Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

A new cuckoo search algorithm with hybrid strategies for flow shop scheduling problems

Abstract: Cuckoo search (CS) is a recently developed meta-heuristic algorithm, which has shown good performance on many continuous optimization problems. In this paper, we present a new CS algorithm, called NCS, for solving flow shop scheduling problems (FSSP). The NCS hybridizes four strategies: (1) The FSSP is a typical NP-hard problem with discrete characteristics. To deal with the discrete variables, the smallest position value (SPV) rule is employed to convert continuous solutions into discrete job permutations; (2) To generate high quality initial solutions, a new method based on the Nawaz-Enscore-Ham (NEH) heuristic is used for population initialization; (3) A modified generalized opposition-based learning (GOBL) is utilized to accelerate the convergence speed; and (4) To enhance the exploitation, a local search strategy is proposed. Experimental study is conducted on a set of Taillard's benchmark instances. Results show that NCS obtains better performance than the standard CS and some other meta-heuristic algorithms.

Generalized Shape Optimization Using X-FEM and Level Set Methods

Abstract: This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization.

Spacecraft Reliability-Based Design Optimization Under Uncertainty Including Discrete Variables

Abstract: computationally expensive sampling techniques. The computational cost of optimization approaches becomes prohibitivewhenconsideringdiscretetechnology andredundancychoicesasvariables.Thisworkpresentsagenetic algorithm with Monte Carlo sampling for probabilistic reliability-based design optimization of satellite systems. In thisapproach,confidence-levelconstraintsensurethatsystemreliabilityrequirementsaremetwithhighprobability. Thegeneticalgorithm–MonteCarlosamplingapproachiscomparedtoadeterministic margin-basedapproachthat enforcesmarginsorsafetyfactorsonthereliabilityofindividualcomponents.Thecomparisonshowsthatthegenetic algorithm–Monte Carlo sampling approach produces satellite designs that have low launch mass (a surrogate for cost) while achieving reliability requirements at specified high confidence levels, while the genetic algorithm– deterministic margin-based approach produces heavy satellite designs with excessive redundancy. Based on this work, extensions of a genetic algorithm-based approach for discrete optimization under uncertainty that may require less computational effort appear possible.