Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Benthic microalgae in coral reef sediments of the southern Great Barrier Reef, Australia

The abundance and productivity of benthic microalgae in coral reef sediments are poorly known compared with other, more conspicuous (e.g. coral zooxanthellae, macroalgae) primary producers of coral reef habitats. A survey of the distribution, biomass, and productivity of benthic microalgae on a platform reef flat and in a cross-shelf transect in the southern Great Barrier Reef indicated that benthic microalgae are ubiquitous, abundant (up to 995.0 mg chlorophyll (chl) a m(-2)), and productive (up to 110 mg O-2 m(-2) h(-1)) components of the reef ecosystem. Concentrations of benthic microalgae, expressed as chlorophyll a per surface area, were approximately 100-fold greater than the integrated water column concentrations of microalgae throughout the region. Benthic microalgal biomass was greater on the shallow water platform reef than in the deeper waters of the cross-shelf transect. In both areas the benthic microalgal communities had a similar composition, dominated by pennate diatoms, dinoflagellates, and cyanobacteria. Benthic microalgal populations were potentially nutrient-limited, based on responses to nitrogen and phosphorus enrichments in short-term (7-day) microcosm experiments. Benthic microalgal productivity, measured by O-2 evolution, indicated productive communities responsive to light and nutrient availability. The benthic microalgal concentrations observed (92-995 mg chl a m(-2)) were high relative to other reports, particularly compared with temperate regions. This abundance of productive plants in both reef and shelf sediments in the southern Great Barrier Reef suggests that benthic microalgae are key components of coral reef ecosystems.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.