José Antonio Vázquez-Rodríguez

The hybrid flow shop scheduling problem

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 briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.

HyFlex: a benchmark framework for cross-domain heuristic search

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.

Iterated local search vs. hyper-heuristics: Towards general-purpose search algorithms

An important challenge within hyper-heuristic research is to design search methodologies that work well, not only across different instances of the same problem, but also across different problem domains. This article conducts an empirical study involving three different domains in combinatorial optimisation: bin packing, permutation flow shop and personnel scheduling. Using a common software interface (HyFlex), the same algorithms (high-level strategies or hyper-heuristics) can be readily run on all of them. The study is intended as a proof of concept of the proposed interface and domain modules, as a benchmark for testing the generalisation abilities of heuristic search algorithms. Several algorithms and variants from the literature were implemented and tested. From them, the implementation of iterated local search produced the best overall performance. Interestingly, this is one of the most conceptually simple competing algorithms, its advantage as a robust algorithm is probably due to two factors: (i) the simple yet powerful exploration/exploitation balance achieved by systematically combining a perturbation followed by local search; and (ii) its parameter-less nature. We believe that the challenge is still open for the design of robust algorithms that can learn and adapt to the available low-level heuristics, and thus select and apply them accordingly.

A new dispatching rule based genetic algorithm for the multi-objective job shop problem

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 multi-objective 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.

Dispatching rules for production scheduling: A hyper-heuristic landscape analysis

Hyper-heuristics or “heuristics to chose heuristics” are an emergent search methodology that seeks to automate the process of selecting or combining simpler heuristics in order to solve hard computational search problems. The distinguishing feature of hyper-heuristics, as compared to other heuristic search algorithms, is that they operate on a search space of heuristics rather than directly on the search space of solutions to the underlying problem. Therefore, a detailed understanding of the properties of these heuristic search spaces is of utmost importance for understanding the behaviour and improving the design of hyper-heuristic methods. Heuristics search spaces can be studied using the metaphor of fitness landscapes. This paper formalises the notion of hyper-heuristic landscapes and performs a landscape analysis of the heuristic search space induced by a dispatching-rule-based hyper-heuristic for production scheduling. The studied hyper-heuristic spaces are found to be “easy” to search. They also exhibit some special features such as positional bias and neutrality. It is argued that search methods that exploit these features may enhance the performance of hyper-heuristics.

On the automatic discovery of variants of the NEH procedure for flow shop scheduling using genetic programming

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.

A mixture experiments multi-objective hyper-heuristic

This paper proposes a hyper-heuristic that combines genetic algorithm with mixture experiments to solve multi-objective optimisation problems. At every iteration, the proposed algorithm combines the selection criterion (rank indicator) of a number of well-established evolutionary algorithms including NSGA-II, SPEA2 and two versions of IBEA. Each indicator is called according to an associated probability calculated and updated during the search by means of mixture experiments. Mixture experiments are a particular type of experimental design suitable for the calibration of parameters that represent probabilities. Their main output is an explanatory model of algorithm performance as a function of its parameters. By finding the maximum (probability distribution) of the surface represented by this model, we also find a good algorithm parameterisation. The design of mixture experiments approach allowed the authors to identify and exploit synergies between the different rank indicators at the different stages of the search. This is demonstrated by our experimental results in which the proposed algorithm compared favourably against other well-established algorithms.

Match-up approaches to a dynamic rescheduling problem

This article considers the problem of inserting arriving jobs into an existing schedule of a real world manufacturer. A number of match-up strategies, which collect the idle time on machines of a current schedule for the insertion of new jobs, are proposed. Their aim is to obtain new schedules with a good performance which are at the same time highly stable, meaning that they resemble as closely as possible the initial schedule. Basic rescheduling strategies such as ‘total rescheduling’, ‘right shift’ and ‘insertion in the end’ deliver either good performance or stability, but not both. Contrarily, our experimentation and statistical analysis reveal that the proposed match-up strategies deliver high performing schedules with a high stability. An analysis of the problem parameters that determine the behaviour of the proposed match-up algorithms is included in this article.

Towards the decathlon challenge of search heuristics

We present an object oriented framework for designing and evaluating heuristic search algorithms that achieve a high level of generality and work well on a wide range of combinatorial optimization problems. Our framework, named HyFlex, differs from most software tools for meta-heuristics and evolutionary computation in that it provides the algorithm components that are problem-specific instead of those which are problem-independent. In this way, we simultaneously liberate algorithm designers from needing to know the details of the problem domains; and prevent them from incorporating additional problem specific information in their algorithms. The efforts need instead to be focused on designing high-level strategies to intelligently combine the provided problem specific algorithmic components. We plan to propose a challenge, based on our framework, where the winners will be those algorithms with a better overall performance across all of the different domains. Using an Olympic metaphor, we are not solely focussed on the 100 meters race, but instead on the decathlon of modern search methodologies.

Calibrating continuous multi-objective heuristics using mixture experiments

A genetic algorithm heuristic that uses multiple rank indicators taken from a number of well established evolutionary algorithms including NSGA-II, IBEA and SPEA2 is developed. It is named Multi-Indicator GA (MIGA). At every iteration, MIGA uses one among the available indicators to select the individuals which will participate as parents in the next iteration. MIGA chooses the indicators according to predefined probabilities found through the analysis of mixture experiments. Mixture experiments are a particular type of experimental design suitable for the calibration of parameters that represent probabilities. Their main output is an explanatory model of algorithm performance as a function of its parameters. By finding the point that provides the maximum we also find good algorithm parameters. To the best of our knowledge, this is the first paper where mixture experiments are used for heuristic tuning. The design of mixture experiments approach allowed the authors to identify and exploit synergy between the different rank indicators. This is demonstrated by our experimental results in which the tuned MIGA compares favorably to other well established algorithms, an uncalibrated multi-indicator algorithm, and a multi-indicator algorithm calibrated using a more conventional approach.