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2001•Electronics and Communications in Japan (Part III Fundamental Electronic Science)Requires access

Calculating the upper bound of the Multiple‐Choice Knapsack Problem

Yuji Nakagawa, Masachika Kitao, Mitsuhiro Tsuji, Yoshinobu Teraoka

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Abstract

Abstract An upper bound or a lower bound of the Multiple‐Choice Knapsack Problem can be calculated by solving LP relaxation. In 1979, Sinha and Zoltners proposed a branch‐and‐bound algorithm for solving the Multiple‐Choice Knapsack Problem, and provided a method to obtain the strict upper bound. In this paper, we propose a new calculation method to obtain a stricter upper bound than the upper bound of Sinha–Zoltners and compare the results of the two methods. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 22–27, 2001

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Abstract An upper bound or a lower bound of the Multiple‐Choice Knapsack Problem can be calculated by solving LP relaxation. In 1979, Sinha and Zoltners proposed a branch‐and‐bound algorithm for solving the Multiple‐Choice Knapsack Problem, and provided a method to obtain the strict upper bound. In this paper, we propose a new calculation method to obtain a stricter upper bound than the upper bound of Sinha–Zoltners and compare the results of the two methods. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 22–27, 2001

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Available abstract

Abstract An upper bound or a lower bound of the Multiple‐Choice Knapsack Problem can be calculated by solving LP relaxation. In 1979, Sinha and Zoltners proposed a branch‐and‐bound algorithm for solving the Multiple‐Choice Knapsack Problem, and provided a method to obtain the strict upper bound. In this paper, we propose a new calculation method to obtain a stricter upper bound than the upper bound of Sinha–Zoltners and compare the results of the two methods. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 22–27, 2001

Key concepts: Knapsack problem, Upper and lower bounds, Mathematics, Relaxation (psychology), Branch and bound, Mathematical optimization, Combinatorics, Mathematical analysis

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