Binary bacterial foraging optimization for 0/1 knapsack problem

Knapsack problem is famous NP-complete problem where one has to maximize the benefit of objects in a knapsack without exceeding its capacity. In this paper, a binary bacterial foraging optimization (BBFO) is proposed to find solutions of 0/1 knapsack problems. The original BFO chemotaxis equation is modified to operate in discrete space by using a mapping function, where some new variables and parameter, i.e., binary matrix y, logistic transformation S, and limiting transformation L is built to transform the bacterial position to a binary matrix. By using this schema, the proposed BBFO model can also be easily applied in other discrete problem solving. To further validate the efficiency of the BFO-based approach, an improved version BFO named BFO with linear decreasing chemotaxis step (BFO-LDC) is used to evaluate on six different instances. Comparisons with particle swarm optimization (PSO) and original BFO are presented and discussed.