Abstract
Several reviews have been made regarding the methods and application of multi-objective optimization (MOO). There are two methods of MOO that do not require complicated mathematical equations, so the problem becomes simple. These two methods are the Pareto and scalarization. In the Pareto method, there is a dominated solution and a non-dominated solution obtained by a continuously updated algorithm. Meanwhile, the scalarization method creates multi-objective functions made into a single solution using weights. There are three types of weights in scalarization which are equal weights, rank order centroid weights, and rank-sum weights. Next, the solution using the Pareto method is a performance indicators component that forms MOO a separate and produces a compromise solution and can be displayed in the form of Pareto optimal front, while the solution using the scalarization method is a performance indicators component that forms a scalar function which is incorporated in the fitness function.
Highlights
The optimal value or the best solution can be found through the optimization process
The scalarization method creates multi-objective functions made into a single solution using weights
The solution using the Pareto method is a performance indicators component that forms multi-objective optimization (MOO) a separate and produces a compromise solution and can be displayed in the form of Pareto optimal front, while the solution using the scalarization method is a performance indicators component that forms a scalar function which is incorporated in the fitness function
Summary
The optimal value or the best solution can be found through the optimization process. The dominance solution and optimal value in MOO are usually achieved when one objective function cannot increase without reducing the other objective function. Where (according to example Figure 3), ðQÃ1; QÃ2Þ are the coordinates for the Utopia point of the objective function f1ðxÞ whose minimum value is searched for, and objective function f2ðxÞ which needs the minimum value to be determined,ðQ1; Q2Þ are the point coordinates on the POF, and ðQ1norm; Q2normÞ are normalization point coordinates in the problem areas. Scalarization method The scalarization method makes the multi-objective function create a single solution and the weight is determined before the optimization process. The algorithm can be a metaheuristic algorithm that is a GA, particle swarm optimization (PSO), ant colonyoptimization, etc
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