## 1 Introduction
More sophisticated shape of the arms in the optimal design has been considered in the case of topological optimization, but the disadvantages of such an approach have been described above. Furthermore, for the topological optimization, only single objective optimization tasks have been considered. Bi-objective optimization of the U-beam actuator has been presented in [18], whereas in the present paper, a novel and efficient method of multiobjective optimization for higher number of criteria is proposed. The proposal combines an algorithm based on artificial immune systems (AIS) and elements of game theory (GT); it has been developed and implemented by authors. Game theory deals with the analysis of conflict situations and can be applied to problems in fields such as economics, psychology and recently, engineering as well. The work which is assumed to be the beginning of game theory is accredited to [PERSON] and [PERSON] [19]. In game theory, the conflict situations are named games. They have several essential features:  
* Number of players is known and finite;* Full game rules are set;
* Payoffs are determined by payoff functions, which depend on strategies chosen by players. A strategy is a complete description of a player's activity in all situations. Ideas of multiobjective optimization (MOO) and game theory have several common features. The game theory problems were considered applying multiobjective optimization concepts. MOO solutions which best take into account all criteria (so called non-dominated solutions) are sought, and in game theory, players are looking for best strategies. Finally, in game theory we try to find equilibrium and in MOO we try to find a set of solutions optimal in a Pareto sense. Several papers which considered these approaches were published [20; 21; 22; 23; 24]. Artificial immune systems, on the other hand, are one of the systems which belong to a wide range of methods of computational intelligence. The most developed algorithms are: immune networks, clonal selection and negative selection. Clonal selection, used in this present paper, is dedicated to solving optimization problems: fitness functions correspond to the affinities of antibodies to antigens. Solutions in a population are represented by antibodies. Each antibody is cloned several times like in the real immune system. The number of clones is proportional to an antibody's affinity to antigen (its value of the fitness function) and then the hypermutation is applied. These ideas are extended with the suppression that takes place [25]. Immune systems and algorithms succeed in their application to global and multimodal optimization [26]. There are several adaptations and modifications of the clonal selection algorithm applied to problems with many criteria [27; 28; 29; 30; 31]. Artificial immune systems, compared to the population-based metaheuristic algorithms, seem to be predisposed to solve multiobjective problems. The main features of them are directly inspired by the immune system. Diversity of solutions is preserved thanks to a suppression mechanism, which eliminates similar and useless solutions, and as a result, controls the size of population. The elitism mechanism helps preserve the best solutions during the optimization course. When more than two criteria are considered, the proposed multiobjective optimization algorithm significantly outperforms other metaheuristic multiobjective algorithms (NSGAII, SPEA2) [17; 32]. In the present paper, six objective functionals have been proposed, formulated and implemented. The shape optimization method proposed in the paper allows the design of the arms of the chevron type microactuator with the smooth nonuniform cross sectional area and smooth transition between arms and anchors or central shaft. Non uniform, rational B-splines (NURBS) have been applied for the parametrization of the arms [33]. It is obvious that stress concentration is located in sharp corners (see Figure 1b).