User:Neha patankar/Probability collectives

Probability Collectives Probability Collectives (PC) is an emerging Artificial Intelligence (AI) tool in the framework of Collective Intelligence (COIN) for modeling and controlling distributed Multi-Agent System (MAS). It is inspired from a sociophysics viewpoint with deep connections to Game Theory, Statistical Physics, and Optimization. From another viewpoint, the method of PC theory is an efficient way of sampling the joint probability space, converting the problem into the convex space of probability distribution.

History
Since its first introduction in a technical report presented to NASA in 1999 by Dr. David Wolpert, the approach of PC was applied solving a variety of unconstrained problems as well as constrained problems. Dr. A.J. Kulkarni and Dr. Kang Tai further modified and improved the approach of PC by using BFGS algorithm, K-update rule, feasibility based rule, penalty function approach. The approach of PC has been successfully applied solving combinatorial problems such as airplane fleet assignment problem and various cases of the Multi-Depot Multiple Traveling Salesmen Problems (MDMTSPs), Single Depot Multiple Traveling Salesmen Problems (SDMTSPs), continuous constrained problems such as benchmark test problems, two variations of the Circle Packing Problem (CPP) and practically important Sensor Network Coverage Problem as well as fault-tolerant system in association with the CPP. Furthermore, the segmented beam problem, multimodal, nonlinear and non-separable test problems comparing the performance with Genetic Algorithm (GA) as well as joint optimization of the routing and resource allocation in wireless networks have been solved as continuous unconstrained problems. In addition, performance of the centralized and decentralized architectures of PC was evaluated solving continuous unconstrained 8-Queens problem which underscored superiority of the decentralized approach of PC methodology. Probability collectives may have applications in various areas such as machine shop scheduling, urban traffic control, sensor network, telecommunication infrastructure, internet search, supply chain, structural optimization (truss, scaffolding, and formwork weight optimization), etc.