Many problems in this world that have these conflicting objectives that may be solved. But many of these problems are often treated as a single-objective optimization problem with the objective to transfer all the constraints. The general form of Multi-Objective Optimization are as follows :
where :
: vector of n decision variables
: variable limit and restrict each decision variable xi. This limitation is the decision variable space D
: constraint functions
In a multi obejctive programming approach, optimal solution is a solution that delivers maximum results for all destinations simultaneously. In general, there is no optimal solution to the issue of multi-purpose. In cases like this, which might be an efficient solution. Efficient solution is a solution that can not be increased further achievements in one of the goals without lowering the achievement of other objectives (trade off). Area-efficient solution is not a point of particular solutions but it is a set of solution points that form a line or area efficient solutions. So in other words, the best solution or solutions “optimum” in the context of multi-objective (an efficient solution) is something to be desired (preferred), understood, accepted, supported and implemented by decision makers with confidence.
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