Driver helper dispatching problems: Three essays

The driver helper dispatching problems (DHDPs) have received scant research attention in past literature. In this three essay format dissertation, we proposed two ideas: 1) minimizing of the total cost as the new objective function to replace minimizing the total distance cost that is mostly used in past traveling salesman problem (TSP) and vehicle routing problem (VRP) algorithms and 2) dispatching vehicle either with a helper or not as part of the routing decision. The first study shows that simply separating a single with-helper route into two different types of sub-routes can significantly reduce total costs. It also proposes a new dependent driver helper (DDH) model to boost the utilization rate of the helpers to higher levels. In the second study, a new hybrid driver helper (HDH) model is proposed to solve DHDPs. The proposed HDH model provides the flexibility to relax the constraints that a helper can only work at one predetermined location in current-practice independent driver helper (IDH) model and that a helper always travels with the vehicle in the current-practice DDH model. We conducted a series of full-factorial experiments to prove that the proposed HDH model performs better than both two current solutions in terms of savings in both cost and time. The last study proposes a mathematical model to solve the VRPTW version of DHDPs and conducts a series of full factorial computational experiments. The results show that the proposed model can achieve more cost savings while reducing a similar level of dispatched vehicles as the current-practice DDH solution. All these three studies also investigate the conditions under which the proposed models would work most, or least, effectively

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

Reinforced Lin-Kernighan-Helsgaun Algorithms for the Traveling Salesman Problems

TSP is a classical NP-hard combinatorial optimization problem with many practical variants. LKH is one of the state-of-the-art local search algorithms for the TSP. LKH-3 is a powerful extension of LKH that can solve many TSP variants. Both LKH and LKH-3 associate a candidate set to each city to improve the efficiency, and have two different methods, $\alpha$-measure and POPMUSIC, to decide the candidate sets. In this work, we first propose a Variable Strategy Reinforced LKH (VSR-LKH) algorithm, which incorporates three reinforcement learning methods (Q-learning, Sarsa, Monte Carlo) with LKH, for the TSP. We further propose a new algorithm called VSR-LKH-3 that combines the variable strategy reinforcement learning method with LKH-3 for typical TSP variants, including the TSP with time windows (TSPTW) and Colored TSP (CTSP). The proposed algorithms replace the inflexible traversal operations in LKH and LKH-3 and let the algorithms learn to make a choice at each search step by reinforcement learning. Both LKH and LKH-3, with either $\alpha$-measure or POPMUSIC, can be significantly improved by our methods. Extensive experiments on 236 widely-used TSP benchmarks with up to 85,900 cities demonstrate the excellent performance of VSR-LKH. VSR-LKH-3 also significantly outperforms the state-of-the-art heuristics for TSPTW and CTSP.Comment: arXiv admin note: text overlap with arXiv:2107.0687

Resolución del problema del viajante de comercio (TSP) y su variante con ventanas de tiempo (TSPTW) usando métodos heurísticos de búsqueda local

En el presente proyecto se llevará a cabo el estudio del Problema del Viajante de Comercio (TSP) y su variante con Ventanas de Tiempo (TSPTW). Para cada uno de estos problemas se presentará una explicación del mismo, aplicaciones, formulación matemática y resolución. Dicha resolución se llevará a cabo mediante métodos exactos y heurísticas de búsqueda local. Entre las heurísticas se incluyen dos novedosas propuestas: Threshold Acceptance y Late Acceptance Hill-Climbing, y dos ampliamente conocidas y estudiadas: Simulated Annealing y Hill-Climbing. Se pretende realizar una comparativa entre ellas, tomando como base los resultados obtenidos por el método exacto y los mejores resultados conocidos, de cara a conocer el algoritmo que mejor rendimiento presenta para estos problemas. Para el caso del TSPTW veremos una heurística más, variante de las anteriores, llamada Compressed-Annealing SimulatedDepartamento de Estadística e Investigación OperativaGrado en Ingeniería en Organización Industria

Algoritmi euristici per il problema del Commesso Viaggiatore con finestre temporali

La tesi riguarda il problema del Commesso Viaggiatore con Finestre Temporali(TSPTW), in particolare l'applicazione di due euristici: il Simulated Annealing ed il Proximity Search. I due euristici verranno utilizzati insieme formando un algoritmo chiamato SAPS che verrà confrontato con sei euristici specifici per il TSP con Finestre Temporali. Inoltre verrà provata l'efficacia del Proximity Search come postprocessing per il miglioramento di soluzioni ottenute da algoritmi euristic

Balanced task allocation by partitioning the multiple traveling salesperson problem

Task assignment and routing are tightly coupled problems for teams of mobile agents. To fairly balance the workload, each agent should be assigned a set of tasks which take a similar amount of time to complete. The completion time depends on the time needed to travel between tasks which depends on the order of tasks. We formulate the task assignment problem as the minimum Hamiltonian partition problem (MHPP) form agents, which is equivalent to the minmax multiple traveling salesperson problem (m-TSP). While the MHPP’s cost function depends on the order of tasks, its solutions are similar to solutions of the average Hamiltonian partition problem (AHPP) whose cost function is order-invariant. We prove that the AHPP is NP-hard and present an effective heuristic, AHP, for solving it. AHP improves a partitions of a graph using a series of transfer and swap operations which are guaranteed to improve the solution’s quality. The solution generated by AHP is used as an initial partition for an algorithm, AHP-mTSP, which solves the combined task assignment and routing problems to near optimality. For n tasks and m agents, each iteration of AHP is O(n2) and AHP-mTSP has an average run-time that scales with n2.11m0.33. Compared to state-of-the-art approaches, our approach found approximately 10% better solutions for large problems in a similar run-time