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A common approach, called the Pareto approach, is to consider a dominance rule such that a solution dominates another one if it is better in at least one objective and not worse in all objectives.
Inferior plans were eliminated by applying the Law of Dominance rule.
We propose here a new type of approximate stochastic dominance rule which implies other existing approximate stochastic dominance rules.
Therefore the dominance rule is modified as follows: if two tours visit the same set of control points, the one with the shorter duration dominates the other one.
A problem-specific feature of the BOOP requires to define a specific dominance rule: for a given set of k control points, there exists up to k ! feasible tours, i.e. different solutions, all with the same objective vector.
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In figure 5, scenario 3, based on an n = 7 ancestor, dominance rules are consistent with the previous scenario for A1, A9, A11 as dominant ancestral chromosomes and the derived duplicated A5(S), A8(S), and A12(S) chromosomes, respectively.
They developed a branch-and-bound with some dominance rules as well as a two-phase algorithm.
In this paper, we propose a branch-and-bound algorithm incorporating a lower bound and two dominance rules.
A branch and bound algorithm is designed for solving these subproblems via developing a lower bound and dominance rules.
The proposed approach includes a labeling algorithm in which we introduced appropriate dominance rules, which do not compromise optimality.
This means that the dominance rules (i.e., feasibility test and utility bound) can be employed to discard the most infeasible and unnecessary nodes before computing f(p).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com