Constructive cooperative coevolution
The constructive cooperative coevolutionary algorithm is a global optimisation algorithm in artificial intelligence based on the multi-start architecture of the greedy randomized adaptive search procedure. It incorporates the existing cooperative coevolutionary algorithm. The considered problem is decomposed into subproblems. These subproblems are optimised separately while exchanging information in order to solve the complete problem. An optimisation algorithm, usually but not necessarily an evolutionary algorithm, is embedded in C3 for optimising those subproblems. The nature of the embedded optimisation algorithm determines whether C3's behaviour is deterministic or stochastic.
The C3 optimisation algorithm was originally designed for simulation-based optimisation but it can be used for global optimisation problems in general. Its strength over other optimisation algorithms, specifically cooperative coevolution, is that it is better able to handle non-separable optimisation problems.
An improved version was proposed later, called the Improved Constructive Cooperative Coevolutionary Differential Evolution, which removes several limitations with the previous version. A novel element of C3iDE is the advanced initialisation of the subpopulations. C3iDE initially optimises the subpopulations in a partially co-adaptive fashion. During the initial optimisation of a subpopulation, only a subset of the other subcomponents is considered for the co-adaptation. This subset increases stepwise until all subcomponents are considered. This makes C3iDE very effective on large-scale global optimisation problems compared to cooperative coevolutionary algorithm and Differential evolution.
The improved algorithm has then been adapted for multi-objective optimization.
Algorithm
As shown in the pseudo code below, an iteration of C3 exists of two phases. In Phase I, the constructive phase, a feasible solution for the entire problem is constructed in a stepwise manner. Considering a different subproblem in each step. After the final step, all subproblems are considered and a solution for the complete problem has been constructed. This constructed solution is then used as the initial solution in Phase II, the local improvement phase. The CC algorithm is employed to further optimise the constructed solution. A cycle of Phase II includes optimising the subproblems separately while keeping the parameters of the other subproblems fixed to a central blackboard solution. When this is done for each subproblem, the found solution are combined during a "collaboration" step, and the best one among the produced combinations becomes the blackboard solution for the next cycle. In the next cycle, the same is repeated. Phase II, and thereby the current iteration, are terminated when the search of the CC algorithm stagnates and no significantly better solutions are being found. Then, the next iteration is started. At the start of the next iteration, a new feasible solution is constructed, utilising solutions that were found during the Phase I of the previous. This constructed solution is then used as the initial solution in Phase II in the same way as in the first iteration. This is repeated until one of the termination criteria for the optimisation is reached, e.g. a maximum number of evaluations.← ∅
while termination criteria not satisfied do
if = ∅ then
← SubOpt
end if
while 'pphase1 not completely constructed do
p'phase1 ← GetBest
← SubOpt
end while
pphase2 ← GetBest
while not stagnate do
← ∅
for each subproblem i do
← SubOpt
end for
← Collab
pphase2 ← GetBest
end while
'''end while'''