The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution.The paper discusses several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.

This paper presents HyFlex, a software framework for the development of cross-domain search methodologies. The framework features a common software interface for dealing with different combinatorial optimisation problems and provides the algorithm components that are problem specific. In this way, the algorithm designer does not require a detailed knowledge of the problem domains and thus can concentrate his/her efforts on designing adaptive general-purpose optimisation algorithms. Six hard combinatorial problems are fully implemented: maximum satisfiability, one dimensional bin packing, permutation flow shop, personnel scheduling, traveling salesman and vehicle routing. Each domain contains a varied set of instances, including real-world industrial data and an extensive set of state-of-the-art problem specific heuristics and search operators. HyFlex represents a valuable new benchmark of heuristic search generality, with which adaptive cross-domain algorithms are being easily developed and reliably compared.This article serves both as a tutorial and a as survey of the research achievements and publications so far using HyFlex.

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We use genetic programming to find variants of the well-known Nawaz, En-score and Ham (NEH) heuristic for the permutation flow shop problem. Each variant uses a different ranking function to prioritize operations during schedule construction. We have tested our ideas on problems where jobs have release times, due dates, and weights and have considered five objective functions: makespan, sum of tardiness, sum of weighted tardiness, sum of completion times and sum of weighted completion times. The implemented genetic programming system has been carefully tuned and used to generate one variant of NEH for each objective function. The new NEHs, obtained with genetic programming, have been compared with the original NEH and randomized NEH versions on a large set of benchmark problems. Our results indicate that the NEH variants discovered by genetic programming are superior to the original NEH and its stochastic version on most of the problems investigated

Hyper-heuristics or "methodologies to choose heuristics" are becoming increasingly popular given their suitability to solve hard real world combinatorial optimisation problems. Their distinguishing feature is that they operate in the space of heuristics or heuristic components rather than in the solution space. In Dispatching Rule Based Genetic Algorithms (DRGA) solutions are represented as sequences of dispatching rules which are called one at a time and used to sequence a number of operations onto machines. The number of operations that each dispatching rule in the sequence handles is a parameter to which DRGA is notoriously sensitive. This paper proposes a new hybrid DRGA which searches simultaneously for the best sequence of dispatching rules and the number of operations to be handled by each dispatching rule. The investigated DRGA uses the selection mechanism of NSGA-II when handling multi-objective problems.The proposed representation was used to solve different variants of the multiobjective job shop problem as well as the single objective problem with the sum of weighted tardiness objective. Our results, supported by the statistical analysis, confirm that DRGAs that use the proposed representation obtained better results in both the single and multi-objective environment overall and on each particular set of instances than DRGAs using the conventional dispatching rule representation and a GA that uses the more common permutation representation.