Naturally, the 0-1MKP is a generalized version of the 0-1KP. For example, the constraints can be a weight besides a size. In the case of the 0-1MKP, the number of capacity constraints is more than one. The objective is to find an assignment that maximizes the total profit not exceeding the given capacity. The knapsack has a certain capacity for size. In the 0-1KP, given a set of objects, each object that can go into the knapsack has a size and a profit. It can be considered as an extended version of the well-known 0-1 knapsack problem (0-1KP). The 0-1 multidimensional knapsack problem (0-1MKP) is an NP-hard problem, but not strongly NP-hard. The knapsack problems have a number of applications in various fields, for example, cryptography, economy, network, and so forth. We show the efficiency of the proposed method by the experiments on well-known benchmark data. So we use a memetic algorithm to find the optimal Lagrange multipliers. Potentiality of using a memetic algorithm. Through empirical investigation of Lagrangian space, we can see the However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. Our method is based on Lagrangian relaxation. We tackle the problem using duality concept, differently from traditional approaches.
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No commercial reproduction, distribution, display or performance rights in this work are provided.We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. On Measurement and Modeling of Computer Systems (SIGMETRICS ’21Ībstracts), June 14–18, 2021, Virtual Event, China. In Abstract Proceedings of the 2021 ACM SIGMETRICS / International Conference Knapsack Problem with Application to Electric Vehicle Charging. Competitive Algorithms for the Online Multiple Online knapsack problems one-way trading online algorithms Įlectric vehicle charging online primal-dual analysisīo Sun, Ali Zeynali, Tongxin Li, Mohammad Hajiesmaili, Adam Wierman,Īnd Danny H.K.
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Xiaoqi Tan (University of Toronto) for insightful and useful discussions. Adam Wierman acknowledges the support received from NSF grants (AitF-1637598 and NSF CNS-1518941). Tongxin Li’s research is supported by NSF grants (CPS ECCS 1932611 and CPS ECCS 1739355). Ali Zeynali and Mohammad Hajiesmaili’s research is supported by NSF CNS-1908298 and CAREER 2045641. Tsang acknowledge the support received from the Hong Kong Research Grant Council (RGC) General Research Fund (Project 16202619 and Project 16211220). © 2021 Copyright held by the owner/author(s).īo Sun and Danny H.K.
#Multiple knapsack problem full version#
Finally, in the full version of this paper, we illustrate the proposed algorithm via trace-based experiments of EV charging. Moreover, our analysis provides a novel approach to online algorithm design based on an instance-dependent primal-dual analysis that connects the identification of worst-case instances to the design of algorithms.
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We introduce a new algorithm that achieves a competitive ratio within an additive factor of the best achievable competitive ratios for the general problem and matches or improves upon the best-known competitive ratio for special cases in the knapsack and one-way trading literatures. This problem generalizes variations of the knapsack problem and of the one-way trading problem that have previously been treated separately, and additionally finds application to the real-time control of electric vehicle (EV) charging. We introduce and study a general version of the fractional online knapsack problem with multiple knapsacks, heterogeneous constraints on which items can be assigned to which knapsack, and rate-limiting constraints on the assignment of items to knapsacks.