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Multiprocessor open shop makes a generalization to classical open shop by allowing parallel machines for the same task. Scheduling of this shop environment to minimize the makespan is a strongly NP-Hard problem. Despite its wide application areas in industry, the research in the field is still limited. In this paper, the proportionate case is considered where a task requires a fixed processing time independent of the job identity. A novel highly efficient solution representation is developed for the problem. An ant colony optimization model based on this representation is proposed with makespan minimization objective. It carries out a random exploration of the solution space and allows to search for good solution characteristics in a less time-consuming way. The algorithm performs full exploitation of search knowledge, and it successfully incorporates problem knowledge. To increase solution quality, a local exploration approach analogous to a local search, is further employed on the solution constructed. The proposed algorithm is tested over 100 benchmark instances from the literature. It outperforms the current state-of-the-art algorithm both in terms of solution quality and computational time.
相似文献We study a scheduling problem where the jobs we have to perform are composed of one or more tasks. If two jobs sharing a non-empty subset of tasks are scheduled on the same machine, then these shared tasks have to be performed only once. This kind of problem is known in the literature under the names of VM-PACKING or PAGINATION. Our objective is to schedule a set of these objects on two parallel identical machines, with the aim of minimizing the makespan. This problem is NP-complete as an extension of the PARTITION problem. In this paper we present three exact algorithms with worst-case time-complexity guarantees, by exploring different branching techniques. Our first algorithm focuses on the relation between jobs sharing one or more symbols in common, whereas the two other algorithms branches on the shared symbols.
相似文献The Neotropical region has been subjected to massive urbanization, which poses high risks for some global biodiversity hotspots and losses of ecosystem functions and services. In this study, we investigate how distance from large patches of native forests (source areas) and vegetation (green)/and infrastructure (gray) characteristics affect bird species richness and functional diversity in São Paulo megacity, southeastern Brazil. We analyzed the effects of source areas and green/gray characteristics on species richness and functional diversity (richness, evenness, and divergence) indices. We detected 231 bird species, and our data confirmed our predictions: (1) bird species richness in urbanized habitats was found to be (~?50–85%) lower than in source habitats; (2) species richness and trait composition significantly decreased as the distance from the source area increased, while functional richness was not affected by this metric; and (3) shrub and herbaceous covers and maximum height of trees were positively correlated with species richness and unique functional traits regarding habitat, diet, foraging and nesting strata and dispersal ability of birds in the forest-urban matrix. The number of buildings was negatively correlated with bird species richness and functional richness. Maximum height of buildings caused dramatic declines in functional evenness. Functional divergence was notably lower in sites with high shrub cover. Our study stresses the complexity of vegetation embedded in large Neotropical urban settlements and the need to maintain large protected areas surrounding megacities to mitigate the impacts of urbanization on birds.
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