Fractional Combinatorial Optimization

Radzik, Tomasz

doi:10.1007/978-1-4419-7997-1_62

Cited by 18 publications

(40 citation statements)

References 51 publications

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“…In order to obtain feasibility (optimality in the dual) the intervals between these bounds should contain the right-hand sides wj. The following is proved in l u [17]" If wj (-5) <_ wj < wj (~), Vj, then c~ is optimal in the LP relaxation of SPLPE.…”

Section: The Dual Ascent and Adjustment Methodmentioning

confidence: 99%

“…As the model is fairly new, one cannot find many solution methods proposed in the literature. A dual ascent procedure for this problem has been developed, see [17]. Another method, based on the same dual, is Lagrangian relaxation and subgradient optimization, investigated in [18].…”

Section: _ [ 1 If a Plant At Location I Is Openedmentioning

confidence: 99%

“…In these cases the problem is then completely solved by simply solving the primal subproblem, (PS), once. In computational tests in [16], [17], [18] and [13], this occurs when -~ is smaller than 0.0001 or larger than 0.1, while for ~ -0.01 the differences to the solutions mentioned above are the largest.…”

Section: (Z)llmentioning

confidence: 99%

“…FRAT (facilities relative allocation technique) [21] assumes that all the facilities have equal areas. TSP (terminal sampling procedure) [17] carries out the interchange of the placement, in the block plan, of pairs of facilities on a selective basis. The program has the ability to use improved block plans as input and to fix the placement of certain facilities.…”

mentioning

confidence: 99%

“…SPACECRAFT [20] is an extension of CRAFT to multifloor FL problems. See [17] for a perturbation scheme, and [18] for a new FL system which accommodates a variety of types of spaces, including solid, circulation, and empty. A multicriteria objective function involves transportation cost, REL chart scores, the percentage of unused area, and block plan structure.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Bi-objective assignment problem; Decision support systems with multiple criteria; Estimating data for multicriteria decision making problems: Optimization techniques; Financial applications of multicriteria analysis; Multi-objective combinatorial optimization; Multi-objective integer linear programming; Multi-objective optimization and decision support systems; Multi-objective optimization: Interaction of design and control; Multi-objective optimization: Interactive methods for preference value functions;

Słowiński¹

2001

Encyclopedia of Optimization

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F FACILITIES LAYOUT PROBLEMS, FLP Facilities layout (FL) is concerned with the placement, relative to one another, of the facilities of some physical system. This area differs from planar multifacilities location (MFL; cf. also Multifacility and r e s t r i c t e d location problems) in that in FL the facilities are all assumed to have a significant physical area and are to be placed in a finite total area which represents their physical system. In MFL the facilities are assumed to be dimensionless points.The aim of FL is to produce a scale plan (in some scenarios called a block plan) of the physical system to be designed. The plan depicts the facilities of the system (each one having its given area and shape) laid out relative to each other. An example of a simple block plan is shown in Fig. 1.

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Section: The Dual Ascent and Adjustment Methodmentioning

confidence: 99%

Section: _ [ 1 If a Plant At Location I Is Openedmentioning

confidence: 99%

Section: (Z)llmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Bi-objective assignment problem; Decision support systems with multiple criteria; Estimating data for multicriteria decision making problems: Optimization techniques; Financial applications of multicriteria analysis; Multi-objective combinatorial optimization; Multi-objective integer linear programming; Multi-objective optimization and decision support systems; Multi-objective optimization: Interaction of design and control; Multi-objective optimization: Interactive methods for preference value functions;

Słowiński¹

2001

Encyclopedia of Optimization

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On maximum ratio clique relaxations

et al. 2022

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This article introduces and studies two clique relaxation models with fractional objectives: the maximum ratio s$$ s $$‐plex problem and the maximum ratio s$$ s $$‐defective clique problem. The decision version of each problem is shown to be strongly NP$$ NP $$‐complete; we also discuss some related computational complexity issues. The base optimization models are single‐ratio fractional 0‐1 problems. We describe two general types of solution methods: the first one is based on mixed‐integer linear programs (MILPs) obtained by linearizing the original nonlinear 0‐1 models; the other one exploits parametric methods (namely, a binary search and Newton's method) that solve MILPs in an iterative manner. For the proposed MILPs, we derive valid inequalities that are shown to substantially improve the performance of an off‐the‐shelf MILP solver. Finally, the considered solution approaches are compared via extensive numerical experiments using a set of artificially generated and real‐life network instances.

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Faster Algorithms for Security Games on Matroids

Baı̈ou

Barahona

2018

Algorithmica

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Fractional Combinatorial Optimization

Cited by 18 publications

References 51 publications

On maximum ratio clique relaxations

Faster Algorithms for Security Games on Matroids

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