Topic
Greedy algorithm
About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.
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TL;DR: In this article, the authors consider the problem of approximating a given element f from a Hilbert space by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory.
Abstract: We consider the problem of approximating a given element f from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. For all these algorithms, we prove convergence results for a variety of function classes and not simply those that are related to the convex hull of the dictionary. We then show how these bounds for convergence rates lead to a new theory for the performance of greedy algorithms in learning. In particular, we build upon the results in [IEEE Trans. Inform. Theory 42 (1996) 2118–2132] to construct learning algorithms based on greedy approximations which are universally consistent and provide provable convergence rates for large classes of functions. The use of greedy algorithms in the context of learning is very appealing since it greatly reduces the computational burden when compared with standard model selection using general dictionaries.
239 citations
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TL;DR: Numerical simulations show that the proposed distributed framework for the demand response based on cost minimization will result in lower cost for the consumers, lower generation costs for the utility companies, lower peak load, and lower load fluctuations.
Abstract: Demand side management encourages the users in a smart grid to shift their electricity consumption in response to varying electricity prices. In this paper, we propose a distributed framework for the demand response based on cost minimization. Each user in the system will find an optimal start time and operating mode for the appliances in response to the varying electricity prices. We model the cost function for each user and the constraints for the appliances. We then propose an approximate greedy iterative algorithm that can be employed by each user to schedule appliances. In the proposed algorithm, each user requires only the knowledge of the price of the electricity, which depends on the aggregated load of other users, instead of the load profiles of individual users. In order for the users to coordinate with each other, we introduce a penalty term in the cost function, which penalizes large changes in the scheduling between successive iterations. Numerical simulations show that our optimization method will result in lower cost for the consumers, lower generation costs for the utility companies, lower peak load, and lower load fluctuations.
238 citations
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TL;DR: In this article, the authors formalize the problem as a mathematical program where the objective of the firm is either profit or total welfare, and they develop a new greedy heuristic for the profit problem, and its application to simulated problems shows that it too runs quickly, and with better performance than various alternatives and previously published heuristics.
Abstract: Designing and pricing a product-line is the very essence of every business. In recent years quantitative methods to assist managers in this task have been gaining in popularity. Conjoint analysis is already widely used to measure preferences for different product profiles, and build market simulation models. In the last few years several papers have been published that suggest how to optimally choose a product-line based on such data.
We formalize this problem as a mathematical program where the objective of the firm is either profit or total welfare. Unlike alternative published approaches, we introduce fixed and variable costs for each product profile. The number of products to be introduced is endogenously determined on the basis of their desirability, fixed and variable costs, and in the case of profits, their cannibalization effect on other products. While the problem is difficult NP-complete, we show that the maximum welfare problem is equivalent to the uncapacitated plant location problem, which can be solved very efficiently using the greedy interchange heuristic. Based on past published experience with this problem, and on simulations we perform, we show that optimal or near optimal solutions are obtained in seconds for large problems. We develop a new greedy heuristic for the profit problem, and its application to simulated problems shows that it too runs quickly, and with better performance than various alternatives and previously published heuristics. We also show how the methodology can be applied, taking existing products of both the firm and the competition into account.
237 citations
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TL;DR: An efficient genetic algorithm (GA) to solve the traveling salesman problem with precedence constraints is presented and the key concept is a topological sort (TS), which is defined as an ordering of vertices in a directed graph.
237 citations
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TL;DR: This paper forms the energy consumption minimization problem as a mixed interger nonlinear programming (MINLP) problem, which is subject to specific application latency constraints, and proposes a reformulation-linearization-technique-based Branch-and-Bound (RLTBB) method, which can obtain the optimal result or a suboptimal result by setting the solving accuracy.
Abstract: Mobile edge computing (MEC) providing information technology and cloud-computing capabilities within the radio access network is an emerging technique in fifth-generation networks MEC can extend the computational capacity of smart mobile devices (SMDs) and economize SMDs’ energy consumption by migrating the computation-intensive task to the MEC server In this paper, we consider a multi-mobile-users MEC system, where multiple SMDs ask for computation offloading to a MEC server In order to minimize the energy consumption on SMDs, we jointly optimize the offloading selection, radio resource allocation, and computational resource allocation coordinately We formulate the energy consumption minimization problem as a mixed interger nonlinear programming (MINLP) problem, which is subject to specific application latency constraints In order to solve the problem, we propose a reformulation-linearization-technique-based Branch-and-Bound (RLTBB) method, which can obtain the optimal result or a suboptimal result by setting the solving accuracy Considering the complexity of RTLBB cannot be guaranteed, we further design a Gini coefficient-based greedy heuristic (GCGH) to solve the MINLP problem in polynomial complexity by degrading the MINLP problem into the convex problem Many simulation results demonstrate the energy saving enhancements of RLTBB and GCGH
235 citations