Conical algorithm in global optimization for optimizing over efficient sets (Q5929998)

The problem of optimizing a continuous function over the efficient set of a multiple objective programming problem is discussed. The problem is formulated as a global optimization problem with special structure and a conical branch and bound algorithm proposed for its solution. The algorithm is based on some well known results from multi-objective optimization, reproved here. A simple implementation for biobjective problems is given and finite termination for linear biobjective problems proven. Numerical results for multi-objective linear programming problems with 2, 3, and 4 objectives are reported.