  Non-polynomial hard (NP-hard) problems are challenging because no
polynomial-time algorithm has yet been discovered to solve them in polynomial
time. The Bacteria Foraging Optimization (BFO) algorithm is one of the
metaheuristics algorithms that is mostly used for NP-hard problems. BFO is
inspired by the behavior of the bacteria foraging such as Escherichia coli
(E-coli). The aim of BFO is to eliminate those bacteria that have weak foraging
properties and maintain those bacteria that have breakthrough foraging
properties toward the optimum. Despite the strength of this algorithm, most of
the problems reaching optimal solutions are time-demanding or impossible. In
this paper, we modified single objective BFO by adding a mutation operator and
multi-objective BFO (MOBFO) by adding mutation and crossover from genetic
algorithm operators to update the solutions in each generation, and local tabu
search algorithm to reach the local optimum solution. Additionally, we used a
fast nondominated sort algorithm in MOBFO to find the best-nondominated
solutions in each generation. We evaluated the performance of the proposed
algorithms through a number of single and multi-objective Quadratic Assignment
Problem (QAP) instances. The experimental results show that our approaches
outperform some previous optimization algorithms in both convergent and
divergent solutions.
