西南石油大学学报(自然科学版) ›› 2000, Vol. 22 ›› Issue (4): 80-83.DOI: 10.3863/j.issn.1000-2634.2000.04.022

• 基础理论研究 • Previous Articles     Next Articles

NEW ALGORITHM OF INTERIOR POINT TO SOLVE MOLP PROBLEMS

ZHONG Yi-hua WANG Yu JIANG Mao-ze   

  1. Southwest Petroleum inst
  • Received:2000-04-06 Revised:1900-01-01 Online:2000-11-20 Published:2000-11-20

Abstract: According to the efficient anchoring point for generating search directions in interior multiobjective linear programming (MOLP), the paper presented the new affine-scaling interior MOLP algorithm. First the contribution rate of each objective function to optimal solution was found as the initial value, then
a single - objective linear programming problem was solved and got an efficient anchor point with which to start the iterative process. During the iterative process, in light of the projected individual cost vectors (the coefficient of objective function) ,we can get the projected gradients and real contribution rates of them to optimal solution for the anchor point. Using these contribution rates, we generate a combined step direction along
which the next step is taken. Before proceeding the next iteration, use the scale - weight transformation method in AHP to confirm whether anchor point is always efficient. Scale weight transformation method in AHP and affinescaling interior points algorithm reduced the number of efficient anchor
points to one. The computing examples proved that this method is feasible.

Key words: multiobjective linear programming, efficient anchor points, analytic hierarchy process, scale weight transformation method, affine scaling interior point algorithm

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