given multimodal route for every container. April 28, 2021 1The content of this thesis is the sole responsibility of the author and does not reflect the view of the supervisor, second assessor, Erasmus School of Economics or Erasmus University. Contents 1 Introduction 1 2 Problem description 4 3 Literature review 5 3.1 Container transportation . .5 3.2 Quantum annealer . .6 3.2.1 QUBO formulation container assignment problem . .7 3.3 Multicommodity flow problem . .8 3.4 Genetic algorithms . .8 4 Methodology 9 4.1 Representation . 10 4.2 Initialization . 11 4.2.1 The first population . 12 4.2.2 First initialization method . 13 4.2.3 Second initialization method . 14 4.3 Fitness function . 15 4.4 Selection procedure . 16 4.4.1 Elitism . 16 4.4.2 Best and worst populations . 16 4.4.3 Binary tournament . 16 4.5 Cross-over operator . 17 4.5.1 One-point cross-over operator . 18 4.5.2 Two-point cross-over operator . 19 4.5.3 Partial cross-over operator . 19 4.6 Mutation and learning operators . 21 4.6.1 Mutation operator . 21 4.6.2 Learning operator 1 . 22 4.6.3 Learning operator 2 . 23 4.7 Removal procedure . 25 5 Data 25 5.1 Networks . 25 5.1.1 Random networks . 25 5.1.2 Dutch network . 26 5.1.3 Graph 17 and graph 30 . 27 5.2 Container sets . 27 6 Tuning 29 6.1 Determining the best methods . 30 6.2 Parameter tuning . 31 7 Results 36 7.1 Results using the simulated annealer . 36 7.2 Results using the optimal solution . 40 7.3 Results using the quantum annealer . 42 7.4 Comparison . 46 7.5 Long run with the optimal solution . 46 8 Discussion 48 9 Conclusion 48 References 50 A Quantum annealing 54 i B Complexity of the problem that is solved with the quantum annealer 55 C Network descriptions 57 C.1 Random graph . 57 C.2 Dutch graph . 64 D Container sets 65 D.1 Container set random graph 15 nodes . 65 D.2 Container set random graph 20 nodes . 67 D.3 Container set random graph 25 nodes . 67 D.4 Container sets Dutch graph . 68 D.5 Container set graph 17 . 71 D.6 Container set graph 30 . 71 E Optimal solutions 76 E.1 Random graph 15 nodes . 76 E.2 Random graph 20 nodes . 77 E.3 Random graph 25 nodes . 79 E.4 Dutch graph . 80 E.5 Graph 17 . 82 E.6 Graph 30 . 83 F Values for every possible combination of methods 87 G Comparing number of pairs and iterations 89 H Average optimality gaps for different annealing parameters 89 H.1 Random network 15 nodes container set 1 . 89 H.2 Random network 15 nodes container set 2 . 91 H.3 Random network 15 nodes container set 3 . 92 H.4 Random network 20 nodes container set 1 . 93 H.5 Random network 20 nodes container set 2 . 94 H.6 Random network 20 nodes container set 3 . 95 H.7 Random network 25 nodes container set 1 . 96 H.8 Random network 25 nodes container set 2 . 97 H.9 Random network 25 nodes container set 3 . 98 H.10 Dutch network container set 1 . 99 H.11 Dutch network container set 2 . 100 H.12 Dutch network container set 3 . 101 H.13 Graph 17 container set 1 . 102 H.14 Graph 17 container set 2 . 103 H.15 Graph 17 container set 3 . 104 I Mutation rate tune 105 J Results using the simulated annealer 110 J.1 Found solutions . 110 J.2 Course of the algorithm using the simulated annealer . 120 K Results using the optimal solution 123 K.1 Found solutions using the optimal solution . 123 K.2 Course of the algorithm using the optimal solution . 133 L Results using the quantum annealer 136 L.1 Found solution using the quantum annealer . 136 L.2 Course of the algorithm using the quantum annealer . 145 M Results using the optimal solution, long run 148 M.1 Found solutions . 148 M.2 Course of the algorithm using the optimal solution, long run . 158 ii N Code description 161 iii 1 Introduction Nowadays there is a lot of import and export all over the world. Containers are more often used to transport these packages from their origin to their destination. Reasons for this containerization are the safety of the cargo, standardization and accessibility to multiple modes of transportation, as stated in Crainic and Kim (2007) and SteadieSeifi et al. (2014). To accommodate the increasing freight demand, it is important to transport the containers from their origin to their destination in a very efficient way. There are different definitions within container transportation. Relevant examples are unimodal trans- portation, multimodal transportation, intermodal and synchromodal transportation and the Physical In- ternet (Mankabady (1983), Ballot et al. (2014) and SteadieSeifi et al. (2014)). Different transportation modes are available for container shipments, examples are trucks and barges. When only a single trans- portation mode is being used it is called unimodal transport. The transport is usually done by truck if unimodal transportation is used to transport goods on land, because it is the most efficient way to move products from door to door. Multimodal transport means that multiple transportation modes are used to transport the cargo. An example is when goods are transported by barge to an intermediate port, where they are transferred to a truck in which they will travel to their final destination. Intermodal transportation is a type of multimodal transportation where the freight is moved within one containment unit, for example a container. This means that the goods themselves are not.
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