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Efficient Tabu Search Algorithm for the Cyclic Inspection Problem
Abstract
Unmanned aerial vehicles (UAVs) are a powerful tool for remote monitoring of objects requiring early anomaly detection, emergency intervention, or measurement data collection. We consider the problem of determining the optimal path of a UAV performing remote inspection of objects. The UAV inspects objects repeatedly (infinitely many times) every specified period of time. We propose an effective heuristic algorithm based on the tabu search method. In its construction, we used some properties of the problem under consideration.
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Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult‐to‐access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.
This paper addresses the close-enough traveling salesman problem. In this problem, rather than visiting the vertex (customer) itself, the salesman must visit a specific region containing such vertex. To solve this problem, we propose a simple yet effective exact algorithm, based on branch-and-bound and second order cone programming. The proposed algorithm was tested in 824 instances suggested in the literature. Optimal solutions are obtained for open problems with up to a thousand vertices. We consider instances both in twoand three-dimensional space.
This paper addresses a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood set of that node. The problem is known as the close-enough traveling salesman problem. We introduce a new effective discretization scheme that allows us to compute both a lower and an upper bound for the optimal solution. Moreover, we apply a graph reduction algorithm that significantly reduces the problem size and speeds up computation of the bounds. We evaluate the effectiveness and the performance of our approach on several benchmark instances. The computational results show that our algorithm is faster than the other algorithms available in the literature and that the bounds it provides are almost always more accurate.
This is the second half of a two part series devoted to the tabu search metastrategy for optimization problems. Part I introduced the fundamental ideas of tabu search as an approach for guiding other heuristics to overcome the limitations of local optimality, both in a deterministic and a probabilistic framework. Part I also reported successful applications from a wide range of settings, in which tabu search frequently made it possible to obtain higher quality solutions than previously obtained with competing strategies, generally with less computational effort. Part II, in this issue, examines refinements and more advanced aspects of tabu search. Following a brief review of notation, Part II introduces new dynamic strategies for managing tabu lists, allowing fuller exploitation of underlying evaluation functions. In turn, the elements of staged search and structured move sets are characterized, which bear on the issue of finiteness. Three ways of applying tabu search to the solution of integer programming problems are then described, providing connections also to certain nonlinear programming applications. Finally, the paper concludes with a brief survey of new applications of tabu search that have occurred since the developments reported in Part I. Together with additional comparisons with other methods on a wide body of problems, these include results of parallel processing implementations and the use of tabu search in settings ranging from telecommunications to neural networks.
INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
Integer programming has benefited from many innovations in models and methods. Some of the promising directions for elaborating these innovations in the future may be viewed from a framework that links the perspectives of artificial intelligence and operations research. To demonstrate this, four key areas are examined:
1.(1) controlled randomization,
2.(2) learning strategies,
3.(3) induced decomposition and
4.(4) tabu search. Each of these is shown to have characteristics that appear usefully relevant to developments on the horizon.
This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range of problems for which it is best suited. This paper undertakes to present the major ideas and findings to date, and to indicate challenges for future research. Part I of this study indicates the basic principles, ranging from the short-term memory process at the core of the search to the intermediate and long term memory processes for intensifying and diversifying the search. Included are illustrative data structures for implementing the tabu conditions (and associated aspiration criteria) that underlie these processes. Part I concludes with a discussion of probabilistic tabu search and a summary of computational experience for a variety of applications. Part II of this study (to appear in a subsequent issue) examines more advanced considerations, applying the basic ideas to special settings and outlining a dynamic move structure to insure finiteness. Part II also describes tabu search methods for solving mixed integer programming problems and gives a brief summary of additional practical experience, including the use of tabu search to guide other types of processes, such as those of neural networks.
INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
This paper addresses the traveling salesman problem with arbitrary neighbourhoods, which is an NP-hard problem in combinatorial optimization and is important in operations research and theoretical computer science. Existing methods based on neighbourhood predigestion and discretization are impractical in cases in which the neighbourhoods are arbitrary. In this paper, the neighbourhoods of the traveling salesman problem are generalized to arbitrarily connected regions in planar Euclidean space. A novel approach to solving this problem is proposed, including a boundary-based encoding scheme and a double-loop hybrid algorithm based on particle swarm optimization and genetic algorithm. In the hybrid algorithm, linear descending inertia weight particle swarm optimization is adopted to search continuous visiting positions in the outer loop, and the genetic algorithm is used to optimize the discrete visiting sequence in the inner loop. The boundary-based encoding scheme can reduce the search space significantly without degrading the solution quality, and the hybrid algorithm can find a high-quality solution in a reasonable time. The computational results on both small and large instances demonstrate that the proposed approach can guarantee a high-quality solution in a reasonable time, compared with three other state-of-the-art algorithms: iterative algorithm, branch-and-bound algorithm, and upper and lower bound algorithm. Moreover, the proposed approach works efficiently in a real-world application that cannot be solved by existing algorithms.
W e address a variant of the Euclidean traveling salesman problem known as the close-enough traveling salesman problem (CETSP), where the traveler visits a node if it enters a compact neighborhood set of that node. We formulate a mixed-integer programming model based on a discretization scheme for the problem. Both lower and upper bounds on the optimal CETSP tour length can be derived from the solution of this model, and the quality of the bounds obtained depends on the granularity of the discretization scheme. Our approach first develops valid inequalities that enhance the bound and solvability of this formulation. We then provide two alternative formulations, one that yields an improved lower bound on the optimal CETSP tour length, and one that greatly improves the solvability of the original formulation by recasting it as a two-stage problem amenable to decomposition. Computational results demonstrate the effectiveness of the proposed methods.
)Cristian S. MataJoseph S. B. Mitchelly1 IntroductionIn this paper, we provide a simple method to obtainprovably good approximation algorithms for a variety ofNP-hard geometric optimization problems having to dowith computing shortest constrained tours and networks:Red-Blue Separation Problem (RBSP): Considerthe problem of finding a minimum-perimeter Jordancurve (necessarily, a simple polygon) that separates a setof "red" points, R, from a set of "blue" points, B. Thisproblem...
We explore synergies among mobile robots and wireless sensor networks in environmental monitoring through a system in which robotic data mules collect measurements gathered by sensing nodes. A proof-of-concept implementation demonstrates that this approach significantly increases the lifetime of the system by conserving energy that the sensing nodes otherwise would use for communication.
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this paper, we present new approximation results for the TSPN, including (1) a constant-factor approximation algorithm for the case of arbitrary connected neighborhoods having comparable diameters; and (2) a PTAS for the important special case of disjoint unit disk neighborhoods (or nearly disjoint, nearly-unit disks). Our methods also yield improved approximation ratios for various special classes of neighborhoods, which have previously been studied. Further, we give a linear-time O(1)-approximation algorithm for the case of neighborhoods that are (infinite) straight lines.
We introduce a geometric version of the Covering Salesman Problem: Each of the n salesman's clients specifies a neighborhood in which they are willing to meet the salesman. Identifying a tour of minimum length that visits all neighborhoods is an NP-hard problem, since it is a generalization of the Traveling Salesman Problem. We present simple heuristic procedures for constructing tours, for a variety of neighborhood types, whose length is guaranteed to be within a constant factor of the length of an optimal tour. The neighborhoods we consider include, parallel unit segments, translates of a polygonal region, and circles. y Partially supported by NSF Grants DMS 8903304 and ECSE-8857642. 1
Heuristics for solving three routing problems: close-enough traveling salesman problem, close-enough vehicle routing problem, sequence-dependent team orienteering problem
- W K Mennell