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Adaptive Population-based Simulated Annealing for Uncertain Resource Constrained Job Scheduling

Dhananjay Thiruvady, Su Nguyen, Yuan Sun, Fatemeh Shiri, Nayyar Zaidi, Xiaodong Li

TL;DR

This paper tackles resource constrained job scheduling under uncertainty (RCJSU) in mining supply chains by proposing an adaptive population-based simulated annealing (APSA). APSA combines a small population of solutions, a accelerated Metropolis-Hastings cooling schedule, and adaptive perturbation probabilities to balance exploration and exploitation, aiming to produce robust schedules across multiple uncertainty samples. Empirical results show APSA outperforms state-of-the-art ACS and SACS methods and achieves new best-known solutions on most RCJSU instances, with notable gains on larger, more uncertain problems. The approach yields robust schedules suitable for real-world mining operations and suggests directions for integrating decomposition techniques to provide solution bounds in the future.

Abstract

Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating their resources to reduce operational costs. This problem has been previously investigated in the literature as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that cannot be solved efficiently with existing optimisation methods. This study proposes an adaptive population-based simulated annealing algorithm that can overcome the limitations of existing methods for RCJS with uncertainty including the premature convergence, the excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm is designed to effectively balance exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods across a wide range of benchmark RCJS instances and uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.

Adaptive Population-based Simulated Annealing for Uncertain Resource Constrained Job Scheduling

TL;DR

This paper tackles resource constrained job scheduling under uncertainty (RCJSU) in mining supply chains by proposing an adaptive population-based simulated annealing (APSA). APSA combines a small population of solutions, a accelerated Metropolis-Hastings cooling schedule, and adaptive perturbation probabilities to balance exploration and exploitation, aiming to produce robust schedules across multiple uncertainty samples. Empirical results show APSA outperforms state-of-the-art ACS and SACS methods and achieves new best-known solutions on most RCJSU instances, with notable gains on larger, more uncertain problems. The approach yields robust schedules suitable for real-world mining operations and suggests directions for integrating decomposition techniques to provide solution bounds in the future.

Abstract

Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating their resources to reduce operational costs. This problem has been previously investigated in the literature as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that cannot be solved efficiently with existing optimisation methods. This study proposes an adaptive population-based simulated annealing algorithm that can overcome the limitations of existing methods for RCJS with uncertainty including the premature convergence, the excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm is designed to effectively balance exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods across a wide range of benchmark RCJS instances and uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.
Paper Structure (19 sections, 1 theorem, 4 equations, 6 figures, 6 tables, 2 algorithms)

This paper contains 19 sections, 1 theorem, 4 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Optimisation techniques for tackling RCJS
  4. Scheduling on problems with uncertainty
  5. Hybrid optimisation methods
  6. Problem Formulation
  7. Population-based Simulated Annealing
  8. The APSA Algorithm
  9. The Metropolis-Hastings Algorithm
  10. Adaptive Perturbation
  11. Convergence of Probabilities
  12. Scheduling Heuristic
  13. Experimental Setting
  14. Results
  15. Convergence Characteristics of APSA
  16. ...and 4 more sections

Key Result

Theorem 1

For any initial condition of $p_b^0$, $p_j^0$, $p_r^0 \in [0,1]$ and $p_b^0 + p_j^0 + p_r^0 = 1$, the probability values converge to $p_b = p_j = p_r = 1/3$.

Figures (6)

  • Figure 1: An example that demonstrates $\beta$-sampling. From the sequence $\pi$, a subset of jobs is selected (7, 9, 10, 3, 11) and moved to the end of the sequence.
  • Figure 2: An example that demonstrates job swapping. Two indices are selected randomly, and the corresponding jobs are swapped. In this example, indices 3 and 9 are selected, and the jobs within those indices, 2 and 9, are swapped.
  • Figure 3: Adaptive probabilities over 200 simulations.
  • Figure 4: An example of a problem with three machines and 15 jobs. From $\pi$, jobs are selected in order (left to right) and scheduled on machines that they belong to (e.g. orange jobs on $m_2$). Those jobs that have predecessors that are not yet scheduled will be put on the waiting list $\hat{\pi}$; (a) Job 8 requires Job 2 to be scheduled before it can be scheduled. (b) Job 8 is scheduled once Job 2 has been scheduled, and this will be done as early as possible considering resources.
  • Figure 5: Comparison of ACS, SACS and APSA by uncertainty levels.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof