Low-cost Heuristics Research Articles

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.

An ant colony hyperheuristic approach for matrix bandwidth reduction

This paper considers the bandwidth reduction problem for large-scale matrices in serial computations. A heuristic for bandwidth reduction reorders the rows and columns of a given sparse matrix so that the method places entries with a nonzero value as close to the main diagonal as possible. Bandwidth optimization is a critical issue for many scientific and engineering applications. In this regard, this paper proposes an ant colony hyperheuristic approach for the bandwidth reduction of symmetric and nonsymmetric matrices. The ant colony hyperheuristic approach evolves and selects graph theory bandwidth reduction algorithms for application areas. This paper evaluates the resulting heuristics for bandwidth reduction in each application area against the most promising low-cost heuristics for bandwidth reduction. This paper also includes a numerical examination of the current state-of-the-art metaheuristic algorithms for matrix bandwidth reduction. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed approach outperformed state-of-the-art low-cost heuristics for bandwidth reduction when applied to problem cases arising from several application areas, clearly indicating the promise of the proposal.

An evaluation of low-cost heuristics for matrix bandwidth and profile reductions

Hundreds of heuristics have been proposed to resolve the problems of bandwidth and profile reductions since the 1960s. We found 132 heuristics that have been applied to these problems in reviews of the literature. Among them, 14 were selected for which no other simulation or comparison revealed that the heuristic could be superseded by any other algorithm in the analyzed articles with respect to bandwidth or profile reduction. We also considered the computational costs of the heuristics during this process. Therefore, these 14 heuristics were selected as potentially being the best low-cost methods to solve the bandwidth and/or profile reduction problems. Results of the 14 selected heuristics are evaluated in this work. For evaluation on the set of test problems, a metric based on the relative percentage distance to the best possible bandwidth or profile is proposed. The most promising heuristics for several application areas are identified. Moreover, it was found that the FNCHC and GPS heuristics showed the best overall results in reducing the bandwidth of symmetric and asymmetric matrices among the evaluated heuristics, respectively. In addition, the NSloan and MPG heuristics showed the best overall results in reducing the profile of symmetric and asymmetric matrices among the heuristics among the evaluated heuristics, respectively.

Over-confidence and Low-cost Heuristics: An Experimental Investigation of Choice Behavior

Abstract This paper extends choice theory by allowing for the interaction between cognitive costs and imitative dynamics. The authors experimentally investigate the role of imitation when participants face a task which is costly in cognitive terms. In order to disentangle different choice dynamics, they devise a laboratory experiment with a novel experimental task in which they model the choice of different alternatives through high or low cognitive costs and feedback information provided to subjects. Their results provide evidence for imitative behavior driven by under-confidence about own skills and by the beliefs regarding others’ performance. They also find a temporal pattern in the distribution of choices, both in the highcost and low-cost cognitive conditions, that may represent another cognitive shortcut.

Bounded rationality, social and cultural norms, and interdependence via reference groups

This paper presents an axiomatic theory of preference orderings similar in abstraction to the standard preference model, but developed for the analysis of bounded rationality where social norms and reference groups serve as sources of low-cost heuristics that can absorb costly deliberation and other limits to rationality. A two-step choice process is proposed, in which physical wants are satisfied sequentially with social want reducing choice indeterminacy. Social want is captured by emulation–avoidance of reference groups, and the serviceabilities of a commodity bundle to it are imputed. The resulting norm-guided behavior is rationalizable in the traditional sense.