A multiobjective optimization approach to statistical mechanics

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions involve a compromise between both. The theory of Pareto (or multi objective) optimization provides a general framework to explore these problems and find the space of possible solutions compatible with the underlying tradeoffs, known as the {\em Pareto front}. Conflicts between constraints can lead to complex landscapes of Pareto optimal solutions with interesting implications in economy, engineering, or evolutionary biology. Despite their disparate nature, here we show how the structure of the Pareto front uncovers profound universal features that can be understood in the context of thermodynamics. In particular, our study reveals that different fronts are connected to different classes of phase transitions, which we can define robustly, along with critical points and thermodynamic potentials. These equivalences are illustrated with classic thermodynamic examples.Comment: 14 pages, 8 figure

Power Saving Experiments for Large Scale Global Optimization

Green computing, an emerging field of research that seeks to reduce excess power consumption in high performance computing (HPC), is gaining popularity among researchers. Research in this field often relies on simulation or only uses a small cluster, typically 8 or 16 nodes, because of the lack of hardware support. In contrast, System G at Virginia Tech is a 2592 processor supercomputer equipped with power aware components suitable for large scale green computing research. DIRECT is a deterministic global optimization algorithm, implemented in the mathematical software package VTDIRECT95. This paper explores the potential energy savings for the parallel implementation of DIRECT, called pVTdirect, when used with a large scale computational biology application, parameter estimation for a budding yeast cell cycle model, on System G. Two power aware approaches for pVTdirect are developed and compared against the CPUSPEED power saving system tool. The results show that knowledge of the parallel workload of the underlying application is beneficial for power management

Design and Implementation of a Massively Parallel Version of DIRECT

This paper describes several massively parallel implementations for a global search algorithm DIRECT. Two parallel schemes take different approaches to address DIRECT's design challenges imposed by memory requirements and data dependency. Three design aspects in topology, data structures, and task allocation are compared in detail. The goal is to analytically investigate the strengths and weaknesses of these parallel schemes, identify several key sources of inefficiency, and experimentally evaluate a number of improvements in the latest parallel DIRECT implementation. The performance studies demonstrate improved data structure efficiency and load balancing on a 2200 processor cluster