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We also introduce a heuristic approach to get a good feasible solution.
A heuristic algorithm is generated to further improve it till a good feasible solution is reached.
The clustering procedure increases the likelihood that the solution will converge to an optimal value, between-route operations (relocate, 2-opt* exchange, and swap move) in the heuristic algorithm will improve the initial solution, and the within-route (dynamic programming) procedure will calculate a good feasible solution for each vehicle route.
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Nevertheless, good feasible solutions can be found by relaxing the minimization problem and applying the majorization-minimization (MM algorithm (see [36] for details).
In their paper, cross-docking was modeled as a three-stage hybrid flow shop, and for obtaining good feasible solutions, they have developed several heuristic schemes.
A branch exchange heuristic procedure makes modifications to each infeasible solution of the Lagrangian relaxation in order to find good feasible solutions.
Next, we propose a local search heuristic to find "good" feasible solutions of the global model within a reasonable amount of time.
Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide good feasible solutions quickly.
However, it is possible to compute good feasible solutions of the sink location and routing problems easily, when the sensors are deployed and their locations in the sensor field become known.
It is important to search through the infeasible space of the problem, because it leads to reach appropriate diversity for the proposed GA and good feasible solutions can most efficiently be reached by breeding between a feasible and an infeasible solution.
Namely, a DPAP-specific population initialization that seeds the initial solutions into promising regions, problem-specific genetic operators (i.e. M-tournament selection, adaptive crossover and mutation) for generating good, feasible solutions and a DPAP-specific Repair Heuristhat(RH) transformsforms an infeasible solution into a feasible one and maintains the MOEA/D's efficiency simultaneously.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com