Given a set of items, weight and profit associated with each item, and an upper bound for the capacity of the knapsack. There is a trade-off between profit and weight. Given set of solutions and two members A,B of the set. A. Those solutions that are nondominated regarding the entire search space are called Pareto optimal .
Selection represents the competition for resources among living beings.
Some are better than others and more likely to survive and to reproduce their genetic information. In evolutionary algorithms, natural selection is simulated by a stochastic selection process. Thereby, quality is assessed by evaluating the individuals and assigning them scalar fitness values. Although simplistic from a biologist's viewpoint, these algorithms have proven themselves as a general, robust and powerful search mechanism. Moreover, EAs seem to be especially suited to multiobjective optimization because they are able to capture multiple Pareto-optimal solutions in a single simulation run and may exploit similarities of solutions by recombination.