Local search heuristics for multi-index assignment problems with decomposable costs.

The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise for instance in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighborhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighborhood in polynomial time. Based on this neighborhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward tabu search is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.Assignment; Costs; Heuristics; Problems; Applications; Performance;

A Memetic Algorithm for the Multidimensional Assignment Problem

The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the state-of-the art 3-AP memetic algorithm.Comment: 14 page

A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

Occlusion reasoning for multiple object visual tracking

Thesis (Ph.D.)--Boston UniversityOcclusion reasoning for visual object tracking in uncontrolled environments is a challenging problem. It becomes significantly more difficult when dense groups of indistinguishable objects are present in the scene that cause frequent inter-object interactions and occlusions. We present several practical solutions that tackle the inter-object occlusions for video surveillance applications. In particular, this thesis proposes three methods. First, we propose "reconstruction-tracking," an online multi-camera spatial-temporal data association method for tracking large groups of objects imaged with low resolution. As a variant of the well-known Multiple-Hypothesis-Tracker, our approach localizes the positions of objects in 3D space with possibly occluded observations from multiple camera views and performs temporal data association in 3D. Second, we develop "track linking," a class of offline batch processing algorithms for long-term occlusions, where the decision has to be made based on the observations from the entire tracking sequence. We construct a graph representation to characterize occlusion events and propose an efficient graph-based/combinatorial algorithm to resolve occlusions. Third, we propose a novel Bayesian framework where detection and data association are combined into a single module and solved jointly. Almost all traditional tracking systems address the detection and data association tasks separately in sequential order. Such a design implies that the output of the detector has to be reliable in order to make the data association work. Our framework takes advantage of the often complementary nature of the two subproblems, which not only avoids the error propagation issue from which traditional "detection-tracking approaches" suffer but also eschews common heuristics such as "nonmaximum suppression" of hypotheses by modeling the likelihood of the entire image. The thesis describes a substantial number of experiments, involving challenging, notably distinct simulated and real data, including infrared and visible-light data sets recorded ourselves or taken from data sets publicly available. In these videos, the number of objects ranges from a dozen to a hundred per frame in both monocular and multiple views. The experiments demonstrate that our approaches achieve results comparable to those of state-of-the-art approaches

Construction-based metaheuristics for personnel scheduling problems

This thesis investigates the idea of balancing different constraints in order to find optimal solutions to two personnel scheduling problems, within the framework of constructive metaheuristic approaches. The two problems considered are a nurse scheduling problem, for which finding feasible solutions is known to be difficult and for which the hard and soft constraints are in direct conflict, and a medical student scheduling problem for which there is little relevant literature this second problem also has conflicting hard and soft constraints, but presents further conflict between the different soft constraints. The methods used to solve these problems are focused on two constructive metaheuristics in particular: Greedy Randomised Adaptive Search Procedures (GRASP) and Ant Colony Optimisation (ACO) and for each approach several construction heuristics are introduced and compared. Using GRASP, a number of local search neighbourhoods are established for each problem, while for ACO the suitability of three trail definitions are compared. In order to further explore the balance which may obtained between the different constraints and objectives for the two problems, hybrid constructions are investigated, incorporating exact methods which take advantage of the underlying structures of each problem with regards to feasibility. For medical student scheduling, this exact method was developed into a new type of construction mechanism providing much improved results over a standard heuristic approach. Further enhancements investigated include the use of problem-specific feedback for nurse scheduling and the use of an intelligent memory procedure for the medical student scheduling problem. For the nurse scheduling problem, the final algorithm developed was able to rival the best in the literature so far and produce optimal solutions for all available datasets. For the medical student scheduling problem, optimal solutions are not known, but the results obtained are very promising and provide a good basis for further study of the problem.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Construction-based metaheuristics for personnel scheduling problems.

This thesis investigates the idea of balancing different constraints in order to find optimal solutions to two personnel scheduling problems, within the framework of constructive metaheuristic approaches. The two problems considered are a nurse scheduling problem, for which finding feasible solutions is known to be difficult and for which the hard and soft constraints are in direct conflict, and a medical student scheduling problem for which there is little relevant literature this second problem also has conflicting hard and soft constraints, but presents further conflict between the different soft constraints. The methods used to solve these problems are focused on two constructive metaheuristics in particular: Greedy Randomised Adaptive Search Procedures (GRASP) and Ant Colony Optimisation (ACO) and for each approach several construction heuristics are introduced and compared. Using GRASP, a number of local search neighbourhoods are established for each problem, while for ACO the suitability of three trail definitions are compared. In order to further explore the balance which may obtained between the different constraints and objectives for the two problems, hybrid constructions are investigated, incorporating exact methods which take advantage of the underlying structures of each problem with regards to feasibility. For medical student scheduling, this exact method was developed into a new type of construction mechanism providing much improved results over a standard heuristic approach. Further enhancements investigated include the use of problem-specific feedback for nurse scheduling and the use of an intelligent memory procedure for the medical student scheduling problem. For the nurse scheduling problem, the final algorithm developed was able to rival the best in the literature so far and produce optimal solutions for all available datasets. For the medical student scheduling problem, optimal solutions are not known, but the results obtained are very promising and provide a good basis for further study of the problem