A decision space algorithm for multiobjective convex quadratic integer optimization

We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks efficient points by fixing subsets of variables to values and using lower bounds in the form hyperplanes image space derived from continuous relaxations restricted functions. show that stops after finitely many fixings with detecting both full nondominated set multiobjective strictly problems. A major advantage approach is expensive calculations are done preprocessing phase so nodes tree can be enumerated fast. numerical experiments on biobjective instances three four objectives.