429 research outputs found
Packing and Covering with Non-Piercing Regions
In this paper, we design the first polynomial time approximation schemes for the Set Cover and Dominating Set problems when the underlying sets are non-piercing regions (which include pseudodisks). We show that the local
search algorithm that yields PTASs when the regions are disks [Aschner/Katz/Morgenstern/Yuditsky, WALCOM 2013; Gibson/Pirwani, 2005; Mustafa/Raman/Ray, 2015] can be extended to work for non-piercing regions. While such an extension is intuitive and natural, attempts to settle this question have failed even for pseudodisks. The techniques used for analysis when the regions are disks rely heavily on the underlying geometry, and do not extend to topologically defined settings such as pseudodisks. In order to prove our results, we introduce novel techniques that we believe will find applications in other problems.
We then consider the Capacitated Region Packing problem. Here, the input consists of a set of points with capacities, and a set of regions. The objective is to pick a maximum cardinality subset of regions so that no point is covered by more regions than its capacity. We show that this problem admits a PTAS when the regions are k-admissible regions (pseudodisks are 2-admissible), and the capacities are bounded. Our result settles a conjecture of Har-Peled (see Conclusion of [Har-Peled, SoCG 2014]) in the affirmative. The conjecture was for a weaker version of the problem, namely when the regions are pseudodisks, the capacities are uniform, and the point set consists of all points in the plane.
Finally, we consider the Capacitated Point Packing problem. In this setting, the regions have capacities, and our
objective is to find a maximum cardinality subset of points such that no region has more points than its capacity. We show that this problem admits a PTAS when the capacity is unity, extending one of the results of Ene et al. [Ene/Har-Peled/Raichel, SoCG 2012]
A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms
Parameterization and approximation are two popular ways of coping with
NP-hard problems. More recently, the two have also been combined to derive many
interesting results. We survey developments in the area both from the
algorithmic and hardness perspectives, with emphasis on new techniques and
potential future research directions
Network design decisions in supply chain planning
Structuring global supply chain networks is a complex decision-making process. The typical inputs to such a process consist of a set of customer zones to serve, a set of products to be manufactured and distributed, demand projections for the different customer zones, and information about future conditions, costs (e.g. for production and transportation) and resources (e.g. capacities, available raw materials). Given the above inputs, companies have to decide where to locate new service facilities (e.g. plants, warehouses), how to allocate procurement and production activities to the variousmanufacturing facilities, and how to manage the transportation of products through the supply chain network in order to satisfy customer demands. We propose a mathematical modelling framework capturing many practical aspects of network design problems simultaneously. For problems of reasonable size we report on computational experience with standard mathematical programming software. The discussion is extended with other decisions required by many real-life applications in strategic supply chain planning. In particular, the multi-period nature of some decisions is addressed by a more comprehensivemodel, which is solved by a specially tailored heuristic approach. The numerical results suggest that the solution procedure can identify high quality solutions within reasonable computational time
Experimental Evaluation of Meta-Heuristics for Multi-Objective Capacitated Multiple Allocation Hub Location Problem
Multi-objective capacitated multiple allocation hub location problem (MOCMAHLP) is a variation of classic
hub location problem, which deals with network design, considering both the number and the location
of the hubs and the connections between hubs and spokes, as well as routing of flow on the network.
In this study, we offer two meta-heuristic approaches based on the non-dominated sorting genetic algorithm
(NSGA-II) and archived multi-objective simulated annealing method (AMOSA) to solve
MOCMAHLP. We attuned AMOSA based approach to obtain feasible solutions for the problem and developed
five different neighborhood operators in this approach. Moreover, for NSGA-II based approach, we
developed two novel problem-specific mutation operators. To statistically analyze the behavior of both
algorithms, we conducted experiments on two well-known data sets, namely Turkish and Australian
Post (AP). Hypervolume indicator is used as the performance metric to measure the effectiveness of both
approaches on the given data sets. In the experimental study, thorough tests are conducted to fine-tune
the proposed mutation types for NSGA-II and proposed neighborhood operators for AMOSA. Fine-tuning
tests reveal that for NSGA-II, mutation probability does not have a real effect on Turkish data set, whereas
lower mutation probabilities are slightly better for AP data set. Moreover, among the AMOSA based
neighborhood operators, the one which adds/removes a specific number of links according to temperature
(NS-5) performs better than the others for both data sets. After analyzing different operators for both
algorithms, a comparison between our NSGA-II based and AMOSA based approaches is performed with
the best settings. As a result, we conclude that both of our algorithms are able to find feasible solutions
of the problem. Moreover, NSGA-II performs better for larger, whereas AMOSA performs better for smaller
size networks
An improved Ant Colony System for the Sequential Ordering Problem
It is not rare that the performance of one metaheuristic algorithm can be
improved by incorporating ideas taken from another. In this article we present
how Simulated Annealing (SA) can be used to improve the efficiency of the Ant
Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering
Problem (SOP). Moreover, we show how the very same ideas can be applied to
improve the convergence of a dedicated local search, i.e. the SOP-3-exchange
algorithm. A statistical analysis of the proposed algorithms both in terms of
finding suitable parameter values and the quality of the generated solutions is
presented based on a series of computational experiments conducted on SOP
instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed
ACS-SA and EACS-SA algorithms often generate solutions of better quality than
the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with
the proposed SOP-3-exchange-SA local search was able to find 10 new best
solutions for the SOP instances from the SOPLIB2006 repository, thus improving
the state-of-the-art results as known from the literature. Overall, the best
known or improved solutions were found in 41 out of 48 cases.Comment: 30 pages, 8 tables, 11 figure
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