Heuristic computational intelligence techniques are widely used in combinatorial optimization problems, essentially in large size configurations. Bio-inspired heuristics such as PSO, FA or FPA showed their capacities to solve such problems. Bi-heuristic optimization consists of using a couple of techniques and a collaboration mechanism. This paper reviews the major contributions in solving TSP with bi-heuristics and presents a new hybridization scheme based on FPA, ACO with Ls, ant supervised by flower pollination with local search, ASFPA-Ls; as well as the impact of social and cognitive PSO for the ant supervised by PSO with local search, ASPSO-Ls. AS-chaotic-PSO-Ls which stands for ant supervised by chaotic PSO local search is also investigated. The meta-heuristic algorithms (FPA, PSO or chaotic PSO) and ant colony optimization are used with a hierarchical collaboration schema in addition to a local search mechanism. In this work, the local search strategy, Ls, used is the 2-opt method; the proposals are called, respectively, ASFPA-Ls, cognitive ant supervised by PSO with local search, Co-ASPSO-Ls, social-ASPSO-Ls and AS-chaotic-PSO-Ls; where ACO is coupled with a local search heuristic mechanism called 2-opt, and a set of meta-heuristics, FA, FPA and PSO asked to adapt ACO parameters while running. Comparative experimental investigations are conducted using the TSP test bench. Proposed hybridizations attended fair solutions for the TSP problems used in the experimental investigations including berlin52, St70, eil76, rat 99, eil101, KroA100, Ch150 and kroA200. A good balance performance/time is found with the social ant supervised by PSO with local search, So-ASPSO-Ls. The cognitive ant supervised by PSO with local search, Co-ASPSO-Ls comes in the second position in terms of time effectiveness with close performances to AS-chaoticPS0-LS, all proposed approaches returned low rate errors or BKS for used test benches: berlin52, st70, eil76, rat99, kroA100 and kroA200.
