Over the course of the last decade, there have been several improvements in the performance of Boolean Satisfiability (SAT), Integer Linear Programming (ILP) and PseudoBoolean Optimization (PBO) solvers. These improvements have encouraged the applications of SAT, ILP and PBO techniques in modeling complex engineering problems. One such problem is the Virtual Machine Consolidation. The Virtual Machine Consolidation problem consists in placing a set of virtual machines in a set of hardware in a way to increase workload on hardware where they can operate more energy-efficient. This paper proposes an improved PBO formulation of the Virtual Machine Consolidation problem, PBFVMC. The improved formulation and enhancements are built on top of a previous work and a new set of constraints is created and rationalized to work more friendly with current PBO solvers. It is observed that this new formulation goes a step ahead and more problems can now be solved.
The multidimensional knapsack problem (MKP) is an NP-hard combinatorial optimization problem whose solution consists of determining a subset of items of maximum total profit that does not violate capacity constraints. Due to its hardness, large-scale MKP instances are usually a target for metaheuristics, a context in which effective feasibility maintenance strategies are crucial. In 1998, Chu and Beasley proposed an effective heuristic repair that is still relevant for recent metaheuristics. However, due to its deterministic nature, the diversity of solutions such heuristic provides is not sufficient for long runs. As a result, the search ceases to find new solutions after a while. This paper proposes an efficiency-based randomization strategy for the heuristic repair that increases the variability of the repaired solutions, without deteriorating quality and improves the overall results.
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