On a model-free meta-heuristic approach for unconstrained optimization

The efficacy of meta-heuristic algorithms has been demonstrated in solving unconstrained optimization problems. Inspired by the food foraging behavior of beetles, we propose herein a model-free meta-heuristic optimization algorithm, referred to as the Beetle Antennae Search-Bellwether Swarm, which incorporates the schemes of adaptive antenna fiber length and direction vector. A joint annealing-heating scheme along with the re-initialization mechanism is proposed such that each antenna fiber length could simultaneously gradually decrease or increase in different circumstances. We also propose to adapt each individual antenna fiber length based on the best smell perception direction (bellwether). The proposed schemes of adaptive antenna fiber length yield the algorithm almost insusceptible to different initial antenna fiber lengths for a relatively large range of initial antenna fiber lengths. The softmax combiner is leveraged to obtain the direction vector such that the beetle would be steered to step toward the new randomly combined direction and arrive at a candidate position. The beetle position is further updated by evaluating whether the candidate position is conducive to minimizing the objective function. The illustrative simulations demonstrate the fast initial convergence, cost-effectiveness and feasibility of the proposed algorithm.