Design of a dependable peer-to-peer system for numerical optimization

Abstract

Numerical Optimization is an integral part of most engineering, scientific work and is a computationally intensive job. Most optimization frameworks developed so far executes numerical algorithms in a single processor or in a dedicated cluster of machines. A single system based optimizer is plagued by the resources and a dedicated high performance computational cluster is extremely cost prohibitive. Further with the increase in dimensions of the decision / objective space variables / functions, it is difficult to foresee and plan a computation cluster ahead of time. A peer-to-peer system provides a viable alternative to this problem. A peer-topeer (P2P) system has no central co-ordination and is generally a loose union of a set of nondedicated machines glued via a logical network for fast dissemination of information. The advantage to cost-effectiveness and elasticity with a P2P system however comes with a price. A P2P system lacks trust and malicious nodes can jeopardize the application to a significant extent. The nodes\/communication links are prone to failure of various types such a fail-stop, omission, timing (value) and response (value). As a result there is no guarantee of completion of an optimization job. Furthermore, if a certain section of nodes are susceptible to Byzantine faults, it could lead to a misleading front in the objective space where there is absolute un-certainty of reaching a global minimum. Redundancy, failure detection and recovery are an essential part in the design of such a system. In essence, since in a large scale distributed system "Failure is not an exception but a norm", dependability in design of the system is not just a choice but an absolute requirement.In this presentation, we would like to put forth the challenges of designing such a P2P system together with the algorithms that has been used, designed and developed by us in creating a P2P optimization framework. The presentation is divided into three sections: firstly in identifying the challenges, secondly, the solutions to mitigate the challenges and thirdly the results that we have obtained by applying the solutions to the problem sets.