Single Approximation for Biobjective Max TSP

Bazgan, Cristina; Gourvès, Laurent; Monnot, Jérôme; Pascual, Fanny

doi:10.1007/978-3-642-29116-6_5

Cited by 2 publications

(2 citation statements)

References 23 publications

(45 reference statements)

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“…then, by (14) and (16) we get respectively ℓ(M 2 ) ≥ 1 2 ℓ(M ℓ ) and ℓ(M 6 A computer-aided approach Lemma 2 establishes the existence of 1/2-approximate matchings for complete graphs with at most n = 6 nodes. It seems difficult to establish a general result, and our proofs become more and more tedious as n grows.…”

Section: Approximationmentioning

confidence: 98%

“…The ideal point approach has also been used on the bi-objective version of the traveling salesman problem [12][13][14]. For the maximization version of the problem, the best ratios for the approximation of the ideal point come from [14]: 5/12 − ε if the two objectives satisfy the triangle inequality, 3/8 − ε if only one objective satisfies the triangle inequality, and…”

Section: Related Workmentioning

confidence: 99%

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Bi-objective matchings with the triangle inequality

Gourvès¹,

Monnot²,

Pascual³

et al. 2017

Theoretical Computer Science

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This article deals with a bi-objective matching problem. The input is a complete graph and two values on each edge (a weight and a length) which satisfy the triangle inequality. It is unlikely that every instance admits a matching with maximum weight and maximum length at the same time. Therefore, we look for a compromise solution, i.e. a matching that simultaneously approximates the best weight and the best length. For which approximation ratio ρ can we guarantee that any instance admits a ρ-approximate matching? We propose a general method which relies on the existence of an approximate matching in any graph of small size. An algorithm for computing a 1/3-approximate matching in any instance is provided. The algorithm uses an analytical result stating that every instance on at most 6 nodes must admit a 1/2-approximate matching. We extend our analysis with a computer-aided approach for larger graphs, indicating that the general method may produce a 2/5-approximate matching. We conjecture that a 1/2-approximate matching exists in any bi-objective instance satisfying the triangle inequality.

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Section: Approximationmentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

Bi-objective matchings with the triangle inequality

Gourvès¹,

Monnot²,

Pascual³

et al. 2017

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

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Optimization Algorithm of Holes Machining Path

Zhang¹

2012

Proceedings of the 2nd International Conference on Electronic and Mechanical Engineering and Information Technology (2012)

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Abstract. Holes machining path planning is of great significance to improve the efficiency and quality of the processing of porous parts. Hole group on the characteristics of size, shape, and location of different multi-bit processing optimization and process optimization, a reasonable choice of the machining path planning method. Verified by an example of this optimization method significantly improved in the holes machining CNC machining efficiency, reduce processing costs. Holes machining path optimization analysis and description of the problem, to clear this problem are essentially multi-point optimization method and process optimization, and the optimization method to determine the selection principle. IntroductionPeople tend to focus on how to improve the processing time for each hole, to the neglect of the tool shift, tool change and other auxiliary time. In fact, the auxiliary time holes machining productivity is greater than the processing time, especially when to be a huge amount of processing hole, especially. The survey shows that the average occupancy of 70% of the total processing time in the movement of the tool and the workpiece during machining. The hole diameter, depth, errors and surface roughness of the base requirements, you need a large number of different tools and tool change operation, a considerable amount of time spent on tool transposition processing and tool change operation. Therefore, how to plan the holes machining path group, in order to shorten the tool mobile path, reducing the number of tool changes and tool change times, holes machining of key issues.However, in generating the NC instruction, the existing PCB automatic programming software used by hole position of the X, Y coordinates to an agreed method of successive arrangement to determine drilling pass sequence. Obviously, the thus generated drilling cutting line is not the optimum route, affect the production efficiency. For those thousands of pieces of annual production, mass production scale to tens of ten thousand PCB dedicated manufacturers, the extent of its impact is considerable. In order to improve processing efficiency, the drilling tool path planning is a very important issue.

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Single Approximation for Biobjective Max TSP

Cited by 2 publications

References 23 publications

Bi-objective matchings with the triangle inequality

Bi-objective matchings with the triangle inequality

Optimization Algorithm of Holes Machining Path

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