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Future Trends in the Design of Memetic Algorithms: the Case of the Linear Ordering Problem

Lázaro Lugo, Carlos Segura, Gara Miranda

TL;DR

This paper investigates how memetic algorithms for the Linear Ordering Problem (LOP) should adapt as computing power increases. It compares the current leading MA (MA-EDM) with a more intensive variant that uses Iterated Local Search (MA-EDM$ei$) under long-running, HPC-enabled experiments, establishing new Best-Known Solutions on large xLOLIB2 instances up to $n=1000$. The results show that MA-EDM$ei$ can significantly outperform MA-EDM in very long runs and that parallel HPC approaches can achieve substantial speedups, revealing that only intensification-heavy, possibly matheuristic strategies can fully exploit immense compute resources. The study highlights that LOP remains highly challenging at large scales and points to future directions involving deeper intensification, matheuristics, and integrated optimization techniques within evolutionary frameworks to push the frontier further.

Abstract

The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Such has been the case for the Linear Ordering Problem (LOP), a field in which trajectory-based strategies led the way during the 1990s, but which have now been surpassed by memetic schemes.This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions.On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months.Our analyses show that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating.And on the other, the best-known results for today's most challenging set of instances (xLOLIB2) were significantly outperformed. New bounds were established in this benchmark, which provides a new frame of reference for future research.

Future Trends in the Design of Memetic Algorithms: the Case of the Linear Ordering Problem

TL;DR

This paper investigates how memetic algorithms for the Linear Ordering Problem (LOP) should adapt as computing power increases. It compares the current leading MA (MA-EDM) with a more intensive variant that uses Iterated Local Search (MA-EDM) under long-running, HPC-enabled experiments, establishing new Best-Known Solutions on large xLOLIB2 instances up to . The results show that MA-EDM can significantly outperform MA-EDM in very long runs and that parallel HPC approaches can achieve substantial speedups, revealing that only intensification-heavy, possibly matheuristic strategies can fully exploit immense compute resources. The study highlights that LOP remains highly challenging at large scales and points to future directions involving deeper intensification, matheuristics, and integrated optimization techniques within evolutionary frameworks to push the frontier further.

Abstract

The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Such has been the case for the Linear Ordering Problem (LOP), a field in which trajectory-based strategies led the way during the 1990s, but which have now been surpassed by memetic schemes.This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions.On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months.Our analyses show that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating.And on the other, the best-known results for today's most challenging set of instances (xLOLIB2) were significantly outperformed. New bounds were established in this benchmark, which provides a new frame of reference for future research.
Paper Structure (9 sections, 1 equation, 6 figures, 3 tables, 2 algorithms)

This paper contains 9 sections, 1 equation, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Future and Limitations of Memetic Algorithms for the LOP
  3. Using High Performance Computing Environments
  4. Adaptations of MA-EDM to Improve its Long-Term Effectiveness
  5. Experimental Validation
  6. Relative performance between population-based algorithms and trajectory algorithms
  7. Relationship between the scalability and components of MA-EDM
  8. Analysis of performance in the very long-term
  9. Conclusion

Figures (6)

  • Figure 1: Flowchart of the PMA-EDM algorithm
  • Figure 2: Comparative analysis of trajectory-based and population-based algorithms with the stopping criterion set to 192 hours
  • Figure 3: Comparison between MA-EDM and MA-EDM$ei$ with three stopping criteria
  • Figure 4: Comparative analysis of population size in 192-hour runs for MA-EDM and MA-EDM$ei$
  • Figure 5: Comparative performance analysis between PMA-EDM$ei$ and MA-EDM$ei$
  • ...and 1 more figures