ABSTRACT
An optimization problem involving more than one objective to be optimized is referred as multiobjective optimization problem (MOOP). The optimum solution corresponding to a single objective optimization problem refers to
ASHISH M. GUJARATHI1 and B. V. BABU2
1Department of Petroleum and Chemical Engineering, College of Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khod, Muscat-123, Sultanate of Oman, Phone: +968 2414 1320, E-mail: ashishgujrathi@gmail.com, ashishg@squ.edu.om
2Professor of Chemical Engineering and Vice Chancellor, Galgotias University, Greater Noida, India, E-mail: profbvbabu@gmail.com
the optimal basic feasible solution (satisfying bounds of variables and the constraints). However, in case of multiobjective optimization, the optimum solution refers to a compromised (not necessarily the optimum with respect to any objective) set of multiple feasible solutions. In the most general form, the multiobjective optimization problem (with m objectives, n variables, p inequality constraints and q equality constraints) can be expressed as given by Eq. (1.1):
Min f x f x f x f x
u x j
( ) ( ), ( ),......, ( )
( ) ,
= [ ]
≥
0 subject to
=
= =
≤ ≤ =
1 2
0 1 2
1 2
, ,...,
( ) , , ,...,
p v x k q x x x i n k i
(1.1)
The optimization algorithms can be broadly classified into two categories, i.e., traditional or classical methods and the non-traditional or population based search algorithms. The traditional algorithms often start with a single point (guess value) and end up with a single point solution. The ideal outcome of a single objective optimization problem is a single global solution. However, the outcome of gradient-based traditional algorithms largely depends on its control parameters such as the step size and the direction of search that are being used. In a complex and non-linear search space (as shown in Figure 1.1), which may involve multiple local and a single global solution, an inefficient local search algorithm may get trapped at local optimal solution. In contrast, evolutionary algorithms, which mimic nature’s principle of survival of the fittest, start with multiple population points [7, 8, 16, 17, 19, 20]. Due to the strong genetic operators, evolutionary algorithms are found to achieve the global optimum in majority of industrial applications for single objective optimization [2].
