This course will be concerned with providing developments and applications of theory and methods pertinent to decision making with multiple objectives. Goal programming and multi-criteria optimization methods (particularly interactive optimization schemes) are given special emphasis. Special emphasis will also be given to multi-objective linear programming. An interesting feature of the course is the discussion of interior point methods for multi-objective linear programming problems. Applications of neural networks in multi-objective optimization will also be discussed.
The first part of the course (12 weeks) will consist of lectures by Dr. Theodore B. Trafalis. Following these lectures, there will be individual presentations by the students on selected topics (last 4 weeks).
Prerequisite
Basic knowledge of linear programming.
Required Textbook
K. M. Miettinen. Nonlinear Multiobjective Optimization. Springer, 1998.
Exams and Grading
Course grades will be based on homework assignments, term project, mid-term exam, and class presentation-all weighted equally. There will be no final exam.
Project Guidelines
- The project is to be done individually.
- Each student should select a project falling in at least one of the following categories:
- A direct application of an MCDM model from a text or journal by collecting data and solving it using the computer.
- Improving and extending the results of a given study (e.g., with single objective) for a more realistic solution (e.g., with multiple objectives). Here, you may use the same data available in the study and compare your results to the existing one.
- Developing a new and different MCDM model for a real problem and present solution approach. Here, you may just use fictitious data to illustrate your methodology.
- Developing or improving a computer program for an MCDM algorithm.
- Experiments with different MCDM algorithms on problems.
- Preliminary Report: A two to three page statement explaining the project. Note: Before submitting the report, you may discuss the project informally to ascertain whether your project will meet the desired objectives and standards.
- Final Report: Due final day of classes. To be limited to 15 pages (excluding computer printout and appendices). Your final report should discuss the model formulation and solution, highlighting the major contribution made by you through the project work, and difficulties encountered, deviation from the preliminary objectives, and significant conclusions. Note: You are welcome to discuss the progress of your project from time to time.
- The following points will be taken into consideration while awarding the project grade:
- Complexity of the project.
- Adherence to the project guidelines.
- Presentation of final report.
- Results and major contributions.
- Completeness.