Estimating Problem Instance Difficulty

In this paper, we define a class of combinatorial search problems in which the objective is to find a set of paths in a graph whose elements' value is as close as possible to some target value. Unlike the usual shortest path prob-lem, the goal is not necessarily to find paths with minimum length. We show that in most cases it is possible to decom-pose the problem into components where heuristic search can be used. We demonstrate the benefits of this approach on a synthetic domain and illustrate an instantiation of the approach for a problem in model-based diagnosis.

2010

Lecture Notes in Computer Science, 2005

This paper considers the primary and secondary path generation problem in traffic engineering. We first present a standard MILP model. Since its size and integrality gap are very large, we then apply a Benders decomposition to isolate the failure case capacity constraints, related linearisation variables and linearisation constraints. The disaggregated Benders cuts are generated, which is actually the set of violated failure case capacity constraints with their linearisation variables and the required linearisation constraints. This corresponds to adding the failure case capacity constraints, their linearisation variables and linearisation constraints only as they are needed. Some results on generated test cases for different network topologies are given. In comparison with the standard MILP formulation, we reduce execution times on average by a factor of 1000 using the Benders decomposition. We also compare with a scheme of accepting demands one-by-one, which can handle more large-scale problems at the cost of loosing optimality.

Computer Applications in Engineering Education, 2009

The study of four-bar linkages to trace a desired path is an important part of teaching in mechanical design. When the number of precision points exceeds a certain number, most recent approaches utilize intelligent optimization methods based on too complex computer science theories to be implemented by an engineering student. In this article we develop and implement new mechanism design results, reducing simultaneously the design space to facilitate finding the optimal mechanism. Finally, we apply global optimization methods that do not require analytical expression of the objective function and are freely available for educational use with Matlab. The proposed computerized methodology focuses student motivation on the mechanical aspects of the problem. Design examples presented illustrate the effectiveness of the approach that provides a solution quality comparable to that of the recently proposed intelligent optimization methods with simplicity of implementation and fast convergence.ß

Information Sciences, 1979

The purpose of this paper is to propose a formal framework for structuring and embedding the heuristic information, in o_rder to allow an algorithmic computation, in quite general cases, of the evaluation function An) of the classical Hart-Nilsson-Raphael algorithm. The notion of semantic graph is first introduced, in which the atomic notion of node is expanded by associating to it an internal structure where the heuristic information is inserted. It is proved that h(n) can be computed by solving an auxiliaq problem, obtained from the original one by adding new arcs, and of s4er complexity than that onw. A new algorithm is then defined for the computation of h(n) and for the determination of minimal solutions. The validity of the model proposed is discussed in detail.

2009

Traditionally, heuristic search algorithms have relied on an estimate of the cost-to-go to speed up problem-solving. In many domains, operators have different costs and estimated cost-to-go is not the same as estimated search-distance-togo. We investigate further accelerating search by using a distance-to-go function. We evaluate two previous proposals: Dynamically weighted A * and A * ǫ. We present a revision to dynamically weighted A * which improves its performance substantially in domains where solutions are not at fixed depths. We show how to incorporate search distance to go estimates into weighted A * in order to improve its performance in pathfinding problems. We present a proof showing that weighted A * can ignore duplicate states, leading to large improvements in performance for pathfinding problems.

Operations Research, 1969

1998

We analyze the asymptotic time complexity of admissible heuristic search algorithms such as A*, IDA*, and depth-first branch-and-bound. Previous analyses relied on an abstract analytical model, and characterize the heuristic function in terms of its accuracy, but do not apply to real problems. In contrast, our analysis allows us to accurately predict the performance of these algorithms on problems such as the slidingtile puzzles and l~ubik's Cube. The heuristic function is characterized simply by the distribution of heuristic values in the problem space. Contrary to conventional wisdom, our analysis shows that the asymptotic heuristic branching factor is the same as the bruteforce branching factor, and that the effect of a heuristic function is to reduce the effective depth of search, rather than the effective branching factor.

Transportation Research Part B, 2012

The multiobjective shortest path problem arises in many transportation and logistics applications, either as a stand-alone network routing problem or a subroutine of a more complex multiobjective network optimization problem. It has been addressed by different solution strategies, including labeling methods, ranking methods, constraint methods, and parametric methods. Increasing attention has been paid to parametric methods in recent years, partially because of its simple algorithmic logic and its flexibility of being used in different user-preference decision-making environments. The core idea of a parametric algorithm is scalarization, by which a multiobjective shortest path problem can be tackled by repeatedly solving a single-objective subproblem. However, existing parametric algorithms suffer two notorious deficiencies, which considerably limit its further applications: first, typical subroutines for the single-objective subproblem in general cannot capture nonextreme Pareto-optimal paths; second, parametric algorithms for biobjective problems cannot be directly extended to solving multiobjective problems. This paper provides some algorithmic improvements that can partially overcome these deficiencies. In particular, the contribution of this work is twofold: first, in the biobjective parametric solution framework, we propose an approximate label-setting algorithm for the parameterized, constrained single-objective subproblem, which is capable of identifying all extreme paths and a large percentage (i.e., 85–100%) of nonextreme paths; second, we suggest a general projection scheme that can decompose a multiobjective problem into a number of biobjective problems. The approximate parametric algorithm runs in polynomial time. The algorithmic design and solution performance of the algorithm for multiobjective shortest path problems are illustrated, and numerically evaluated and compared with a benchmark algorithm in terms of solution completeness and efficiency.► A parametric algorithm framework and an approximate labeling subroutine for biobjective shortest path problems. ► A problem decomposition scheme for multiobjective optimization problems. ► The parametric algorithm outperforms the benchmark labeling algorithm in terms of computational efficiency. ► The combination of the parametric algorithm and the decomposition scheme outperforms the benchmark algorithm.

European Journal of Operational Research, 1993

An efficient computational implementation of a path deletion K shortest paths algorithm and a new algorithm for the same problem are presented. In a path deletion K shortest paths algorithm a sequence {~'1, ~'2 ..... fir} of networks is defined, such that ~'t is the given network and its k-th shortest path is trivially determined from the shortest path in fig" In essence, as soon as the shortest path in ~'k is determined it is excluded from fig in such a way that no new paths are formed and no more paths are deleted. So, for each ~'k, twO procedures are executed: a shortest path algorithm and a path deletion algorithm. In the presented computational implementation, all the information resulting from the determination of the k-th shortest path is carried throughout ~k+l, ~'k+2,'-', ~K" The new algorithm not only keeps this characteristic but also avoids the last K-1 executions of a shortest path algorithm, which results in a surprising and very substantial reduction in the execution time. In fact, for randomly generated networks with 104 nodes and l0 s arcs, once the shortest path is determined, the new algorithm computes the next 100 shortest paths in times of the order of 10-1 seconds. To illustrate the efficiency of this algorithm, comparative computational experiments are reported.