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.

An algorithm for the equilibrium assignment problem with random link times

Abstract: In this article we offer an equivalent minimization formulation for the traffic assignment problem when the link travel times are flow-dependent random variables. The paper shows the equivalency between the first-order conditions of this program and the stochastic equilibrium conditions as well as the uniqueness of the solution. The paper also describes an algorithmic approach to the solution of this program, including a proof of convergence. Finally, we conduct some limited numerical experiments on the rate of convergence of the algorithm and the merits of the stochastic equilibrium model, in general, as compared with deterministic approaches.

The concept assignment problem in program understanding

Abstract: Concept assignment is a process of recognizing concepts within a computer program and building up an understanding of the program by relating the recognized concepts to portions of the program, its operational context and to one another. The problem of discovering individual human oriented concepts and assigning them to their implementation oriented counterparts for a given program is the concept assignment problem. The authors argue that the solution to this problem requires methods that have a strong plausible reasoning component. They illustrate these ideas through example scenarios using an existing design recovery system called DESIRE. DESIRE is evaluated based on its usage on real-world problems over the years. >

Online budgeted matching in random input models with applications to Adwords

Abstract: We study an online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints. We analyze the performance of the Greedy algorithm (which assigns each query to the highest bidder) in a randomized input model with queries arriving in a random permutation. Our main result is a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1/e for maximizing the value of the assignment. We also consider the more standard i.i.d. model of input, and show that our analysis holds there as well. This is to be contrasted with the worst case analysis of [MSVV05] which shows that Greedy has a ratio of 1/2, and that the optimal algorithm presented there has a ratio of 1 - 1/e. The analysis of Greedy is important in the Adwords setting because it is the natural allocation algorithm for an auction-style process. From a theoretical perspective, our result simplifies and generalizes the classic algorithm of Karp, Vazirani and Vazirani for online bipartite matching. Our results include a new proof to show that the Ranking alforithm of [KVV90] has a ratio of 1 - 1/e in the worst case. It has been recently discovered [KV07] (independent of our results) that one of the crucial lemmas in [KVV90], related to a certain reduction, is incorrect. Our proof is direct, in that it does not go via such a reduction, which also enables us to generalize the analysis to our online assignment problem.

Sensitivity Analysis for Equilibrium Network Flow

Abstract: Direct application of existing sensitivity analysis methods for nonlinear programming problems or for variational inequalities to nonlinear programming or variational inequality formulations of the equilibrium traffic assignment problem is not feasible, since, in general, the solution to the equilibrium traffic assignment problem does not satisfy the uniqueness conditions required by the sensitivity analysis methods. This paper presents an approach for sensitivity analysis of equilibrium traffic assignment problems in which an equivalent restricted problem is developed which has the desired uniqueness properties; the existing methods are applied to this restricted problem to calculate the derivatives of the equilibrium arc flows with respect to perturbations of the cost functions and of the trip table. These derivatives are then shown to be equivalent to the derivatives of the original unrestricted equilibrium traffic assignment problem; therefore, the method yields the desired sensitivity analysis results.

Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment

Abstract: Display Omitted An improved adaptive PSO based on Alpha-stable distribution and dynamic fractional calculus is studied.A new multi-objective optimization model of gate assignment problem is proposed.The actual data are used to demonstrate the effectiveness of the proposed method. Gate is a key resource in the airport, which can realize rapid and safe docking, ensure the effective connection between flights and improve the capacity and service efficiency of airport. The minimum walking distances of passengers, the minimum idle time variance of each gate, the minimum number of flights at parking apron and the most reasonable utilization of large gates are selected as the optimization objectives, then an efficient multi-objective optimization model of gate assignment problem is proposed in this paper. Then an improved adaptive particle swarm optimization(DOADAPO) algorithm based on making full use of the advantages of Alpha-stable distribution and dynamic fractional calculus is deeply studied. The dynamic fractional calculus with memory characteristic is used to reflect the trajectory information of particle updating in order to improve the convergence speed. The Alpha-stable distribution theory is used to replace the uniform distribution in order to escape from the local minima in a certain probability and improve the global search ability. Next, the DOADAPO algorithm is used to solve the constructed multi-objective optimization model of gate assignment in order to fast and effectively assign the gates to different flights in different time. Finally, the actual flight data in one domestic airport is used to verify the effectiveness of the proposed method. The experiment results show that the DOADAPO algorithm can improve the convergence speed and enhance the local search ability and global search ability, and the multi-objective optimization model of gate assignment can improve the comprehensive service of gate assignment. It can effectively provide a valuable reference for assigning the gates in hub airport.