On Solving Close Enough Orienteering Problem with Overlapped Neighborhoods

The Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of the classic Traveling Salesman Problem whereby the agent may complete its mission at any point within a target neighborhood. Heuristics based on overlapped neighborhoods, known as Steiner Zones (SZ), have gained attention in addressing CETSPs. While SZs offer effective approximations to the original graph, their inherent overlap imposes constraints on the search space, potentially conflicting with global optimization objectives. Here we present the Close Enough Orienteering Problem with Non-uniform Neighborhoods (CEOP-N), which extends CETSP by introducing variable prize attributes and non-uniform cost considerations for prize collection. To tackle CEOP-N, we develop a new approach featuring a Randomized Steiner Zone Discretization (RSZD) scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Ant Colony System (ACS) - CRaSZe-AntS. The RSZD scheme identifies sub-regions for PSO exploration, and ACS determines the discrete visiting sequence. We evaluate the RSZD's discretization performance on CEOP instances derived from established CETSP instances, and compare CRaSZe-AntS against the most relevant state-of-the-art heuristic focused on single-neighborhood optimization for CEOP. We also compare the performance of the interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-N. Our results show CRaSZe-AntS can yield comparable solution quality with significantly reduced computation time compared to the single-neighborhood strategy, where we observe an averaged 140.44% increase in prize collection and 55.18% reduction of execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.Comment: 26 pages, 10 figure

Solving the Physical Traveling Salesman Problem: Tree Search and Macro Actions

This paper presents a number of approaches for solving a real-time game consisting of a ship that must visit a number of waypoints scattered around a 2-D maze full of obstacles. The game, the Physical Traveling Salesman Problem (PTSP), which featured in two IEEE conference competitions during 2012, provides a good balance between long-term planning (finding the optimal sequence of waypoints to visit), and short-term planning (driving the ship in the maze). This paper focuses on the algorithm that won both PTSP competitions: it takes advantage of the physics of the game to calculate the optimal order of waypoints, and it employs Monte Carlo tree search (MCTS) to drive the ship. The algorithm uses repetitions of actions (macro actions) to reduce the search space for navigation. Variations of this algorithm are presented and analyzed, in order to understand the strength of each one of its constituents and to comprehend what makes such an approach the best controller found so far for the PTSP. © 2009-2012 IEEE

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Shared Mobility Optimization in Large Scale Transportation Networks: Methodology and Applications

abstract: Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). Previous research has made a number of important contributions to the challenging pickup and delivery problem along different formulation or solution approaches. However, there are a number of modeling and algorithmic challenges for a large-scale deployment of a vehicle routing and scheduling algorithm, especially for regional networks with various road capacity and traffic delay constraints on freeway bottlenecks and signal timing on urban streets. The main thrust of this research is constructing hyper-networks to implicitly impose complicated constraints of a vehicle routing problem (VRP) into the model within the network construction. This research introduces a new methodology based on hyper-networks to solve the very important vehicle routing problem for the case of generic ride-sharing problem. Then, the idea of hyper-networks is applied for (1) solving the pickup and delivery problem with synchronized transfers, (2) computing resource hyper-prisms for sustainable transportation planning in the field of time-geography, and (3) providing an integrated framework that fully captures the interactions between supply and demand dimensions of travel to model the implications of advanced technologies and mobility services on traveler behavior.Dissertation/ThesisDoctoral Dissertation Civil, Environmental and Sustainable Engineering 201