A Gentle Introduction to Multi-Criteria Optimization with SPOT

Multi-criteria optimization has gained increasing attention during the last decades. This article exemplifies multi-criteria features, which are implemented in the statistical software package SPOT. It describes related software packages such as moo and emoa and gives a comprehensive introduction to simple multi criteria optimization tasks. Several hands-on examples are used for illustration. The article is wellsuited as a starting point for performing multi-criteria optimization tasks with SPOT. 1 Multi Criteria Optimization: A Simple Example Optimization in general is fully integrated into todays life. We decide for the best prize when comparing similar groceries or choose the best quality when comparing different jackets. However, such decisions are generally more difficult, more complex than just deciding either for the best price or the best quality. Some sort of compromise solution might be preferable. This is where multicriteria optimization comes into play. Of course, the same holds for industrial processes. Input material has to be selected and the process itself can be steered in different directions via controlling some input variables. All these decisions will influence the quality of the final product, whereas quality can be expressed in form of different criteria or objectives (e.g., price, robustness, speed). As a consequence, a decision regarding the above mentioned input parameters can rarely be made without considering multiple criteria at once. There are some aspects that make such decisions more complicated than classical single objective problems. The most apparent one is the loss of total order. Comparing two products or processes just based on their price is easy. The cheaper is the better. If quality comes into play, life is much harder. Several products might exist which represent different compromises between quality and price. For example, let us consider the choice of selecting a car. Car no. 1 may be the cheapest, but also the one with the highest milage, whereas car no. 2 is the one with the least milage but also most expensive one. There may exist several MCO with SPOT 3 more cars which represent different compromises between milage and price. An example of that situation is represented in Fig. 1. Price [€] Milage [l / 100 km]