Particle Swarm Optimization - A Survey <s> Multiobjective Optimization <s> In recent years population based methods such as genetic algorithms, evolutionary programming, evolution strategies and genetic programming have been increasingly employed to solve a variety of optimisation problems. Recently, another novel population based optimisation algorithm - namely the particle swarm optimisation (PSO) algorithm, was introduced by R. Eberhart and J. Kennedy (1995). Although the PSO algorithm possesses some attractive properties, its solution quality has been somewhat inferior to other evolutionary optimisation algorithms (P. Angeline, 1998). We propose a number of techniques to improve the standard PSO algorithm. Similar techniques have been employed in the context of self organising maps and neural-gas networks (T. Kohonen, 1990; T.M. Martinez et al., 1994). <s> BIB001 </s> Particle Swarm Optimization - A Survey <s> Multiobjective Optimization <s> This paper presents a modified dynamic neighborhood particle swarm optimization (DNPSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and one-dimension optimization to deal with multiple objectives. An extended memory is introduced to store global Pareto optimal solutions to reduce computation time. Several benchmark cases were tested and the results show that the modified DNPSO is much more efficient than the original DNPSO and other multiobjective optimization techniques. <s> BIB002 </s> Particle Swarm Optimization - A Survey <s> Multiobjective Optimization <s> This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems. <s> BIB003
Modifications to PSO for solving multiobjective optimization problems (MOP) have been introduced by several authors. The objective in this case is to find the Pareto front in the search space, as a set of points satisfying the Pareto optimality. In BIB002 , Hu et al. applies PSO to MOPs by employing a dynamic neighborhood scheme (as in BIB001 ), with sequential optimization of objective functions, thereby finding the Pareto front. Coello Coello et al. BIB003 proposed the multiobjective PSO (MOPSO) which keeps a repository of Pareto optimal points in the search space, and uses one among them as the gbest vector ( g i ) in the velocity updating of each particle. In addition, a mutation operation to avoid the local minima is used. Mutation is also applied to the system parameters (such as w, φ 1 and φ 2 in Eq. (7)), for an extensive exploration.