Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

Abstract: The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.

An efficient Genetic Algorithm with uniform crossover for the multi-objective Airport Gate Assignment Problem

Abstract: Genetic Algorithms (GAs) have a good potential of solving the Gate Assignment Problem (GAP) at airport terminals, and the design of feasible and efficient evolutionary operators, particularly, the crossover operator, is crucial to successful implementations. This paper reports an application of GAs to the multi-objective GAP. The relative positions between aircraft rather than their absolute positions in the queues to gates is used to construct chromosomes in a novel encoding scheme, and a new uniform crossover operator, free of feasibility problems, is then proposed, which is effective and efficient to identify, inherit and protect useful common sub-queues to gates during evolution. Extensive simulation studies illustrate the advantages of the proposed GA scheme with uniform crossover operator.

Swarm Intelligence Based Dynamic Control Channel Assignment in Cogmesh

Abstract: In this paper we address the control channel assignment problem in a cognitive radio based wireless network, namely the CogMesh. Such a network is featured by the dynamic spectrum sharing of the secondary users coexisting with the primary users. The opportunistic nature of the spectrum utilization among the secondary users makes a global control channel infeasible. The self-coordination of the network, hence, becomes a challenge task. Considering the fact that common channels may temporarily exist among a local group of secondary users, we propose an adaptive approach that selects local common control channels independently by each secondary user according to the qualities of the detected spectrum holes and the choices of its neighbors. To achieve this, a swarm intelligence-based algorithm is used to facilitate the common control channel selection. The idea is to use HELLO messages periodically broadcasted by neighbors as the pheromone to rank the common channels so as to expedite the channel selection process. The algorithm is completely distributed and therefore scalable. Moreover, it is simple, flexible, adaptive, and well balanced on the exploitation and exploration of the radio resources. The behaviors and performance of the proposed algorithm are verified by simulation.

A distributed asynchronous relaxation algorithm for the assignment problem

Abstract: Relaxation methods for optimal network flow problems resemble classical coordinate descent, Jacobi, and Gauss-Seidel methods for solving unconstrained non-linear optimization problems or systems of nonlinear equations. In their pure form they modify the dual variables (node prices) one at a time using only local node information while aiming to improve the dual cost. They are particularly well suited for distributed implementation on massively parallel machine. For problems with strictly convex arc costs they can be shown to converge even if relaxation at each node is carried out asynchronously with out-of-date price information from neighboring nodes [1]. For problems with linear arc costs relaxation methods have outperformed by a substantial margin the classical primal simplex and primal-dual methods on standard benchmark problems [2], [3]. However in these particular methods it is necessary to change sometimes the prices of several nodes as a group in addition to carrying out pure relaxation steps. As a result global node price information is needed occasionally, and distributed implementation becomes somewhat complicated. In this paper we describe a distributed algorithm for solving the classical linear cost assignment problem. It employs exclusively pure relaxation steps whereby the prices of sources and sinks are changed individually on the basis of only local (neighbor) node price information. The algorithm can be implemented in an asynchronous (chaotic) manner, and seems quite efficient for problems with a small arc cost range. It has an interesting interpretation as an auction where economic agents compete for resources by making successively higher bids.