Approximation Methods for Multiple Criteria Travelling Salesman Problems

Abstract

There has been considerable interest in the use of Tchebycheff procedures as a means of generating nondominated alternatives in multiple criteria optimization [1], [2], [3], [4], [15], [17], [18]. Such procedures require the solution of problems similar to

$$ \min \max \left[ {{x_1}{f_1}(x),...,{w_r}{f_r}(x)} \right]x \in S $$

((P))

where w₁,...,w_r are criterion weights and f₁,..., f_r are criterion functions. Tchebycheff approaches are attractive for at least two reasons: first, they have the potential to find any nondominated alternative, rather than only those realizable as the solution of optimization problems having an objective function consisting of a weighted sum of criterion functions; second, they avoid the infeasibilities that may result from solving problems in which each criterion function is required to attain some specified goal level.