Abstract
It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure.
| Original language | English |
|---|---|
| Pages (from-to) | 504-523 |
| Number of pages | 20 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 307 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Jul 2005 |
Keywords
- Efficient solutions set
- Multiobjective linear programming
- Solution structure
ASJC Scopus subject areas
- Analysis
- Applied Mathematics