Optimising a nonlinear utility function in multi-objective integer programming

Ozlen, Melih
Azizoğlu, Meral
Burton, Benjamin A.
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.


Implicit monolithic parallel solution algorithm for seismic analysis of dam-reservoir systems
Özmen, Semih; Kurç, Özgür; Department of Civil Engineering (2016)
This research mainly focuses on developing a computationally scalable and efficient solution algorithm that can handle linear dynamic analysis of dam-reservoir interaction problem. Lagrangian fluid finite elements are utilized and compressibility and viscosity of the fluid are taken into consideration during the reservoir modeling. In order to provide computational scalability and efficiency, domain decomposition methods implemented with parallel computing approaches such as Finite Element Tearing and Inter...
Numerical methods for multiphysics flow problems
Belenli Akbaş, Mine; Kaya Merdan, Songül; Rebholz, Leo G.; Department of Mathematics (2016)
In this dissertation, efficient and reliable numerical algorithms for approximating solutions of multiphysics flow problems are investigated by using numerical methods. The interaction of multiple physical processes makes the systems complex, and two fundamental difficulties arise when attempting to obtain numerical solutions of these problems: the need for algorithms that reduce the problems into smaller pieces in a stable and accurate way and for large (sometimes intractable) amount of computational resou...
Nested Iterative Solutions of Electromagnetic Problems Using Approximate Forms of the Multilevel Fast Multipole Algorithm
Onol, Can; Ucuncu, Arif; Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-03-24)
Nested iterative solutions using full and approximate forms of the multilevel fast multipole algorithm (MLFMA) are presented for efficient analysis of electromagnetic problems. The developed mechanism is based on preconditioning an iterative solution via another iterative solution, and this way, nesting multiple solutions as layers. The accuracy is systematically reduced from top to bottom by using the on-the-fly characteristics of MLFMA, as well as the iterative residual errors. As a demonstration, a three...
Inverse design of compressor cascades
Kaplan, B.; Eyi, Sinan (2001-12-01)
In this paper an inverse design method is presented which couples a Navier-Stokes flow solver and a numerical optimization algorithm. The design method generates a compressor cascade, producing a specified surface pressure distribution at a transonic speed. A least-square optimization technique is used to minimize pressure discrepancies between the target and designed cascades. In order to represent the nonlinear, rotational and viscous physics of transonic flows, Navier-Stokes equations are used to predict...
Optimization approaches for classification and feature selection using overlapping hyperboxes
Akbulut, Derya; Özdemirel, Nur Evin; İyigün, Cem; Department of Industrial Engineering (2019)
In this thesis, an optimization approach is proposed for the binary classification problem. A mixed integer programming (MIP) model formulation is used to generate hyperboxes as classifiers. The hyperboxes are determined by lower and upper bounds on the feature values, and overlapping of hyperboxes is allowed to reach a balance between misclassification and overfitting. For the test phase, distance-based heuristic algorithms are also developed to classify the overlap and uncovered samples that are not class...
Citation Formats
M. Ozlen, M. Azizoğlu, and B. A. Burton, “Optimising a nonlinear utility function in multi-objective integer programming,” JOURNAL OF GLOBAL OPTIMIZATION, pp. 93–102, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38095.