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As a hosted solution, instances are easily created and available almost immediately.
In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation.
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One of the main issues when generating the solution instance for the actual set of parameters is that the user does not know in general which is the set of parameter values for which the parametric solution is feasible.
The novel cuts render a stabilizing effect that is directly responsible for the solution of instances up to 80 nodes.
We formulate an integer programming model of the problem using multicommodity flows that allows finding the solution for instances of up to 200 nodes.
In order to deal with the complexity of the scheduling model, we develop a Lagrangian relaxation-based decomposition approach equipped with a variable fixing procedure and a primal heuristics to obtain high-quality solution of instances of the problem.
The concatenation of a path from y to t and a path from t to x in G f proves that there is a path from y to x in G f. □ Now, we show the relation between MCM solutions for instances (X, Y, w) and solutions for sub-instances of the form (X ∖ { x}, Y ∖ { y}, w).
Pareto fronts of the optimal solutions for instances 1, 5 and 10 in Fig. 11 present proper diversity of the generated solutions for NSGA-II, MOSA and MOPSO.
In total, we performed 3,200 executions related to 8 solutions (80 instances × 5 variations × 8).
Open image in new window Fig. 11 Optimal solutions for instances 1, 5 and 10.
Computational results show that the proposed approach can find optimal solutions for instances with up to 30 nodes.
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