L. Mandow

Multicriteria heuristic search

Abstract This paper extends the multicriteria decision paradigm to the heuristic search domain in a systematic way. A useful formal definition of multicriteria heuristic graph search problems is provided. Then the fundamental issues in multicriteria search are described in detail and a general framework is developed. Several new procedures are presented and analyzed for the usual multicriteria decision rules: multiobjective, multiattribute, goal satisfaction, and lexicographic search.

Path recovery in frontier search for multiobjective shortest path problems

Frontier search is a best-first graph search technique that allows significant memory savings over previous best-first algorithms. The fundamental idea is to remove from memory already explored nodes, keeping only open nodes in the search frontier. However, once the goal node is reached, additional techniques are needed to recover the solution path. This paper describes and analyzes a path recovery procedure for frontier search applied to multiobjective shortest path problems. Differences with the scalar case are outlined, and performance is evaluated over a random problem set.

A memory-efficient search strategy for multiobjective shortest path problems

The paper develops vector frontier search, a new multiobjective search strategy that achieves an important reduction in space requirements over previous proposals. The complexity of a resulting multiobjective frontier search algorithm is analyzed and its performance is evaluated over a set of random problems.

Comparison of heuristics in multiobjective a * search

The paper reconsiders the importance of monotonicity and consistency properties on the efficiency of multiobjective A* search. Previous works on the MOA* algorithm (Multi-objective A*) concluded that the importance of the monotone property of heuristics was not as important as in A*. The recent development of an alternative algorithm (NAMOA*), gives a chance to review these results. The paper presents a formal analysis on the comparison of heuristics in NAMOA* and concludes that the properties of consistency and monotonicity are of fundamental importance in search efficiency.

A heuristic search algorithm with lexicographic goals

This paper describes a new general algorithm for graph search problems with additive lexicographic goals. The use of lexicographic goals in the formulation of search problems provides greater control and expressive power over the properties of solution paths. The algorithm, called METAL-A N * can be used to find the set of all solutions to a goal problem. The fundamental concepts of the algorithm are explained and a simple example is used to trace its behaviour. Sufficient conditions that guarantee the completeness and admissibility of METAL-A N * are also presented. r 2002 Elsevier Science Ltd. All rights reserved.

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.

The Role of Multicriteria Problem Solving in Design

The paper analyses the application of multicriteria problem solving methods to design in the light of KLDE 0, a Knowledge Level theory of design. The pros and cons of three usual multicriteria decision rules applied to the resolution of incompleteness, inconsistency, imprecision, and ambiguity is discussed with the aid of a simple example.

A New Approach to Iterative Deepening Multiobjective A

Multiobjective search is a generalization of the Shortest Path Problem where several (usually conflicting) criteria are optimized simultaneously. The paper presents an extension of the single-objective IDA* search algorithm to the multiobjective case. The new algorithm is illustrated with an example, and formal proofs are presented on its termination, completeness, and admissibility. The algorithm is evaluated over a set of random tree search problems, and is found to be more efficient than IDMOA*, a previous extension of IDA* to the multiobjective 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.