University of Jyväskylä

Dissertation: 15.12.2016 New methods help engineers to solve computationally expensive problems significantly fast

Start date: Dec 15, 2016 12:00 PM

End date: Dec 15, 2016 03:00 PM

Location: Mattilanniemi, Agora, Auditorio 3

Mohammad TabatabaeiFM Mohammad Tabatabaei defends his doctoral dissertation in Information Technology ”On Approaches for Solving Computationally Expensive Multiobjective Optimization Problems”. Opponent Professor Ignacy Kaliszewski (Systems Research Institute, Polish Academy of Sciences, Poland) and custos Professor Kaisa Miettinen (University of Jyväskylä). The doctoral dissertation is held in English.

In his research, Mohammad Tabatabaei have developed new methods that assist engineers in finding compromise solutions for their problems significantly fast, e.g., in minutes instead of hours or in few days instead of weeks. These methods are integrated into a decision support system which provides information to engineers regarding limitations of their problems. In this way, they will gain insight into the nature of the problems. Then, based on the information provided, engineers would choose the best solution among all possible solutions.

Engineering design problems such as designing a car, train or an aircraft typically consist of several conflicting objectives. For example, in designing a car, one objective is to minimize its fuel consumption and another objective is to maximize its speed. Naturally, these two objectives are conflicting because by increasing the speed, the fuel consumption is also increased. Due to such a conflict, these kinds of problems are called multiobjective optimization problems. In these problems, instead of one solution, we may have several compromise solutions.

Many real-world multiobjective problems can be modelled mathematically. Once these problems are modeled, computer-based simulations provide information about their behaviour and properties. However, such simulations for obtaining an output for a given input can be tremendously time-consuming, e.g., from seconds to several days or months. Due to this fact, such problems are called computationally expensive multiobjective optimization problems. When applying typical methods to solve such problems, finding a set of compromise solutions takes a lot of time.

Methods developed in this research not only alleviate the computational cost considerably but also provide useful information regarding characteristics of such problems.

 

More information:

Mohammad Tabatabaei, mohammad.tabatabaei@jyu.fi, +358 40 805 3722
Communications Intern Katja Ketola, tiedotus@jyu.fi, +358 40 805 3638

Mohammad Tabatabaei is a member of the Industrial Optimization Group at the Faculty of Information Technology at the University of Jyväskylä. His research interests are multiobjective optimization, mathematical modelling and application of machine learning and data mining in optimization. The research has been financially supported by Jyväskylä Doctoral Program in Computing and Mathematical Sciences (COMAS) and the Academy of Finland. 

 

Abstract

In this thesis, we consider solving computationally expensive multiobjective optimization problems that take into account the preferences of a decision maker (DM). The aim is to support the DM in identifying the most preferred solution for problems that have several conflicting objectives and when the evaluation of the candidate solutions is time consuming. This is conducted by replacing computationally expensive functions with computationally inexpensive functions, known as surrogates. First, based on a literature survey, we introduce two frameworks, i.e., a sequential and an adaptive framework, based on which surrogate-based methods are classified and compared. We then identify relevant challenges that warrant more research efforts. In order to deal with the challenges, we develop two surrogate-based methods: SURROGATE-ASF and ANOVA- MOP. As an interactive method, SURROGATE-ASF has two phases: initialization and decision-making. In the first phase, the decision space is decomposed into a finite number of hyper-boxes. For each hyper-box, a single-objective surrogate problem is built. By solving an appropriate surrogate problem in the latter phase, a solution corresponding to the preferences of the DM is obtained. Numerical results support that SURROGATE- ASF can solve problems with at most 12 decision variables, 5 objective functions and nonconvex and/or disconnected sets of Pareto optimal solutions. To solve problems with high-dimensional decision and objective spaces, we develop the ANOVA-MOP method. Based on information obtained from sensitivity analysis, a problem is decomposed into a few sub-problems with low-dimensional decision and objective spaces. These sub-problems are solved, and the solutions obtained are composed to form approximated solutions for the original problem. ANOVA-MOP can be applied either as a non-interactive or an interactive method. Finally, we discuss the potential of a new metamodeling technique, called T-splines, to be incorporated into ANOVA-MOP to solve problems including non-differentiable functions. By applying the methods developed in this thesis, we extend the applicability of interactive methods to solving computationally expensive problems.

More information

Mohammad Tabatabaei
mohammad.tabatabaei@jyu.fi