Nagging: A scalable, fault-tolerant, paradigm for distributed search

This paper describes Nagging, a technique for parallelizing search in a heterogeneous distributed computing environment. Nagging exploits the speedup anomaly often observed when parallelizing problems by playing multiple reformulations of the problem or portions of the problem against each other. Nagging is both fault tolerant and robust to long message latencies. In this paper, we show how nagging can be used to parallelize several different algorithms drawn from the artificial intelligence literature, and describe how nagging can be combined with partitioning, the more traditional search parallelization strategy. We present a theoretical analysis of the advantage of nagging with respect to partitioning, and give empirical results obtained on a cluster of 64 processors that demonstrate nagging\u27s effectiveness and scalability as applied to A* search, $alpha beta$ minimax game tree search, and the Davis-Putnam algorithm

Metaheuristics for NP-hard combinatorial optimization problems

Ph.DDOCTOR OF PHILOSOPH

The Traveling Salesman Problem

This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances

The probabilistic travelling salesman problem with crowdsourcing

We study a variant of the Probabilistic Travelling Salesman Problem arising when retailers crowdsource last-mile deliveries to their own customers, who can refuse or accept in exchange for a reward. A planner must identify which deliveries to offer, knowing that all deliveries need fulfilment, either via crowdsourcing or using the retailer’s own vehicle. We formalise the problem and position it in both the literature about crowdsourcing and among routing problems in which not all customers need a visit. We show that to evaluate the objective function of this stochastic problem for even one solution, one needs to solve an exponential number of Travelling Salesman Problems. To address this complexity, we propose Machine Learning and Monte Carlo simulation methods to approximate the objective function, and both a branch-and-bound algorithm and heuristics to reduce the number of evaluations. We show that these approaches work well on small size instances and derive managerial insights on the economic and environmental benefits of crowdsourcing to customers.info:eu-repo/semantics/publishedVersio

EUCLIDEAN CORRELATIONS IN COMBINATORIAL OPTIMIZATION PROBLEMS: A STATISTICAL PHYSICS APPROACH

In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this beautiful and deep topic. I give some elements of complexity theory, and I motivate why the point of view of statistical physics, although different from the one adopted in standard complexity theory, leads to many interesting results, as well as new questions. I discuss the connection between combinatorial optimization problems and spin glasses. Finally, I briefly review some topics of large deviation theory, as a way to go beyond average quantities. As a concrete example of this, I show how the replica method can be used to explore the large deviations of a well-known toy model of spin glasses, the p-spin spherical model. In the second chapter I specialize in Euclidean combinatorial optimization problems. In particular, I explain why these problems, when embedded in a finite dimensional Euclidean space, are difficult to deal with. I analyze several problems (the matching and assignment problems, the traveling salesman problem, and the 2-factor problem) in one dimension to explain a quite general technique to deal with one dimensional Euclidean combinatorial optimization problems. Whenever possible, and in a detailed way for the traveling-salesman problem case, I also discuss how to proceed in two (and also more) dimensions. In the last chapter I outline a promising approach to tackle hard combinatorial optimization problems: quantum computing. After giving a quick overview of the paradigm of quantum computation (and its differences with respect to the classical one), I discuss in detail the application of the so-called quantum annealing algorithm to a specific case of the matching problem, also by providing a comparison between the performance of a recent quantum annealer machine (the D-Wave 2000Q) and a classical super-computer equipped with an heuristic algorithm (an implementation of parallel tempering). Finally, I draw the conclusions of my work and I suggest some interesting directions for future studies

A stochastic approach to path planning in the Weighted-Region Problem

Planning efficient long-range movement is a fundamental requirement of most military operations. Intelligent mobile autonomous vehicles designed for battlefield support missions must have this capability. We propose an efficient heuristic algorithm for planning near-optimal high-level routes through complex terrain maps, modeled by the Weighted-Region Problem (WRP). The algorithm is driven by our adaptation of the combinatorial optimization technique called simulated annealing. The WRP provides a cartographically powerful representation for planar maps. Terrain features are modeled by polygonal homogenous-cost regions. A cost efficient assigned to each region indicates the relative cost per unit distance for movement in the region by a point agent no the ground. Region cost coefficients are assumed to be invariant with direction of movement. Given a start and a goal point, a solution (not necessarily optimal) is a set of piecewise-linear connected segments, spanning from start to goal. The cost of a solution path is the sum of the weighted lengths of all segments in the path, where the weighted length of each segment is the product of it Euclidian length and the cost coefficient of the region it crosses. Ideally, we seek the least cost path. However, as problem instances approach the actual complexity of the battlefield, faster solutions become more desirable than absolute optimality. We introduce heuristics designed to replace the search space independently of start and goal locations, thus allowing map preprocessing. We use other heuristics to improve the efficiency of local cost function optimization as well as the annealing process itself.http://archive.org/details/stochasticapproa00kindMajor, United States ArmyApproved for public release; distribution is unlimited