Additive Pattern Database Heuristics

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem

Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

A Hybrid Multicast-Unicast Infrastructure for Efficient Publish-Subscribe in Enterprise Networks

One of the main challenges in building a large scale publish-subscribe infrastructure in an enterprise network, is to provide the subscribers with the required information, while minimizing the consumed host and network resources. Typically, previous approaches utilize either IP multicast or point-to-point unicast for efficient dissemination of the information. In this work, we propose a novel hybrid framework, which is a combination of both multicast and unicast data dissemination. Our hybrid framework allows us to take the advantages of both multicast and unicast, while avoiding their drawbacks. We investigate several algorithms for computing the best mapping of publishers' transmissions into multicast and unicast transport. Using extensive simulations, we show that our hybrid framework reduces consumed host and network resources, outperforming traditional solutions. To insure the subscribers interests closely resemble those of real-world settings, our simulations are based on stock market data and on recorded IBM WebShpere subscriptions

Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

The capacitated transshipment location problem with stochastic handling utilities at the facilities

The problem consists in finding a transshipment facilities location that maximizes the total net utility when the handling utilities at the facilities are stochastic variables, under supply, demand, and lower and upper capacity constraints. The total net utility is given by the expected total shipping utility minus the total fixed cost of the located facilities. Shipping utilities are given by a deterministic utility for shipping freight from origins to destinations via transshipment facilities plus a stochastic handling utility at the facilities, whose probability distribution is unknown. After giving the stochastic model, by means of some results of the extreme values theory, the probability distribution of the maximum stochastic utilities is derived and the expected value of the optimum of the stochastic model is found. An efficient heuristics for solving real-life instances is also given. Computational results show a very good performance of the proposed methods both in terms of accuracy and efficienc