A Multi-Criteria Decision-Making Procedure with an Inherited Set of Starting Points of Local Optimization of the Scalarizing Functions

Abstract

Abstract—This paper proposes a new interactive iterative procedure of searching for a preferred solution of a complicated non-linear multi-criteria optimization problem, in which global optimization of the scalarizing functions of criteria is too difficult because of numerous local extrema of the function and other reasons. In the suggested procedure, instead of global optimization of the scalarizing function of criteria, a large number of local optimization problems are solved on each iteration, while the set of starting points of local optimization processes is generated in a small neighborhood of the decision inherited from the previous iteration and the type of the scalarizing function of varies from iteration to iteration. The proposed procedure, named the Inherited Decisions Method, was applied for multi-criteria selection of rules for controlling the Angara cascade of reservoirs, while the rules are described by hundreds of parameters and the problem is characterized by more than two dozen decision criteria.