Different methodologies have been proposed to solve
these types of multiobjective environmental/economic dispatch problem. In 4
the problem is reduced to a single objective problem by considering the
emission as a constraint with a permissible limit condition. These
multi-objective environmental/economic dispatch problems have different
difficulties during dispatch solution to get correct relation between the cost
and emission. So fuel cost and emissions are to be treated as objective
functions. In paper 5, the linear programming based optimization technique in
which both emission and fuel cost functions as objective function. But by
considering both these functions as objective functions, the
environmental/economic (EED) problem becomes a complicated nonlinear
optimization problem. So many conventional methodologies are available in order
to obtain global optimal solution but all those methods can’t attain the global
solution. Many techniques based on analytic methods having differential
objective functions having the advantage to simplify the above formulated On
the other hand, many mathematical assumptions such as analytic and differential
objective functions have to be given to simplify the above mentioned
environmental/economic (EED) problem. There are so many methods are now
available to consider these two cost function and emission function together
into a single objective function using  the
linear combination of  two objectives as
a weighted sum which is explained 6 and 7. A Pareto optimal solution is
obtained by above mentioned weighted sum method by varying the weights. But
much iteration is required to obtain this Pareto optimal global solution. All
these methods can’t use to obtain the global solution due to non convex Pareto
optimal front. So in 8 and 9, a method is explained to overcome the above
difficulty which is the ?-constraint method for the solution of multiobjective
optimization. This method is based on getting most optimized solution of
multiobjective objective function with some constraints having permissible limits.
Recently some modern techniques  such as
genetic algorithm, evolutionary programming, artificial bee colony, tabu search
algorithm, ant colony, bacterial foraging, flower pollination technique,
efficient particle swarm optimization technique, genetic algorithm with
simulated annealing process have been emerged to solve the complex non linear
problem. During the dispatch we can face some problems of
handling non smooth fuel cost function and emission function. So an effective
and efficient optimization technique is required to solve multiobjective
function. Here this paper proposes the use of Particle Swarm Optimization (PSO)
to solve the bi-objective function which is a global searching technique.

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