# Generating Interior Search Directions for Multiobjective Linear Programming

### A. Arbel and S.S. Oren

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M93/20

1993

Currently existing multiobjective linear programming algorithms (MOLP) are using the simplex algorithm to generate a sequence of steps toward the optimal solution. The difference between the various MOLP algorithms depends on the specifics of generating these steps directions and the amount of involvement required from the decision maker (DM). This paper uses one variant of Karmarkar's interior-point linear programming algorithm and modifies it for solving multiobjective linear programming problems. Specifically, the paper considers the modification of the affine- scaling primal algorithm and develops a procedure for generating search direction that are interior to the polytope formed by the constraints of the linear programming problem. These search directions are combined to a single direction that approximates the gradient of the utility function of the decision maker at the current, interior, solution point. The solution process is comprised of a sequence of steps where search direction are generated and later combined and projected to yield the next interior iterate.

BibTeX citation:

@techreport{Arbel:M93/20, Author = {Arbel, A. and Oren, S.S.}, Title = {Generating Interior Search Directions for Multiobjective Linear Programming}, Institution = {EECS Department, University of California, Berkeley}, Year = {1993}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2303.html}, Number = {UCB/ERL M93/20}, Abstract = {Currently existing multiobjective linear programming algorithms (MOLP) are using the simplex algorithm to generate a sequence of steps toward the optimal solution. The difference between the various MOLP algorithms depends on the specifics of generating these steps directions and the amount of involvement required from the decision maker (DM). This paper uses one variant of Karmarkar's interior-point linear programming algorithm and modifies it for solving multiobjective linear programming problems. Specifically, the paper considers the modification of the affine- scaling primal algorithm and develops a procedure for generating search direction that are interior to the polytope formed by the constraints of the linear programming problem. These search directions are combined to a single direction that approximates the gradient of the utility function of the decision maker at the current, interior, solution point. The solution process is comprised of a sequence of steps where search direction are generated and later combined and projected to yield the next interior iterate.} }

EndNote citation:

%0 Report %A Arbel, A. %A Oren, S.S. %T Generating Interior Search Directions for Multiobjective Linear Programming %I EECS Department, University of California, Berkeley %D 1993 %@ UCB/ERL M93/20 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2303.html %F Arbel:M93/20