A Swarm of Salesmen: Algorithmic Approaches to Multiagent Modeling

This honors thesis describes the algorithmic abstraction of a problem modeling a swarm of Mars rovers, where many agents must together achieve a goal. The algorithmic formulation of this problem is based on the traveling salesman problem (TSP), and so in this thesis I offer a review of the mathematical technique of linear programming in the context of its application to the TSP, an overview of some variations of the TSP and algorithms for approximating and solving them, and formulations without solutions of two novel TSP variations which are useful for modeling the original problem

A Swarm of Salesmen: Algorithmic Approaches to Multiagent Modeling

This honors thesis describes the algorithmic abstraction of a problem modeling a swarm of Mars rovers, where many agents must together achieve a goal. The algorithmic formulation of this problem is based on the traveling salesman problem (TSP), and so in this thesis I offer a review of the mathematical technique of linear programming in the context of its application to the TSP, an overview of some variations of the TSP and algorithms for approximating and solving them, and formulations without solutions of two novel TSP variations which are useful for modeling the original problem

Online traveling salesman problems with rejection options

In this article, we consider online versions of the traveling salesman problem on metric spaces for which requests to visit points are not mandatory. Associated with each request is a penalty (if rejected). Requests are revealed over time (at their release dates) to a server who must decide which requests to accept and serve in order to minimize a linear combination of the time to serve all accepted requests and the total penalties of all rejected requests. In the basic online version of the problem, a request can be accepted any time after its release date. In the real-time online version, a request must be accepted or rejected at the time of its release date. For the basic version, we provide a best possible 2-competitive online algorithm for the problem on a general metric space. For the real-time version, we first consider special metric spaces: on the nonnegative real line, we provide a best possible 2.5-competitive polynomial time online algorithm; on the real line, we prove a Ω(√ln n) lower bound of 2.64 on any competitive ratios and give a 3-competitive online algorithm. We then consider the case of a general metric space and prove a inline image lower bound on the competitive ratio of any online algorithms. Finally, among the restricted class of online algorithms with prior knowledge about the total number of requests n, we propose an asymptotically best possible O(√ln n)-competitive algorithm.United States. Office of Naval Research (Grant N00014-09-1-0326)United States. Office of Naval Research (Grant N00014-12-1-0033)United States. Air Force Office of Scientific Research (Grant FA9550-10-1-0437

Prize-Collecting TSP with a Budget Constraint

We consider constrained versions of the prize-collecting traveling salesman and the minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. We present a 2-approximation algorithm for these problems based on a primal-dual approach. The algorithm relies on finding a threshold value for the dual variable corresponding to the budget constraint in the primal and then carefully constructing a tour/tree that is just within budget. Thereby, we improve the best-known guarantees from 3+epsilon and 2+epsilon for the tree and the tour version, respectively. Our analysis extends to the setting with weighted vertices, in which we want to maximize the total weight of vertices in the tour/tree subject to the same budget constraint

Improved Approximation Algorithms for the Expanding Search Problem

A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a (2e+?)-approximation for any ? > 0. For the case that all vertices have unit weight, we provide a 2e-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an 8-approximation was known

Multi-Strategy <em>MAX-MIN</em> Ant System for Solving Quota Traveling Salesman Problem with Passengers, Incomplete Ride and Collection Time

This study proposes a novel adaptation of MAX-MIN Ant System algorithm for the Quota Traveling Salesman Problem with Passengers, Incomplete Ride, and Collection Time. There are different types of decisions to solve this problem: satisfaction of the minimum quota, acceptance of ride requests, and minimization of travel costs under the viewpoint of the salesman. The Algorithmic components proposed regards vehicle capacity, travel time, passenger limitations, and a penalty for delivering a passenger deliverance out of the required destination. The ant-based algorithm incorporates different sources of heuristic information for the ants and memory-based principles. Computational results are reported, showing the effectiveness of this ant-based algorithm

The Covering Canadian Traveller Problem Revisited

In this paper, we consider the k-Covering Canadian Traveller Problem (k-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of k-CCTP is finding the shortest tour for a traveller to visit a set of locations in a given graph and return to the origin. Crucially, unknown to the traveller, up to k edges of the graph are blocked and the traveller only discovers blocked edges online at one of their respective endpoints. The currently best known upper bound for k-CCTP is O(?k) which was shown in [Huang and Liao, ISAAC \u2712]. We improve this polynomial bound to a logarithmic one by presenting a deterministic O(log k)-competitive algorithm that runs in polynomial time. Further, we demonstrate the tightness of our analysis by giving a lower bound instance for our algorithm

Exact and Heuristic Algorithms for Risk-Aware Stochastic Physical Search

We consider an intelligent agent seeking to obtain an item from one of several physical locations, where the cost to obtain the item at each location is stochastic. We study risk-aware stochastic physical search (RA-SPS), where both the cost to travel and the cost to obtain the item are taken from the same budget and where the objective is to maximize the probability of success while minimizing the required budget. This type of problem models many task-planning scenarios, such as space exploration, shopping, or surveillance. In these types of scenarios, the actual cost of completing an objective at a location may only be revealed when an agent physically arrives at the location, and the agent may need to use a single resource to both search for and acquire the item of interest. We present exact and heuristic algorithms for solving RA-SPS problems on complete metric graphs. We first formulate the problem as mixed integer linear programming problem. We then develop custom branch and bound algorithms that result in a dramatic reduction in computation time. Using these algorithms, we generate empirical insights into the hardness landscape of the RA-SPS problem and compare the performance of several heuristics