## Pareto Optimization or Cascaded Weighted Sum:  
A Comparison of Concepts  
**[PERSON] 1,* and [PERSON] 2**  
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where one of the criteria can be improved only by worsening at least one of the others. This approach is called _Pareto optimization_[1], and the set of all good compromises is called _Pareto optimal solutions_ or _non-dominated solutions_. In practice, usually only one solution is required. Thus, multi-objective optimization based on Pareto optimality is divided into two phases: At first, the set of Pareto optimal solutions is determined, out of which one must be chosen as the final result by a human decision maker according to more or less subjective preferences. This is in contrast to single-objective optimization tasks, where no second selection step is required. Most population-based search procedures, like evolutionary algorithms, particle swarm or ant colony optimization, require a single quality value called e.g., fitness in the context of evolutionary algorithms. This may be one reason for the frequent aggregation of different optimization criteria to a single quality value. Two methods, the frequently used _weighted sum_ and the _\(\varepsilon\)-constrained method_, are described briefly. Another commonly used method is to express everything in costs. On closer inspection, it becomes apparent that this is equal to the weighted sum approach using suitable weights. Additionally, the conversion into costs requires an artificial redefinition of the original goals and this is often not really appropriate. Thus, most multi-objective optimization problems have meanwhile been solved based on Pareto optimization, at least in academia. The computational effort to determine all or at least most of the Pareto front increases significantly with the number of conflicting objectives, as will be shown later in the paper. However, what if the complete Pareto front is not needed at all, because the area of interest is already known? In this paper we will introduce an aggregation method called the _cascaded weighted sum_ (CWS) and discuss application scenarios, where aggregation methods like the CWS can compete with Pareto-optimality-based approaches. Not to be misunderstood: We agree that in many fields of application, Pareto optimization is the appropriate method for multi-objective problems. Although we will concentrate on evolutionary multi-objective optimization later in the paper, the issues discussed here can be applied to other global optimization procedures as well and especially to those, which optimize a set of solutions simultaneously instead of just one. The paper is organized as follows: In Section 2 the basics of Pareto optimization are described, followed by the weighted sum and the \(\varepsilon\)-constrained method, including a brief discussion of their properties. In Section 3, the cascaded weighted sum is introduced.