Elsevier

Parallel Computing

Volume 103, June 2021, 102755
Parallel Computing

Speedup vs. quality: Asynchronous and cluster-based distributed adaptive genetic algorithms for ordered problems

https://doi.org/10.1016/j.parco.2021.102755Get rights and content

Abstract

While the main motivation for Parallel Genetic Algorithms (PGAs) has been to improve the scalability of Genetic Algorithms (GAs), techniques and strategies for maintaining population diversity is an equally active research topic. Island Model Genetic Algorithms (IMGAs) represent one of the most mature strategies for developing PGAs in an effective and scalable manner. However, identifying how much migration and which individuals should migrate are open research problems. Meanwhile, recent developments in Adaptive Genetic Algorithms (AGAs) have led to techniques for monitoring and maintaining population diversity in an online manner. The aim of the present work is to introduce adaptive techniques and mechanisms into PGAs in order to determine when, how much and which individuals are most suitable for migration. We present a number of adaptive PGAs that aim to maintain diversity and maximise coverage of the solution space by minimising the overlap between islands. PGAs presented in this work are empirically assessed for their abilities in scalability, ability to find good quality solutions and maintain population diversity in ordered problems. These metrics are compared to existing adaptive and parallel GAs selected from the literature for their performance. We estimated the overhead costs of monitoring diversity and communication would result in a trade off between scalability and search capabilities. Our results suggest that an asynchronous adaptive PGA has the greatest speedup potential. However, while localising adaptive populations by k-means clustering is less scalable, results indicate that the method is more effective at directing the search in order to reduce the likelihood of islands searching in the same areas of the solution space. For this reason, an adaptive PGA with clustering-based migration demonstrates greater potential in solution quality while maintaining good speedup performance.

Introduction

Solving a combinatorial optimisation problem is the process of finding the optimal solution within a finite set of possible solutions. In many instances, this set of possible solutions is too large for exhaustive search. These problems can be further complicated through introducing constraints in order to restrict the set of valid solutions. The travelling salesman problem (TSP), capacitated vehicle routing problem (CVRP) and the job-shop scheduling problem (JSP) can be considered as unique from general optimisation problems due to the ordering constraints that valid solutions must adhere to [1], [2]. Both the TSP and CVRP are problems derived from applications in planning and logistics while JSP is a scheduling problem often encountered in manufacturing. All three problems are NP-hard combinatorial optimisation problems that are encountered daily in many industries. In practice, industries require a solution that balances the trade off between solution quality and the time taken to find the solution. Innovations in computing architecture have created opportunities for improving performance of existing approaches to scale distributed and parallel genetic algorithms (GAs) to more effectively find good quality solutions within a reasonable time-frame.

GAs are heuristic approaches to solving combinatorial optimisation problems. Inspired by Darwinian theory of evolution, GAs aim to combine known good performing solutions in an effort to improve its known solutions. While this iterative process has been demonstrated for finding good quality solutions to real-world problems [3], a GA’s performance is highly dependent on its ability to effectively balance between exploring the solution space and exploiting its known solutions [4]. Exploration is critical for a GA as a global search of the solution space for where the global optimum may. Meanwhile, exploitation focuses on the local search in order to do incremental improvements on the known optima. However, as the GA continually selects high performing individuals from each generation, it is possible that a population becomes too homogeneous that the GA is effectively unable to conduct any further local search. This phenomenon is known as convergence and if the global optimum has not yet been found, the GA is considered to have prematurely converged. In order to prevent premature convergence, it is critical for a GA to maintain a healthy level of population diversity.

Two common methods for maintaining population diversity are adaptive GAs and multi-population GAs [5], [6]. Adaptive GAs monitor the state of the population and aim to inject diversity when it is necessary. While common methods of measuring population diversity include measuring the Euclidean distance or Hamming distance between individuals of a population, previous works have demonstrated how these methods are not suitable for the constraints of ordered problems [1], [2], [7]. Furthermore, development of strategies for applying these feedback mechanisms to actively manage population diversity in an online manner is an active research topic.

Alternatively, multi-population parallel GAs manage multiple populations of solutions with diversity being maintained by migrating solutions from one population to another [8]. This has led to a number of approaches such as the Island Model Genetic Algorithm (IMGA) which has demonstrated high scalability and efficiency [9], [10], [11]. Where diversity maintenance is explicitly the focus of adaptive GAs, parallel GAs aim to improve scalability and use those mechanisms to improve diversity. However, few works investigate how the characteristics of these approaches can be complementary to one another. With the aim of addressing open research problems of parallel GAs with adaptive mechanisms, we present the following research questions:

  • RQ1

    How many and which individuals should migrate to an island to sufficiently improve its diversity?

  • RQ2

    How can the cost of communication between islands be reduced during migration?

  • RQ3

    How can a GA be encouraged to concurrently search in different areas of the solution space?

RQ1 aims to determine how much diversity is needed to be injected into a population as well as outlining a process on how the most appropriate individuals from a set of solutions can be selected. RQ2 looks at the cost of communication between islands during the migration process and how these can be reduced using a master–slave hybrid IMGA and asynchronous migration. Finally, RQ3 aims to determine how each of the islands can be guided to search in different areas of the solution space to minimise the amount of overlap in the search process.

In our preliminary work [7], we identified a number of adaptive mechanisms that improved an IMGA’s performance. These included mechanisms for determining when to initiate migration, how much migration an island needs and selecting individuals for migration that contribute the most to the target island’s fitness and diversity. However, while these features allow the IMGA to maintain population diversity within its islands, the proposed adaptive PGAs presented two weaknesses: its synchronous approach to migration and its inability to effectively prevent islands from searching in the same areas. The synchronous approach to migration results in islands interrupting their evolutionary process in order to conduct migration. This resulted in inefficiencies from the islands stopping their evolution in order to process migration even when it was unnecessary. Furthermore, as each island tries to maintain its own balance between exploration and exploitation, the likelihood of islands beginning to converge on the same cluster of local optima increased in later generations. This overlap in search by multiple islands results in inefficiencies in the global search as demonstrated in Fig. 1. While each island itself can have a diverse population, the lack of diversity between the islands themselves results with the islands converging (Fig. 1(a)) and potentially missing areas where the global optima could reside. An ideal distribution of islands (Fig. 1(b)) would minimise the overlap between islands in order to maximise the efficiencies of the global search.

Our Contributions. In this paper we present two methods that aim to address the inefficiencies in communication and global search of the LCSB-AGA based IMGA through asynchronous migration and clustering. Our asynchronous approach demonstrates improvements to speed-up and scalability over our previous work which allows it to find better solutions through more efficient search. By implementing asynchronous migration, we demonstrate how the adaptive migration benefits can be introduced to an IMGA while minimising the wait times during the migration stages leading to improved performance in speed-up. Our second approach localises each island’s population through K-means clustering. Furthermore, by implementing adaptive mechanisms to the clustering-based migration process, the adaptive IMGA is able to more accurately measure when migration is necessary. By combining adaptive migration, adaptive diversity maintenance and K-means clustering, these mechanisms of the LCSB-AGA enables each island to continue further exploration in a more focused manner where a clustering-based IMGA would usually result in early convergence. These approaches are benchmarked against existing adaptive and parallel GAs across a variety of instances from the TSP, CVRP and JSP libraries.

The remainder of this paper is organised as follows. In Section 2 we discuss the underlying technologies of AGAs and PGAs. Section 3 presents our approach to introducing adaptive mechanisms for PGAs that improves on communication and minimising overlap of islands by exploiting the tendency for solutions to converge on local optima. The experiment settings are outlined n Section 4 with the results analysis in Section 5. Finally, a discussion and conclusions are drawn in Section 6.

Section snippets

Preliminaries

GAs delay convergence by maintaining population diversity but IMGAs risk exploring solutions that have already been found by other islands. This can be considered as the efficiency of an IMGA in searching the solution space. However, in order to successfully find the global optimum, GAs must also maintain a balance between exploring the global solution space and exploiting known good solutions to conduct local search. The difficultly of this is highlighted in studies of the fitness landscape.

Our approach

The LCSB-AGA [1] is an adaptive GA that maintains population diversity by managing the diversity between an exploration and an exploitation sub-population. Diversity is measured as the sequence-wise similarity of individuals using the longest common subsequence (LCS). This allows for the GA to take into consideration the effects of the constraints and characteristics of ordered problems when considering the similarities and differences between solutions. The LCS Based Adaptive Island Model

Experiments

A range of instances from the travelling salesman problem (TSP), capacitated vehicle routing problem (CVRP) and the job-shop scheduling problem (JSP) were selected according to their diversity in problem size and their ordered nature. The TSP is generalised optimisation problem where a salesman is required to visit N cities with the objective to minimise the total distance travelled. The main constraint for this problem is the ordered nature of the sequence in that no city can be visited twice

Results

In this section, we present and analyse the results of the experiments. In order to thoroughly investigate the characteristics of the different approaches, we consider the scalability of each approach by measuring its speedup, their ability to find good quality solutions, and their ability to maintain population diversity both within the island population and globally. By analysing these three aspects, we aim to determine the success of each GA’s approach in directing the islands to search

Conclusion and future work

In this paper we proposed three new adaptive parallel genetic algorithms (PGAs) in order to investigate the relationship and effects of scalability, adaptive migration and clustered migration on a PGA’s search capabilities. Through empirical tests and analysis, we find that applying adaptive mechanisms can greatly increase the performance of a PGA without negatively affecting its speedup. Furthermore, we determined that the reduced communication costs of asynchronous adaptive migration allows

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ryoma Ohira is a final year Ph.D. candidate at the School of Information and Communication Technology, Griffith University, Australia. He completed his Bachelor of Information Technology with Honours from Griffith University in 2017. His current research interests include online optimisation, evolutionary computation, artificial intelligence and deep learning.

References (33)

  • WhitleyD. et al.

    The Island model genetic algorithm: On separability, population size and convergence

    J. Comput. Inf. Technol.

    (1999)
  • J.I. Hidalgo, J. Lanchares, F. Fernández de Vega, D. Lombraña, Is the Island model fault tolerant? in: The Genetic and...
  • R. Hashimoto, H. Ishibuchi, N. Masuyama, Y. Nojima, Analysis of evolutionary multi-tasking as an Island model, in:...
  • da SilveiraL.A. et al.

    Parallel Island Model Genetic Algorithms applied in NP-Hard problems

  • ReevesC.R.

    Landscapes, operators and heuristic search

    Ann. Oper. Res.

    (1999)
  • OchoaG. et al.

    Deconstructing the big valley search space hypothesis

  • Cited by (5)

    • On the behavior of parallel island models

      2023, Applied Soft Computing
    • Personalized Recommendation of Educational Resource Information Based on Adaptive Genetic Algorithm

      2023, International Journal of Reliability, Quality and Safety Engineering
    • Research on Multi-objective Shortest Path Based on Genetic Algorithm

      2022, Proceedings - 2022 2nd International Conference on Computer Science and Blockchain, CCSB 2022

    Ryoma Ohira is a final year Ph.D. candidate at the School of Information and Communication Technology, Griffith University, Australia. He completed his Bachelor of Information Technology with Honours from Griffith University in 2017. His current research interests include online optimisation, evolutionary computation, artificial intelligence and deep learning.

    Md. Saiful Islam is a Lecturer at the School of Information and Communication Technology, Griffith University, Australia. He has finished his Ph.D. in Computer Science and Software Engineering from Swinburne University of Technology, Australia, in February 2014. He has received his B.Sc. (Hons) and MS degree in Computer Science and Engineering from University of Dhaka, Bangladesh, in 2005 and 2007, respectively. His current research interests are in the areas of database usability, spatial data management, artificial intelligence and big data analytics.

    Humayun Kayesh is a final year Ph.D. candidate at the School of Information and Communication Technology, Griffith University, Australia. He completed his M.Sc. in Advanced Computer Science and IT Management from The University of Manchester in 2017. His current research interests include natural language processing, causality, social media analytics, conversational AI and deep learning.

    View full text