I would not say that metaheuristics are not preferred for anything at all. When mathematical optimization techniques are available - that is, when they are applicable to the problem - they are always and forever those that should be preferred, and utilized.

My viewpoint is that (meta)heuristics should be used only when alternatives are scarce. The development of multi objective mathematical optimization software is still under way, and some of the later developments can be found in the Nimbus, or www-Nimbus, software. 

Meta-heuristics for multi-objective optimization are, in my opinion, preferred because of the lack of alternatives.

The following discussion of the alternatives (i.e. non-metaheuristic algorithms) is only valid for discrete optimization (which is my field).

For discrete optimization, the two classical approaches are The Epsilon method and The Two-Phase method. These two methods have been applied over the last 20 years (at least), but still no frameworks exists (to the best of my knowledge). Hence, everyone has to program the methods from scratch. This may be a reason for the preference of meta-heuristics. Furthermore, both methods rely on iteratively solving single-objective (optimal) optimization problems. Hence, if the single-objective optimization problem is hard, using these methods is problematic. 

In my opinion, the most successful mathematical model for discrete optimization is Mixed Integer Programming (MIP). Over the last 2-3 years a development has occurred in the solution of Multi-Objective MIP models, using Multi-objective Branch & Bound algorithms. The three papers are referenced below. (I am the first author of one of these papers).  While significant progress has been achieved, we are nowhere near practically useful algorithms. Lots of more research and algorithmic improvements are necessary. The ultimate goal should be a MOMIP solver which can be applied like the single-objective MIP solvers (like CPLEX or Gurobi) are applied, without requiring specialized knowledge by the users. There is however still a long way to go, hence (in my opinion), meta-heuristics are used.

The 3 mentioned articles are:

Vincent T, Seipp F, Ruzika S, Przybylski A, Gandibleux X (2013)

Multiple objective branch and bound for mixed 0-1 linear pro-

gramming: Corrections and improvements for the biobjective

case. Comput. Oper. Res. 40(1):498–509.

Belotti, P. I. E. T. R. O., B. A. N. U. Soylu, and MARGARET M. Wiecek. "A branch-and-bound algorithm for biobjective mixed-integer programs." Optimization Online (2013).

Stidsen, Thomas, Kim Allan Andersen, and Bernd Dammann. "A branch and bound algorithm for a class of biobjective mixed integer programs." Management Science 60.4 (2014): 1009-1032.

I would like to know any  opinion with reference to power distribution network reconfiguration, which is a popular multi objective power system optimization problem.

A question to Sivkumar Mishra: Can you formulate the power distribution network reconfiguration as a MIP model (where the different objectives are added in the objective) ? 

Yes...MIP formulation has been proposed by several researchers for power distribution network reconfiguration even with  conflicting objectives 

Ok, assuming that you can formulate e.g. 2 models, one minimizing one criteria and one minimizing the other criteria. Then you can easily find one of the lexiographic corner points, first minimize crit1, set a constraint that crit1

Sivkumar Mishra, it is very much problem dependent. 

For the case o power distribution network in geral MIP formulations or simplify the problem or take a very long time to deliver the answer. 

The question that you should answer, is the simplifications acceptable? About time it is very unlike that MIP formulations will deliver good answer in very high-dimensions.

In the end of the day choosing an algorithm is a multiobjective optimization problem itself where dimensions such as time, model quality, convergence, among others. 

NSGA-II