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 Additive Branch-and-Bound Algorithm for the Pickup and Delivery Traveling Salesman Problem with LIFO or FIFO Loading

Abstract: This paper introduces an additive branch-and-bound algorithm for two variants of the pickup and delivery traveling salesman problem in which loading and unloading operations have to be performed either in a Last-In-First-Out (LIFO) or in a First-In-First-Out (FIFO) order. Two relaxations are used within the additive approach: the assignment problem and the shortest spanning r-arborescence problem. The quality of the lower bounds is further improved by a set of elimination rules applied at each node of the search tree to remove from the problem arcs that cannot belong to feasible solutions because of precedence relationships. The performance of the algorithm and the effectiveness of the elimination rules are assessed on instances from the literature.

Computationally Eff i cient Multi-Agent Multi-Object Tracking With Labeled Random Finite Sets

Abstract: This paper addresses multi-agent multi-object tracking with labeled random finite sets via Generalized Covariance Intersection (GCI) fusion. While standard GCI fusion of Labeled Multi-Object (LMO) densities is labelwise and hence fully parallelizable, previous work unfortunately revealed that its fusion performance is highly sensitive to the unavoidable label inconsistencies among different agents. In order to overcome the label inconsistency sensitivity problem, we present a novel approach for the GCI fusion of LMO densities that is both robust to label inconsistencies and computationally efficient. The novel approach consists of, first, finding the best matching between labels of different agents by minimization of a suitable label inconsistency indicator, and, then, performing GCI fusion labelwise according to the obtained label matching. Furthermore, it is shown how the label matching problem, which is at the core of the proposed method, can be formulated as a linear assignment problem of finite length (efficiently solvable in polynomial time by the Hungarian algorithm), exactly for Labeled Multi-Bernoulli densities and approximately for arbitrary LMO densities. Simulation experiments are carried out to demonstrate the robustness and effectiveness of the proposed approach in challenging tracking scenarios.

A Multi-armed Bandit Approach to Online Spatial Task Assignment

Abstract: Spatial crowd sourcing uses workers for performing tasks that require travel to different locations in the physical world. This paper considers the online spatial task assignment problem. In this problem, spatial tasks arrive in an online manner and an appropriate worker must be assigned to each task. However, outcome of an assignment is stochastic since the worker can choose to accept or reject the task. Primary goal of the assignment algorithm is to maximize the number of successful assignments over all tasks. This presents an exploration-exploitation challenge, the algorithm must learn the task acceptance behavior of workers while selecting the best worker based on the previous learning. We address this challenge by defining a framework for online spatial task assignment based on the multi-armed bandit formalization of the problem. Furthermore, we adapt a contextual bandit algorithm to assign a worker based on the spatial features of tasks and workers. The algorithm simultaneously adapts the worker assignment strategy based on the observed task acceptance behavior of workers. Finally, we present an evaluation methodology based on a real world dataset, and evaluate the performance of the proposed algorithm against the baseline algorithms. The results demonstrate that the proposed algorithm performs better in terms of the number of successful assignments.

Layer assignment for multichip modules

Abstract: The layer assignment problem that arises in the design of a multichip module, a high-performance compact package for the interconnection of several hundred chips, is studied. The aim is to place each net in a x-y pair of layers, so as to minimize the number of such pairs. An approximation algorithm, running in O(nd) time is presented for minimizing the number of layers, where n is the number of nets and d is the (two-dimensional) density of the problem. >

Optimal Object Association in the Dempster–Shafer Framework

Abstract: Object association is a crucial step in target tracking and data fusion applications. This task can be formalized as the search for a relation between two sets (e.g., a sets of tracks and a set of observations) in such a way that each object in one set is matched with at most one object in the other set. In this paper, this problem is tackled using the formalism of belief functions. Evidence about the possible association of each object pair, usually obtained by comparing the values of some attributes, is modeled by a Dempster-Shafer mass function defined in the frame of all possible relations. These mass functions are combined using Dempster's rule, and the relation with maximal plausibility is found by solving an integer linear programming problem. This problem is shown to be equivalent to a linear assignment problem, which can be solved in polynomial time using, for example, the Hungarian algorithm. This method is demonstrated using simulated and real data. The 3-D extension of this problem (with three object sets) is also formalized and is shown to be NP-Hard.