Application of Genetic Algorithm in Multi-objective Optimization

converge to a set of the solution as close as possible to the true Pareto-optimal set, which is the
common objective of all optimization tasks. However, diversity in the obtained Pareto-optimal set is
the second objective specific to multi-objective problems. With a more diverse set of solutions that
covers all parts of the Pareto-front in the objective space, the decision-making process at the next
level using the higher level information is easier. Since two spaces are involved in MOOP, diversity
of solutions in both decision and objective space is defined. Solutions with a large Euclidean
distance in variable and objective space are referred to as a diverse set of solutions in variable and
objective space, respectively. The diversity in the two spaces is often Symmetric, however in
complex and non-linear problems this property may not be true. Hence, Deb [1] assumes that there
are two goals in multi-objective optimization:
a. To find a set of non-dominated solutions with the least distance to the Pareto-optimal set.
b. To have maximum diversity in the non-dominated set of solutions.
2.2.4 Classification of Multi-Objective Optimization Algorithm (MOOA):
In section 2.1.1 it was mentioned that optimization solving methods are classified into the classical
and the evolutionary methods. That classification is also valid for multi-objective optimization
problems.
2.2.4.1 Classical Method for MOOA:
In the classical method, objectives are transformed into one objective function using different
techniques. The classical methods for MOOA will not be discussed in detail as this research work is
based on the EAs.
2.2.4.2 Evolutionary Algorithms (EAs) for MOOA:
The characteristic of EAs of using a population of solutions that evolve in each generation is well
suited for multi-objective optimization problems. Since one of the main goals of MOOP solvers is
28