A large number of data encoded in DNA molecules can be processed simultaneously by molecular biology techniques, although only a single set of instructions has been implemented in a solution.
The algorithm is able to yield a single solution or a nondominated set of solutions as result (depending on the number of objectives in a problem).
Recently, many authors have studied the problems of finding a common element of the set of fixed points of nonexpansive single valued mappings and the set of solutions of an equilibrium problem in the framework of Hilbert spaces: see, for instance, [15 29] and the references therein.
In 2003, Takahashi and Toyoda [40] introduced an iterative method for finding a common element of the set of fixed points of nonexpansive single-valued mappings and the set of solutions of variational inequalities for ϕ-inverse strongly monotone mappings in Hilbert spaces.
Recently, by using the concept of S-mapping, Kangtunyakarn [41] introduced a new method for finding a common element of the set of fixed points of k-strictly pseudononspreading single-valued mappings and the set of solutions of variational inequality problems in Hilbert spaces.
They proved that the sequence { x n } converges strongly to a common element of the set of fixed points of a relatively nonexpansive single-valued mapping and the set of solutions of an equilibrium problem under appropriate conditions in a uniformly smooth and uniformly convex Banach space.
By returning not just a single solution but a Pareto-optimal set of solutions (i.e., operation sequences, with appropriate part orientations and tools assigned) we have left the engineers freedom to apply further, not yet modeled parts of their domain knowledge.
Instead of identifying a single solution, a MOGA aims to identify a set of solutions in which an improvement in one objective requires a decrease in the other.
Firstly, we adopt a graph based representation scheme to encode so that it can generate a set of solutions with different number of clusters in a single run.
The primary benefit is that a set of solutions provides a picture of the optimal solution space that a single solution cannot.
