TTBCA+: An Enhanced Besiege and Conquer Algorithm with Three-Three Tactics and Collision Theory for Complex Optimization Problems

Besiege and Conquer Algorithm (BCA) is a swarm intelligence algorithm proposed in 2025 based on tactical concepts. However, its besiege and conquer strategies have some problems, such as insufficient diversity and local stagnation. To solve the above problems, this paper proposes an Enhanced Besiege and Conquer Algorithm with Three-Three Tactics and Collision Theory, referred to as TTBCA+. TTBCA+ has four innovations. Firstly, a three-three allocation mechanism of battlefield and roles is proposed to enhance its besiege capability; secondly, a three-three deployment mechanism of soldiers is proposed to enhance its conquer capability; thirdly, the balance factor between exploration and exploitation is modified for three-three tactics implementation; finally, the collision mechanism from collision theory is introduced to deal with soldiers beyond the search space. The performance of the proposed TTBCA+ is verified at the IEEE CEC 2017 and IEEE CEC 2022 benchmark functions, compared with 13 swarm intelligence algorithms, including classical algorithms, well-known algorithms such as JADE, lshade_rsp, AGWO, and recent 5 years algorithms, such as BCA, HOA, PLO, CFOA, HLOA, DBO, BOA. Meanwhile, the proposed algorithms are applied to two practical complex optimization problems. The results show that TTBCA+ effectively solved the limitations in BCA, and it is superior to other compared algorithms.