Zero-One Knapsack Problem

Abstract

The zero-one knapsack problem has the form

$$ {\text{maximize}}\;\sum\limits_{{j = 1}}^{n} {{{c}_{j}}{{x}_{j}}} $$

$$ subject{\mkern 1mu} to\;\sum\limits_{{j = 1}}^{n} {{{a}_{j}}{{x}_{j}}b} $$

$$ {{x}_{{ji}}} = 0\;or\;1\;\left( {j = 1,2, \ldots ,n} \right) $$

such that a_j, b and c_j are nonnegative numbers.