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Register a new userDistance-Based Bias in Model-Directed Optimization of Additively Decomposable Problems
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Martin Pelikan
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.
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The paper analyzes the scalability of multiobjective estimation of distribution algorithms (MOEDAs) on a class of boundedly-difficult additively-separable multiobjective optimization problems. The paper illustrates that even if the linkage is correctly identified, massive multimodality of the search problems can easily overwhelm the nicher and lead to exponential scale-up. Facetwise models are subsequently used to propose a growth rate of the number of differing substructures between the two objectives to avoid the niching method from being overwhelmed and lead to polynomial scalability of MOEDAs.
An automated technique has recently been proposed to transfer learning in the hierarchical Bayesian optimization algorithm (hBOA) based on distance-based statistics. The technique enables practitioners to improve hBOA efficiency by collecting statistics from probabilistic models obtained in previous hBOA runs and using the obtained statistics to bias future hBOA runs on similar problems. The purpose of this paper is threefold: (1) test the technique on several classes of NP-complete problems, including MAXSAT, spin glasses and minimum vertex cover; (2) demonstrate that the technique is effective even when previous runs were done on problems of different size; (3) provide empirical evidence that combining transfer learning with other efficiency enhancement techniques can often yield nearly multiplicative speedups.
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The generalization abilities of heuristic optimizers may deteriorate with the increment of the search space dimensionality. To achieve generalized performance across Large Scale Blackbox Optimization (LSBO) tasks, it ispossible to ensemble several heuristics and devise a meta-heuristic to control their initiation. This paper first proposes a methodology of transforming LSBO problems into online decision processes to maximize efficiency of resource utilization. Then, using the perspective of multi-armed bandits with non-stationary reward distributions, we propose a meta-heuristic based on Temporal Estimation of Rewards (TER) to address such decision process. TER uses a window for temporal credit assignment and Boltzmann exploration to balance the exploration-exploitation tradeoff. The prior-free TER generalizes across LSBO tasks with flexibility for different types of limited computational resources (e.g. time, money, etc.) and is easy to be adapted to new tasks for its simplicity and easy interface for heuristic articulation. Tests on the benchmarks validate the problem formulation and suggest significant effectiveness: when TER is articulated with three heuristics, competitive performance is reported across different sets of benchmark problems with search dimensions up to 10000.
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