Enrique Machuca

Multiobjective heuristic search in road maps

This article considers the application of exact multiobjective techniques to search in large size realistic road maps. In particular, the NAMOA^* algorithm is successfully applied to several road networks from the DIMACS shortest path implementation challenge with two objectives. An efficient heuristic function previously proposed by Tung and Chew is evaluated. Heuristic values are precalculated with search. The precalculation effort is shown to pay off during the multiobjective search stage. An improvement to the calculation procedure is also proposed, resulting in added improved time performance in many problem instances.

A comparison of heuristic best-first algorithms for bicriterion shortest path problems

A variety of algorithms have been proposed to solve the bicriterion shortest path problem. This article analyzes and compares the performance of three best-first (label-setting) algorithms that accept heuristic information to improve efficiency. These are NAMOA∗, MOA∗, and Tung & Chew’s algorithm (TC). A set of experiments explores the impact of heuristic information in search efficiency, and the relative performance of the algorithms. The analysis reveals that NAMOA∗ is the best option for difficult problems. Its time performance can benefit considerably from heuristic information, though not in all cases. The performance of TC is similar but somewhat worse. However, the time performance of MOA∗ is found to degrade considerably with the use of heuristic information in most cases. Explanations are provided for these phenomena.

An empirical comparison of some multiobjective graph search algorithms

This paper compares empirically the performance in time and space of two multiobjective graph search algorithms, MOA* and NAMOA*. Previous theoretical work has shown that NAMOA* is never worse than MOA*. Now, a statistical analysis is presented on the relative performance of both algorithms in space and time over sets of randomly generated problems.

A case of pathology in multiobjective heuristic search

This article considers the performance of the MOA* multiobjective search algorithm with heuristic information. It is shown that in certain cases blind search can be more efficient than perfectly informed search, in terms of both node and label expansions. A class of simple graph search problems is defined for which the number of nodes grows linearly with problem size and the number of nondominated labels grows quadratically. It is proved that for these problems the number of node expansions performed by blind MOA* grows linearly with problem size, while the number of such expansions performed with a perfectly informed heuristic grows quadratically. It is also proved that the number of label expansions grows quadratically in the blind case and cubically in the informed case.

Heuristic multiobjective search for hazmat transportation problems

This paper describes the application of multiobjective heuristic search algorithms to the problem of hazardous material (hazmat) transportation. The selection of optimal routes inherently involves the consideration of multiple conflicting objectives. These include the minimization of risk (e.g. the exposure of the population to hazardous substances in case of accident), transportation cost, time, or distance. Multiobjective analysis is an important tool in hazmat transportation decision making. This paper evaluates the application of multiobjective heuristic search techniques to hazmat route planning. The efficiency of existing algorithms is known to depend on factors like the number of objectives and their correlations. The use of an informed multiobjective heuristic function is shown to significantly improve efficiency in problems with two and three objectives. Test problems are defined over random graphs and over a real road map.

Lower bound sets for biobjective shortest path problems

This article considers the problem of calculating the set of all Pareto-optimal solutions in one-to-one biobjective shortest path problems with positive cost vectors. The efficiency of multiobjective best-first search algorithms can be improved with the use of consistent informed lower bounds. More precisely, the use of the ideal point as a lower bound has recently been shown to effectively increase search performance. In theory, the use of lower bounds that better approximate the Pareto frontier using sets of vectors (bound sets), could further improve performance. This article describes a lower bound set calculation method for biobjective shortest path problems. Improvements in search efficiency with lower bound sets of increasing precision are analyzed and discussed.

An evaluation of best compromise search in graphs

This work evaluates two different approaches for multicriteria graph search problems using compromise preferences. This approach focuses search on a single solution that represents a balanced tradeoff between objectives, rather than on the whole set of Pareto optimal solutions. We review the main concepts underlying compromise preferences, and two main approaches proposed for their solution in heuristic graph problems: naive Pareto search (NAMOA*), and a k-shortest-path approach (kA*). The performance of both approaches is evaluated on sets of standard bicriterion road map problems. The experiments reveal that the k-shortest-path approach looses effectiveness in favor of naive Pareto search as graph size increases. The reasons for this behavior are analyzed and discussed.

An analysis of multiobjective search algorithms and heuristics

This thesis analyzes the performance of multiobjective heuristic graph search algorithms. The analysis is focused on the influence of heuristic information, correlation between objectives and solution depth.