Objective reduction in multiobjective optimization
Tämän tutkielman tavoitteena on tarkastella menetelmiä, jotka pyrkivät ratkaisemaan ongelmia, jotka ilmenevät monitavoiteoptimointitehtävissä tavoitteiden määrän kasvaessa suureksi. Työssä esitellään useita menetelmiä kattaen erilaisia oletuksia optimointitehtävän luonteelta, kuten esimerkiksi lineaaristen tai konveksien tehtävien tapaukset. Lisäksi kommentoidaan menetelmien vahvuuksia ja heikkouksia. Yksi menetelmistä otetaan käytännönläheisempään tarkasteluun toteuttamalla siihen liittyvä abstrakti algoritmi Python-koodina ja tarkastelemalla algoritmin käyttäytymistä esimerkkien avulla. Lisäksi esitetään muutamia tapoja luokitella monitavoiteoptimointitehtävien tavoitteiden vähentämisen menetelmiä. The aim of this thesis is to study methods that have been created to avoid some of the problems related to solving multiobjective optimization problems with a large number of objectives. Multiple methods are presented covering various assumptions on the optimization problem, such as linearity or convexity, and the strengths and weaknesses of the methods are discussed. One of the methods is looked at in a more practical fashion, by presenting a Python code implementation of the abstract algorithm of the method in question and studying its behavior for some examples. Additionally, some criteria for classifying methods of objective reduction in multiobjective optimization are defined.
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