347,015 research outputs found
Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs
In this paper, we introduce a type of latticized optimization problem whose
objective function is the maximum component function and the feasible region is
defined as a system of fuzzy relational equalities (FRE) defined by the Dombi
t-norm. Dombi family of t-norms includes a parametric family of continuous
strict t-norms, whose members are increasing functions of the parameter. This
family of t-norms covers the whole spectrum of t-norms when the parameter is
changed from zero to infinity. Since the feasible solutions set of FREs is
non-convex and the finding of all minimal solutions is an NP-hard problem,
designing an efficient solution procedure for solving such problems is not a
trivial job. Some necessary and sufficient conditions are derived to determine
the feasibility of the problem. The feasible solution set is characterized in
terms of a finite number of closed convex cells. An algorithm is presented for
solving this nonlinear problem. It is proved that the algorithm can find the
exact optimal solution and an example is presented to illustrate the proposed
algorithm.Comment: arXiv admin note: text overlap with arXiv:2206.09716,
arXiv:2207.0637
Optimal staffing under an annualized hours regime using Cross-Entropy optimization
This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis
Optimal Recombination in Genetic Algorithms
This paper surveys results on complexity of the optimal recombination problem
(ORP), which consists in finding the best possible offspring as a result of a
recombination operator in a genetic algorithm, given two parent solutions. We
consider efficient reductions of the ORPs, allowing to establish polynomial
solvability or NP-hardness of the ORPs, as well as direct proofs of hardness
results
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