In this research, we propose an intelligent decision support system for acute lymphoblastic leukaemia (ALL) diagnosis using microscopic images. Two Bare-bones Particle Swarm Optimization (BBPSO) algorithms are proposed to identify the most significant discriminative characteristics of healthy and blast cells to enable efficient ALL classification. The first BBPSO variant incorporates accelerated chaotic search mechanisms of food chasing and enemy avoidance to diversify the search and mitigate the premature convergence of the original BBPSO algorithm. The second BBPSO variant exhibits both of the abovementioned new search mechanisms in a subswarm-based search. Evaluated with the ALL-IDB2 database, both proposed algorithms achieve superior geometric mean performances of 94.94% and 96.25%, respectively, and outperform other metaheuristic search and related methods significantly for ALL classification.