# An Improved Multiobjective Particle Swarm Optimization Based on Culture Algorithms
## 1 Introduction  
Since many real-life problems are in fact multiobjective optimization problems (MOPs), evolutionary algorithms used to solve MOPs have attracted much attention in recent years. Multiobjective optimization evolutionary algorithms (MOEAs) mainly include two branches: dominance-based and decomposition-based [1]. Nondominated sorting genetic algorithm II (NSGA-II) [2], strength Pareto evolutionary algorithm 2 (SPEA2) [3] and multiobjective particle swarm optimization (MOPSO) [4; 5] are in the first branch; multiobjective evolutionary algorithm based on decomposition (MOEA/D) [6; 7] is in the second branch. For those dominance-based algorithms, the main goals of multiobjective optimization are that the non-dominated set obtained by an algorithm is a good approximation to the true Pareto front, and that this non-dominated set is uniformly distributed on the Pareto front [8]. Particle swarm optimization (PSO) is an evolutionary computation technique based on the social behavior of species, such as a flock of birds or a school of fish. To handle MOPs, two problems need to be taken into account. The determination of personal and global guides is the first, and second is to maintain the diversity of the population. Some efforts have been made in selecting the global and local guides. [PERSON] introduced the secondary repository that is based on Pareto optimality to store the non-dominated particles in MOPSO, and the global guide is selected using the adaptive grid [4]. In crowding distance (CD)-MOPSO, the global guide is selected using crowding distance in MOPSO [9]. In clustering MOPSO, the global guide is selected based on the clustering technique [10]. [PERSON] and [PERSON] [11] selected the local guide based on the sigma method, while [PERSON] and [PERSON] [12] compared the results of different methods in selecting the local guide. [PERSON] proposed the use of a cultural algorithm to deal with multiobjective optimization problems, in which the knowledge based on the cultural algorithm will affect the selection of both the global guideand the local guide [13]. Cultural multiobjective quantum particle swarm optimization (MOQPSO) [1], Cultural MOPSO (CMOPSO) [14], constrained CMOPSO [15], and Cultural dynamic PSO (DPSO ) [16] are all based on a cultural evolution mechanism. A special domination principle and genetic operator have been used to raise the diversity of the Pareto front. [PERSON] defined \(\varepsilon\)-box dominance to combine convergence and diversity [17], while [PERSON] introduced the elitism mechanism that performs crossover and mutation on individuals selected from the union of population and repository [18]. Simulated Binary Crossover (SBX) has been used in the work of [PERSON] [19] and [PERSON] [20]. The Borg MOEA represents a class of algorithms whose operators are adaptively selected based on the problem [21]. Diversity-loss-based selection method is used in [22]. Bare-bones (BB)-MOPSO use an approach based on particle diversity to update the global particle leaders [23]. Pareto entropy MOPSO (peMOPSO) using cell distance based individual density to select the global guide [24]. Although there has been considerable research conducted on PSO proposed to solve MOPs, to raise the convergence and diversity of the approximate Pareto front further still remains an issue that needs to be considered. An improved multiobjective particle swam optimization has been developed in this paper. Situational, normative and topographical knowledge are to be used to update the personal and global guides. A polynomial mutation operator is applied to every particle in the swarm and in the repository to enhance the convergence and diversity of the Pareto front. Epsilon domination principle depends both on the situation in the adaptive grid and the objective value that has been used. The paper is structured as follows. The concept of multiobjective problems, cultural algorithms, and particle swarm optimization are briefly reviewed in the next section.