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Ant colony optimization (ACO) is a metaheuristic technique for hard discrete optimization problems that was first proposed in the early 1990s.
The Distance-constrained Capacitated Vehicle Routing Problem, a computationally very hard discrete optimization problem with high industrial relevance, is the selected vehicle for our investigations.
The application of stochastic heuristic, like tabu search or simulated annealing, to address hard discrete optimization problems has been an important advance for efficiently obtaining good solutions in a reasonable amount of computing time.
These solvers are based on Boolean constraint solving technology, and they can solve hard discrete combinatorial search problems, with comparable results with ILP.
Algorithms based on swarm intelligence have been applied successfully to a large number of hard discrete optimization problems including traveling salesman, quadratic assignment and routing in telecommunications networks [ 6, 8].
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Sometimes, it is not suitable for dealing with NP-hard discrete optimization problems.
Branch-and-Bound (B&B) algorithms are well-known tree-based exploratory methods for solving to optimality NP-hard discrete optimization problems.
It can be deemed a classical transform in the compressed sensing field into the following NP-hard discrete optimization problem: min x ∈ ℜ n ∥ x ∥ 0 subject to A x = b, (1.2).
Clinically, it is characterized by solitary or multiple rock-hard discrete lesion(s) in one or both breasts, usually in a subareolar site, but may appear equally in any part of the breast.
The IB part incorporates both particle fluid and particle particle interaction via a direct forcing method and a hard sphere Discrete Particle (DP) approach.
While for the sake of simplicity, the motion of particle phase is tracked by following the hard-sphere discrete particle model (DPM).
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