VEPSOVector Evaluated Particle Swarm Optimization
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The VEPSO algorithm, introduced by Parsopoulos and Vrahatis [1], uses the multiswarms concept from the VEGA algorithm [9].
The flow of the VEPSO algorithm is given as in Algorithm 2.
The Improved VEPSO Algorithm by Incorporating Non-dominated Solutions.
From an algorithm perspective, the VEPSOnds is similar to the conventional VEPSO except that (5) in Algorithm 2 is replaced with (8).
The Improved VEPSO Using Multiple nondominated Leader.
Thus, the use of nondominated solutions to enhance the VEPSO algorithm can be further improved by the use of multileader concept in this work.
Generally, the PSO and VEPSO algorithms have similar process flows, except that all processes are repeated for M swarms when optimising problems with M objective functions.
This improved VEPSO algorithm is represented in Figure 3(b), where g[Best.sup.l] (t) is now a nondominated solution that is best with respect to the first objective function.
In the improved VEPSO algorithm, the generality of conventional VEPSO is not lost; so the gBest(t) of a swarm is the best nondominated solution with respect to the objective function optimised by the swarm.
Therefore, this improved VEPSO algorithm also includes the polynomial mutation mechanism from nondominated sorting genetic algorithm-II [11].
For the average NS measure, the number of nondominated solutions found by both improved VEPSO algorithms was significantly greater for conventional VEPSO.
The nondominated solutions obtained by VEPSO are clearly located very far away from the true Pareto front, which leads to a large GD value.