Abstract
Looking at articles or conference papers published since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems. However, is it always the method of choice for real-world applications, where either more than four objectives have to be considered, or the same type of task is repeated again and again with only minor modifications, in an automated optimization or planning process? This paper presents a classification of application scenarios and compares the Pareto approach with an extended version of the weighted sum, called cascaded weighted sum, for the different scenarios. Its range of application within the field of multi-objective optimization is discussed as well as its strengths and weaknesses.
Highlights
Most nonlinear real-world optimization problems require the optimization of several objectives and usually at least some of them are contradictory
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-optimalitybased approaches
The CWS allows for obtaining parts of a non-convex Pareto front, which were unreachable for the original weighted sum
Summary
Most nonlinear real-world optimization problems require the optimization of several objectives and usually at least some of them are contradictory. 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. 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. 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-optimalitybased approaches. The paper is organized as follows: In Section 2 the basics of Pareto optimization are described, followed by the weighted sum and the ε-constrained method, including a brief discussion of their properties.
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