Algorithm robust for the bicriteria discrete optimization problem

Multiple vector optimization proposes to optimize a vector-valued function rather than a real-valued one. The motivation of that is quite natural, since most of the real-life problems involve more than one measure to be used as objective function. Multiple objective discrete optimization (MODO) problem is defined as minx∈X f(x) = [f1(x), . . . fp(x)] T , where X ⊆ R is a bounded (discrete) set of feasible alternatives, and fj : R n → R, j = 1, . . . , p are objective functions. x̂ ∈ X is called efficient ⇔6 ∃x ∈ X : f(x) ≤ f(x̂). x̂ ∈ X is called weakly efficient ⇔6 ∃x ∈ X : f(x) < f(x̂). The efficient solution characterizes the trade-off among the objective functions. There exist algorithms, that can find all the efficient solutions for the continuous case. But they are far from being practical for real-life large-sized problems. As in single objective case, the MODO problem is more complicated to solve, than the continuous version. The major complication is the existence of so called unsupported solutions, i.e. the efficient solutions, that cannot be reached by shifting the hyperplane as optimal solutions.