200 research outputs found

    Balanced Combinations of Solutions in Multi-Objective Optimization

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    For every list of integers x_1, ..., x_m there is some j such that x_1 + ... + x_j - x_{j+1} - ... - x_m \approx 0. So the list can be nearly balanced and for this we only need one alternation between addition and subtraction. But what if the x_i are k-dimensional integer vectors? Using results from topological degree theory we show that balancing is still possible, now with k alternations. This result is useful in multi-objective optimization, as it allows a polynomial-time computable balance of two alternatives with conflicting costs. The application to two multi-objective optimization problems yields the following results: - A randomized 1/2-approximation for multi-objective maximum asymmetric traveling salesman, which improves and simplifies the best known approximation for this problem. - A deterministic 1/2-approximation for multi-objective maximum weighted satisfiability

    Approximation Algorithms for Multi-Criteria Traveling Salesman Problems

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    In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal solution. Instead, the aim is to compute a so-called Pareto curve of solutions. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We design a deterministic polynomial-time algorithm for multi-criteria g-metric STSP that computes (min{1 +g, 2g^2/(2g^2 -2g +1)} + eps)-approximate Pareto curves for all 1/2<=g<=1. In particular, we obtain a (2+eps)-approximation for multi-criteria metric STSP. We also present two randomized approximation algorithms for multi-criteria g-metric STSP that achieve approximation ratios of (2g^3 +2g^2)/(3g^2 -2g +1) + eps and (1 +g)/(1 +3g -4g^2) + eps, respectively. Moreover, we present randomized approximation algorithms for multi-criteria g-metric ATSP (ratio 1/2 + g^3/(1 -3g^2) + eps) for g < 1/sqrt(3)), STSP with weights 1 and 2 (ratio 4/3) and ATSP with weights 1 and 2 (ratio 3/2). To do this, we design randomized approximation schemes for multi-criteria cycle cover and graph factor problems.Comment: To appear in Algorithmica. A preliminary version has been presented at the 4th Workshop on Approximation and Online Algorithms (WAOA 2006

    Multi-criteria TSP:Min and max combined

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    We present randomized approximation algorithms for multi-criteria traveling salesman problems (TSP), where some objective functions should be minimized while others should be maximized. For the symmetric multi-criteria TSP (STSP), we present an algorithm that computes (2/3,3+ε3+\varepsilon)-approximate Pareto curves. Here, the first parameter is the approximation ratio for the objectives that should be maximized, and the second parameter is the ratio for the objectives that should be minimized. For the asymmetric multi-criteria TSP (ATSP), we obtain an approximation performance of (1/2, log2n+ε\log_2 n + \varepsilon)

    Toward sustainable data centers: a comprehensive energy management strategy

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    Data centers are major contributors to the emission of carbon dioxide to the atmosphere, and this contribution is expected to increase in the following years. This has encouraged the development of techniques to reduce the energy consumption and the environmental footprint of data centers. Whereas some of these techniques have succeeded to reduce the energy consumption of the hardware equipment of data centers (including IT, cooling, and power supply systems), we claim that sustainable data centers will be only possible if the problem is faced by means of a holistic approach that includes not only the aforementioned techniques but also intelligent and unifying solutions that enable a synergistic and energy-aware management of data centers. In this paper, we propose a comprehensive strategy to reduce the carbon footprint of data centers that uses the energy as a driver of their management procedures. In addition, we present a holistic management architecture for sustainable data centers that implements the aforementioned strategy, and we propose design guidelines to accomplish each step of the proposed strategy, referring to related achievements and enumerating the main challenges that must be still solved.Peer ReviewedPostprint (author's final draft
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