MOACOMulti-Objective Ant Colony Optimization (algorithm)
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Components of MOACO. Based on the discussion of Section 4.2, the key stage is to solve the maximization optimization problem (22) which is a classical multiobjective subset problem.
Lopez-Ibanez and Stutzle [34] made a comparison between several state-of-art MOACO algorithms and concluded that it would improve solutions' quality by using more than one pheromone matrices.
In MOACO, each ant selects route (feature) according to the transition probabilities.
Besides, based on our model's characteristic, the heuristic information [[eta].sub.h] of MOACO is defined as the Fisher discriminant rate of hth feature of records' similarity vector.
Equation (26) shows that MOACO selects underlying features with high Fisher discriminant rate, which means they are easily classified.
After one cycle, MOACO uses solutions found by all ants to update its Pareto archive based on their Pareto relations.
In summary, the proposed modified MOACO can be described as Algorithm 1.
We now analyze the time complexity of MOACO in Algorithm 1.
For each classifier and a fixed q, the time complexity for implementing MOACO is O(NC x [q.sup.2] x M).
ALGORITHM 1: Pseudocode of MOACO. Begin Initialize parameters, pheromone matrices, and Pareto archive While not stopping criteria met do Generate weight parameter A by Eq.
The parameters of method 2 were set as follows: the base binary classifier was SVM whose parameters were set as method1, number of base binary classifiers L = 5, cardinality of features q [member of] [1, 20], pheromone matrices number of MOACO n = 2, initial value of pheromone matrices [[tau].sub.ij.sup.0] = 100, factors of importance of pheromone values and heuristic values [alpha] = 1, [beta] = 2, evaporation rate [rho] = 0.2, constant value Q = 0.02, number of ants M = 20, parameter of weight [lambda] [N.sub.weight] = 6, number of solutions in classifier's archive [] = 40, number of solutions in MOACO archive [] = 80, and the stopping criteria of MOACO were set as iterations NC = 40.