Search results for "lineaarinen optimointi"
showing 4 items of 4 documents
Johdatus peliteoriaan : kahden pelaajan nollasummapelien ratkaiseminen ja Nashin tasapainojen olemassaolo usean pelaajan yleisessä summapelissä
2013
Tämän tutkielman tarkoituksena on osoittaa, että jokaisella usean pelaajan yleisellä summapelillä on olemassa vähintään yksi Nashin tasapaino. Lisäksi osoitetaan, että kahden pelaajan nollasummapeleissä Nashin tasapainojen mukaiset pelaajien voittojen odotusarvojen suuruudet ovat yksikäsitteiset, ja näytetään kuinka kyseiset odotusarvot voidaan ratkaista lineaarisen optimoinnin avulla. Tutkielmassa määritellään yleiset summapelit kolmikkoina, jotka muodostuvat äärellisestä määrästä pelaajia, joista jokaiseen on liitetty äärellinen joukko. Näiden joukkojen alkioita kutsutaan pelaajien puhtaiksi strategioiksi. Kolmikon viimeisen jäsenen muodostaa jokaiselle pelaajalle erikseen määritelty kuva…
Surrogate-assisted evolutionary multiobjective shape optimization of an air intake ventilation system
2017
We tackle three different challenges in solving a real-world industrial problem: formulating the optimization problem, connecting different simulation tools and dealing with computationally expensive objective functions. The problem to be optimized is an air intake ventilation system of a tractor and consists of three computationally expensive objective functions. We describe the modeling of the system and its numerical evaluation with a commercial software. To obtain solutions in few function evaluations, a recently proposed surrogate-assisted evolutionary algorithm K-RVEA is applied. The diameters of four different outlets of the ventilation system are considered as decision variables. Fr…
DESDEO: The Modular and Open Source Framework for Interactive Multiobjective Optimization
2021
Interactive multiobjective optimization methods incorporate preferences from a human decision maker in the optimization process iteratively. This allows the decision maker to focus on a subset of solutions, learn about the underlying trade-offs among the conflicting objective functions in the problem and adjust preferences during the solution process. Incorporating preference information allows computing only solutions that are interesting to the decision maker, decreasing computation time significantly. Thus, interactive methods have many strengths making them viable for various applications. However, there is a lack of existing software frameworks to apply and experiment with interactive …
An Investigation of the Robustness in the Travelling Salesman Problem Routes Using Special Structured Matrices
2020
In this study, the robustness of the Travelling Salesman Problem (TSP) routes is investigated by recognising the special combinatorial structures of Kalmanson matrices. A recognition algorithm encompassing three procedures based on combinatorial and linear programming (LP) is developed and executed on several randomly generated instances. These procedures produce three lower bounds which provide guarantees on the optimality of the solutions. Computational experiments show that the proposed LP-based procedure performs efficiently well across all problem dimensions and provides the best lower bounds to the TSP. This is supported by an average deviation of less than 7% between the TSP tour len…