Local Optima Networks of the Permutation Flow-Shop Problem

International audienceThis article extracts and analyzes local optima networks for the permutation flow-shop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this problem is also analyzed. In particular, we study the correlation between local optima network features and the performance of an iterated local search heuristic. Our analysis reveals that network features can explain and predict problem difficulty. The evidence confirms the superiority of the insertion operator for this problem

On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Multiprocessor task scheduling in multistage hyrid flowshops: a genetic algorithm approach

This paper considers multiprocessor task scheduling in a multistage hybrid flow-shop environment. The objective is to minimize the make-span, that is, the completion time of all the tasks in the last stage. This problem is of practical interest in the textile and process industries. A genetic algorithm (GA) is developed to solve the problem. The GA is tested against a lower bound from the literature as well as against heuristic rules on a test bed comprising 400 problems with up to 100 jobs, 10 stages, and with up to five processors on each stage. For small problems, solutions found by the GA are compared to optimal solutions, which are obtained by total enumeration. For larger problems, optimum solutions are estimated by a statistical prediction technique. Computational results show that the GA is both effective and efficient for the current problem. Test problems are provided in a web site at www.benchmark.ibu.edu.tr/mpt-h; fsp

Multi-layer local optima networks for the analysis of advanced local search-based algorithms

A Local Optima Network (LON) is a graph model that compresses the fitness landscape of a particular combinatorial optimization problem based on a specific neighborhood operator and a local search algorithm. Determining which and how landscape features affect the effectiveness of search algorithms is relevant for both predicting their performance and improving the design process. This paper proposes the concept of multi-layer LONs as well as a methodology to explore these models aiming at extracting metrics for fitness landscape analysis. Constructing such models, extracting and analyzing their metrics are the preliminary steps into the direction of extending the study on single neighborhood operator heuristics to more sophisticated ones that use multiple operators. Therefore, in the present paper we investigate a twolayer LON obtained from instances of a combinatorial problem using bitflip and swap operators. First, we enumerate instances of NK-landscape model and use the hill climbing heuristic to build the corresponding LONs. Then, using LON metrics, we analyze how efficiently the search might be when combining both strategies. The experiments show promising results and demonstrate the ability of multi-layer LONs to provide useful information that could be used for in metaheuristics based on multiple operators such as Variable Neighborhood Search.Comment: Accepted in GECCO202

Local Optima Networks for the Permutation Flowshop Scheduling Problem: Makespan vs. Total Flow Time

Local Optima Networks were proposed to understand the structure of combinatorial landscapes at a coarse-grained level. We consider a compressed variant of such networks with features that are meaningful for the study of search difficulty in the context of local search. In particular, we investigate different landscapes of the Permutation Flowshop Scheduling Problem. The insert and 2-exchange neighbourhoods are considered, and two different objective functions are taken into account: the makespan and the total flow time. The aim is to analyse the network features in order to find differences between the landscape structures, giving insights about which features impact algorithm performance. We evaluate the correlation between landscape properties and the performance of an Iterated Local Search algorithm. Visualisation of the network structure is also given, where evident differences between the makespan and total flow time are observed

NILS: a Neutrality-based Iterated Local Search and its application to Flowshop Scheduling

This paper presents a new methodology that exploits specific characteristics from the fitness landscape. In particular, we are interested in the property of neutrality, that deals with the fact that the same fitness value is assigned to numerous solutions from the search space. Many combinatorial optimization problems share this property, that is generally very inhibiting for local search algorithms. A neutrality-based iterated local search, that allows neutral walks to move on the plateaus, is proposed and experimented on a permutation flowshop scheduling problem with the aim of minimizing the makespan. Our experiments show that the proposed approach is able to find improving solutions compared with a classical iterated local search. Moreover, the tradeoff between the exploitation of neutrality and the exploration of new parts of the search space is deeply analyzed

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Mixed integer programming and adaptive problem solver learned by landscape analysis for clinical laboratory scheduling

This paper attempts to derive a mathematical formulation for real-practice clinical laboratory scheduling, and to present an adaptive problem solver by leveraging landscape structures. After formulating scheduling of medical tests as a distributed scheduling problem in heterogeneous, flexible job shop environment, we establish a mixed integer programming model to minimize mean test turnaround time. Preliminary landscape analysis sustains that these clinics-orientated scheduling instances are difficult to solve. The search difficulty motivates the design of an adaptive problem solver to reduce repetitive algorithm-tuning work, but with a guaranteed convergence. Yet, under a search strategy, relatedness from exploitation competence to landscape topology is not transparent. Under strategies that impose different-magnitude perturbations, we investigate changes in landscape structure and find that disturbance amplitude, local-global optima connectivity, landscape's ruggedness and plateau size fairly predict strategies' efficacy. Medium-size instances of 100 tasks are easier under smaller-perturbation strategies that lead to smoother landscapes with smaller plateaus. For large-size instances of 200-500 tasks, extant strategies at hand, having either larger or smaller perturbations, face more rugged landscapes with larger plateaus that impede search. Our hypothesis that medium perturbations may generate smoother landscapes with smaller plateaus drives our design of this new strategy and its verification by experiments. Composite neighborhoods managed by meta-Lamarckian learning show beyond average performance, implying reliability when prior knowledge of landscape is unknown

Anatomy of the attraction basins: Breaking with the intuition

olving combinatorial optimization problems efficiently requires the development of algorithms that consider the specific properties of the problems. In this sense, local search algorithms are designed over a neighborhood structure that partially accounts for these properties. Considering a neighborhood, the space is usually interpreted as a natural landscape, with valleys and mountains. Under this perception, it is commonly believed that, if maximizing, the solutions located in the slopes of the same mountain belong to the same attraction basin, with the peaks of the mountains being the local optima. Unfortunately, this is a widespread erroneous visualization of a combinatorial landscape. Thus, our aim is to clarify this aspect, providing a detailed analysis of, first, the existence of plateaus where the local optima are involved, and second, the properties that define the topology of the attraction basins, picturing a reliable visualization of the landscapes. Some of the features explored in this article have never been examined before. Hence, new findings about the structure of the attraction basins are shown. The study is focused on instances of permutation-based combinatorial optimization problems considering the 2-exchange and the insert neighborhoods. As a consequence of this work, we break away from the extended belief about the anatomy of attraction basins