Using PSO and SA for optimizing the retardance in dextran-citrate coated ferrofluids

Double-layer coating of dextran and citrate (DC) on the Fe₃O₄ (magnetite) ferrofluids (FFs) has been conducted for biomedical applications such as hyperthermia and magnetic resonance imaging. The magnetic retardance of DC-coated FFs was measured, and the magnetic heating effect was investigated previously. An experiment was conducted using the uniform design method; we enabled the formula to fit with experimental data on retardance through the stepwise regression analysis. Two intelligent search methods, particle swarm optimization (PSO) and simulated annealing (SA), were used to find the maximum retardance. The optimized parametric combinations were decided as [0.0750, 75.7945, 0.3225, 0.6500] and [0.0750, 75.844, 0.323, 0.65], respectively, denoting the Fe₃O₄ concentration, the coating temperature, the mass of citrate and dextran. The corresponding maximum retardances were 119.6576° and 119.6558°. The PSO algorithm was more effective and accessible than the SA algorithm in optimizing retardance. As for the hybrid optimization selected for solving complex problems, such as PSO was used to find a near-global solution, and SA was then used for searching for a global solution, the parameter fine-tuning of SA affects the final result. A hybrid metaheuristic algorithm with the local gradient-based sequential quadratic programming (SQP) algorithm is used to find the global solution because of its effectiveness and convergence speed in research. Overall, we provide some two-level hybrid optimizations for the global exploration of the retardance of DC-coated FFs. The hybrid algorithms, including PSO-SA, PSO-SQP, or SA-SQP, allow us to explore a more accurate global solution with high performance.