## 1 Introduction
Very popular approaches to multiobjective optimization are the weighted sum method or taking only one criterion into account, while imposing other criteria as constraints. Such methods are handy to use, because they do not require modification of the optimization algorithm (the single-objective optimization algorithm can be used). Unfortunately, they have significant limitations, which reduce the scope of their application, such as:  
Figure 1: Chevron type microactuator: (**a**) typical geometry of the microactuator; (**b**) deformation and map of equivalent stress in the microactuator. * Difficulties in selection of the balance between criteria before optimization, having no knowledge of the considered problem;
* Certain assumptions imposed before optimization can lead to improper or unphysical results;
* Performing a single optimization task gives only one solution;
* The impossibility to obtain solutions for non-convex Pareto fronts. Population-based approaches, such as metaheuristic algorithms, are free from the disadvantages mentioned above. Moreover, because such algorithms process not one, but a set of solutions, and the result of multicriteria optimization is a set of optimal solutions in the sense of Pareto, they are an ideal tool for these type of tasks. A group of papers are devoted to the shape optimization of the different types of the thermal actuators: [PERSON] et al., [PERSON] et al. and [PERSON] perform optimization of the characteristic dimension of the laterally driven microactuator [4; 5; 6]. [PERSON] et al. proposed optimization of the chevron type microactuator, assuming nonuniform cross section of the beams [7]. The process of optimal design can be realized assuming the variant analysis [8; 9] or by means of different optimization methods [10]. Some papers are devoted to the topological optimization, which allows finding desired shape of the actuator with respect to applied restriction and criteria. Usually, the optimal shape of the actuator consists of a set of variously shaped arms in a number of geometrical configurations. [PERSON], [PERSON] et al. and [PERSON] et al. demonstrated maximizing the output displacement in a given direction of the actuator by means of topology optimization, obtaining quite complicated optimal shapes of the actuator [11; 12; 13]. [PERSON] et al. and [PERSON] et al. demonstrated the topological optimization for thermoelectric actuators aided by level-set methods [14; 15]. The result of topological optimization can be a good tip for the designer on what the best configuration of the arms is with regard to the considered criterion; however, very complicated shapes (common for topological optimization) can be an obstacle in the design process of practical shapes consisting of repetitive pairs of arms (which is needed for aggregation of the actuation force in the central shaft by multiple arms). [PERSON] and [PERSON] present topological optimization for the rotary thermal actuators [16]. For the majority of cases, a process of finding an optimal design of thermal actuators is dealt with as a single optimization problem. Multiobjective optimization methods are not popular in the design of electrothermal actuators; however, some papers have been devoted to it. [PERSON] et al. solved the bi-objective optimization problem of a U-shaped actuator by means of the NSGAII algorithm (non-dominated, sorting genetic algorithm) [17]. It is a well-known fact that NSGAII algorithm (probably the most popular multiobjective optimization algorithm used in diverse engineering disciplines) does not work well for more than three criteria (practically 2). For the other types of the actuators (e.g., piezoelectric and electrostatic) multiobjective optimization problems generally also deal with the simultaneous consideration of at most two criteria. A review of the literature allows us to claim a lack of research that incorporates many criteria into the optimal design of thermal actuators. Moreover, shape optimization tasks are devoted to the actuators with simplified geometry of the arms.