This paper presents two novel bio-inspired particle swarm optimisation (PSO) variants: biased eavesdropping PSO (BEPSO) and altruistic heterogeneous PSO (AHPSO). These algorithms are inspired by types of group behaviour found in nature that have not previously been exploited in search algorithms. The primary search behaviour of the BEPSO algorithm is inspired by eavesdropping behaviour observed in nature coupled with a cognitive bias mechanism that enables particles to make decisions on cooperation. The second algorithm, AHPSO, conceptualises particles in the swarm as energy-driven agents with bio-inspired altruistic behaviour which allows the formation of lending-borrowing relationships. The mechanisms underlying these algorithms provide new approaches to maintaining swarm diversity which contributes to preventing premature convergence. The new algorithms were tested on the 30, 50 and 100-dimensional CEC'13, CEC'14 and CEC'17 test suites, and various constrained real-world optimisation problems, against 13 well-known PSO variants and the CEC competition winner, differential evolution algorithm L-SHADE. The experimental results show that both algorithms, BEPSO and AHPSO, provide very competitive performance on the unconstrained test suites and the constrained real-world problems. They were significantly better than most other PSO variant on most problem sets and no other comparator algorithm was significantly better than either of them on any of the 50 and 100-d problem sets.