In this paper, the performance appropriateness of population-based metaheuristics for immunotherapy protocols is investigated on a comparative basis while the goal is to stimulate the immune system to defend against cancer. For this purpose, genetic algorithm and particle swarm optimization are employed and compared with modern method of Pontryagin’s minimum principle (PMP). To this end, a well-known mathematical model of cell-based cancer immunotherapy is described and examined to formulate the optimal control problem in which the objective is the annihilation of tumour cells by using the minimum amount of cultured immune cells. In this regard, the main aims are: (i) to introduce a single-objective optimization problem and to design the considered metaheuristics in order to appropriately deal with it; (ii) to use the PMP in order to obtain the necessary conditions for optimality, i.e. the governing boundary value problem; (iii) to measure the results obtained by using the proposed metaheuristics against those results obtained by using an indirect approach called forward-backward sweep method; and finally (iv) to produce a set of optimal treatment strategies by formulating the problem in a bi-objective form and demonstrating its advantages over single-objective optimization problem. A set of obtained results conforms the performance capabilities of the considered metaheuristics.

在本文中，比较性地研究了基于人群的启发式方法在免疫治疗方案中的性能适用性，同时目标是刺激免疫系统防御癌症。为此，采用了遗传算法和粒子群算法，并与庞特里亚金最小原理（PMP）的现代方法进行了比较。为此，描述并检查了公知的基于细胞的癌症免疫疗法的数学模型，以制定最佳控制问题，其目的是通过使用最少量的培养的免疫细胞来消灭肿瘤细胞。在这方面，主要目标是：（i）引入单目标优化问题并设计考虑的元启发式方法，以便适当地处理它；（ii）使用PMP以获得最优的必要条件，即控制性边值问题；（iii）衡量使用拟议的元启发式方法获得的结果与通过使用称为前向后向扫描方法的间接方法获得的结果；最后（iv）通过以双目标形式提出问题并展示其相对于单目标优化问题的优势来产生一组最佳处理策略。一组获得的结果符合所考虑的元启发法的性能。最后（iv）通过以双目标形式提出问题并展示其相对于单目标优化问题的优势来产生一组最佳处理策略。一组获得的结果符合所考虑的元启发法的性能。最后（iv）通过提出双目标形式的问题并展示其相对于单目标优化问题的优势来产生一组最佳处理策略。一组获得的结果符合所考虑的元启发法的性能。