Multiobjective Optimization

Syllabus of the graduate-level course to be offered in the Department of Mathematical Information Technology at the University of Jyvaskyla in Jyvaskyla

During the first term in the spring semester 2010

Lecturer

Prof. Margaret Wiecek (visiting professor at the Department of Mathematical Information Technology)

Department of Mathematical Science, Clemson University, Clemson, SC 29634, USA
email: wmalgor@clemson.edu

I. GENERAL INFORMATION

The emphasis in this course is on the conceptual development of major concept, models, and algorithms in multiple objective programming and decision-making. Important aspects of this development include problem formulation, properties of solutions, algorithmic solution approaches, and applications of multiple criteria decision-making (MCDM).

Goals

Identify major multiobjective programming methods
Identify links between single and multiobjective programming methods and algorithms
Develop competence in the application of these techniques
Analyze applications (case studies) of MCDM

Prerequisites

The course "Nonlinear Programming" or an equivalent advanced undergraduate-level course in nonlinear programming.

Topical outline*

Introduction
Preference modeling
Theory and methodology of multiple objective programming (also included: complex systems optimization (Research Tasks 1 and 2))
Specially structured problems (linear, discrete)
Methods and applications of MCDM (also included: application to production systems in the Finnish paper industry (Research Tasks 3 and 4))

* We will attempt to adhere to the syllabus. However, the actual content may be adjusted at the instructor's discretion.

Formats

Lectures, recitations, homework assignments and a project.

Lectures will cover the topics given below. Homework assignments will be discussed during recitations. Students will work in 2-person teams on a project for which they will be expected to study a research article on an application of MCDM and give a 20-minute oral presentation in class on this subject. The article can be selected from the list of references given in part IV. Other articles are welcome but will have to be approved by the lecturer.

The presentation should include the following:

Description of a real-life problem.
Motivation for choosing a multiple objective model.
Multiple objective model (decision variables, objectives, constraints).
MCDM technique used to solve the problem.
Analysis of results.
Students' opinion about the proposed model and solution approach.

II. SCHEDULE OF LECTURES AND RECITATIONS

Lectures on Mondays at 12-14 and Tuesdays at 10-12 in Ag Beeta. Exercise sessions on Thursdays at 10-12. See table.

III. GRADING

The final grade for the course will be determined based on the following:

Attendance10%
Completion of assignments30%
Project30%
Final examination30%

IV. LITERATURE (most relevant sources are highlighted)

V. Chankong and Y. Y. Haimes, Multiobjective Decision Making: Theory and Methodology, North Holland, New York, 1983.
M. Ehrgott, Multicriteria Optimization, Springer, Berlin, 2005, second edition.
R. L. Keeney and H. Raiffa, Decisions with Multiple Objectives:Preferences and Value Tradeoffs, Wiley, New York, 1976.
K. Miettinen, Nonlinear Multiobjective Optimization, Kluwer, Boston, 1999.
R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, Wiley, New York, 1986.
F. Szidarovszky, M.E. Gershon, L. Duckstein, Techniques for Multiobjective Decision Making in Systems Management, Elsevier, Amsterdam, 1986.
P. L. Yu, Multiple Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, 1985.
M. Zeleny, Multiple Criteria Decision Making, McGraw-Hill, New York, 1982.
Eleven articles published in Omega: Special Issue on Multiple Criteria Decision Making for Engineering, M. M. Wiecek, M. Ehrgott, G. Fadel and J. R. Figueira eds., Vol. 36, Issue 3, pp. 337-504 (June 2008)
More than seven hundred articles collected by D. J. White in the paper "A Bibliography on the Applications of Mathematical Programming Multiple-Objective Methods", Journal of the Operational Research Society, 41(8), pp. 669-691, 1990.