General assignment

Abstract: We consider the generalized assignment problem in which the objective is to find a minimum cost assignment of a set of jobs to a set of agents subject to resource constraints. The presented new approach is based on a previously published, successful hybrid genetic algorithm and includes as new features two alternative initialization heuristics, a modified selection and replacement scheme for handling infeasible solutions more appropriately, and a heuristic mutation operator. Tests are performed on standard test instances from the literature and on newly created, larger and more difficult instances. The presented genetic algorithm with its two initialization variants is compared to the previous genetic algorithm and to the commercial general purpose branch-and-cut system CPLEX. Results indicate that CPLEX is able to solve relatively large instances of the general assignment problem to provable optimality. For the largest and most difficult instances, however, the proposed genetic algorithm yields on average the best results in shortest time.

Abstract: Auction and market-based mechanisms are among the most popular methods for distributed task allocation in multirobot systems. Most of these mechanisms were designed in a heuristic way and analysis of the quality of the resulting assignment solution is rare. This paper presents a new market-based multi-robot task allocation algorithm that produces optimal assignments. Rather than adopting a buyer’s “selfish” bidding perspective as in previous auction/market-based approaches, the proposed method approaches auctioning from a merchant’s point of view, producing a pricing policy that responds to cliques of customers. The algorithm uses price escalation to clear a market of all its goods, producing a state of equilibrium that satisfies both the merchant and customers. The proposed method can be used as a general assignment algorithm as it has a time complexity (O(nlgn)) close to the fastest state-of-the-art algorithms (O(n)) but is extremely easy to implement. As in previous research, the economic model reflects the distributed nature of markets inherently: in this paper it leads directly to a decentralized method ideally suited for distributed multi-robot systems.

Abstract: An iterative procedure is described as a generalization of Bayes' method of updating an a priori assignment over the power set of the frame of discernment using uncertain evidence. In the context of probability kinematics the law of commutativity holds and the convergence is well behaved. the probability assignments of each updating evidence is retained. A general assignment method is also discussed for combining evidences without reference to any prior. the methods described here can be used in the field of Artificial Intelligence for common-sense reasoning and more specifically for treating uncertainty in Expert Systems. They are also relevant for nonmonotonic reasoning, abduction, and learning theory.