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Multi-fidelity constraints in blackbox optimization

Xavier Lebeuf, Stéphane Alarie, Charles Audet, Miguel Diago, Sébastien Le Digabel

TL;DR

This work tackles constrained blackbox optimization with costly evaluations by introducing multi-fidelity feasibility assessments and interruptible direct search via IDS and DIDS. A fidelity controller wraps the blackbox to interrupt infeasible evaluations at low fidelities, guided by an assignment vector that minimizes expected cost, with theoretical guarantees for feasibility preservation. The algorithms are instantiated and validated on concentrated solar power benchmarks, showing substantial improvements in solution quality and cost over a baseline NOMAD run and the Inter-DS approach, particularly for DIDS which exploits intermediary outputs. Overall, the proposed framework enables effective cost reduction in multi-fidelity constrained optimization and provides a path for integrating richer fidelity information into direct-search methods for industrially relevant problems.

Abstract

This work studies constrained blackbox optimization problems that cannot be solved in reasonable time due to prohibitive computational costs. This challenge is especially prevalent in industrial applications, where blackbox evaluations are costly. However, constraints can be evaluated at various fidelities at a lower computational cost. More specifically, this work targets situations in which the infeasibility of each individual constraint can be detected at lower fidelities, and where a large discrete number of fidelities are available. Moreover, highly discontinuous problems which may fail to evaluate are considered, such that direct search methods are preferred to model-based ones. To this effect, the Interruptible Direct Search (IDS) and the Dynamic Interruptible Direct Search (DIDS) algorithms are proposed to leverage feasibility assessments from various fidelity levels to avoid high cost evaluations. The results show highly increased performances from NOMAD when it is paired with IDS or DIDS.

Multi-fidelity constraints in blackbox optimization

TL;DR

This work tackles constrained blackbox optimization with costly evaluations by introducing multi-fidelity feasibility assessments and interruptible direct search via IDS and DIDS. A fidelity controller wraps the blackbox to interrupt infeasible evaluations at low fidelities, guided by an assignment vector that minimizes expected cost, with theoretical guarantees for feasibility preservation. The algorithms are instantiated and validated on concentrated solar power benchmarks, showing substantial improvements in solution quality and cost over a baseline NOMAD run and the Inter-DS approach, particularly for DIDS which exploits intermediary outputs. Overall, the proposed framework enables effective cost reduction in multi-fidelity constrained optimization and provides a path for integrating richer fidelity information into direct-search methods for industrially relevant problems.

Abstract

This work studies constrained blackbox optimization problems that cannot be solved in reasonable time due to prohibitive computational costs. This challenge is especially prevalent in industrial applications, where blackbox evaluations are costly. However, constraints can be evaluated at various fidelities at a lower computational cost. More specifically, this work targets situations in which the infeasibility of each individual constraint can be detected at lower fidelities, and where a large discrete number of fidelities are available. Moreover, highly discontinuous problems which may fail to evaluate are considered, such that direct search methods are preferred to model-based ones. To this effect, the Interruptible Direct Search (IDS) and the Dynamic Interruptible Direct Search (DIDS) algorithms are proposed to leverage feasibility assessments from various fidelity levels to avoid high cost evaluations. The results show highly increased performances from NOMAD when it is paired with IDS or DIDS.
Paper Structure (18 sections, 6 theorems, 20 equations, 9 figures, 4 tables)

This paper contains 18 sections, 6 theorems, 20 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contribution
  4. Organization
  5. Literature review
  6. Algorithmic components
  7. The fidelity controller algorithm
  8. The assignment computation
  9. Theoretical analysis of the assignment problem
  10. Two interruptible direct search algorithms
  11. Interruptible Direct Search ( IDS)
  12. Dynamic Interruptible Direct Search ( DIDS)
  13. Computational results
  14. ${\sf solar 3}$ benchmarks
  15. ${\sf solar 4}$ benchmarks
  16. ...and 3 more sections

Key Result

Lemma 1

When $\text{H}\cap\Omega\neq\varnothing$, for each $j\in J$, $\{r_{ij}\}_{i\in I}$ is monotone increasing with respect to $i$.

Figures (9)

  • Figure 1: Classification of a few multi-fidelity problems with domains of application of IDS and DIDS.
  • Figure 2: Flow chart diagram of the fidelity controller algorithm. The for loop is completed when $\phi$ is greater or equal to the greatest element of $\Phi(a)$, where $a\in I^m$ is the assignment vector.
  • Figure 3: Flow chart diagram showing a particular case of the fidelity controller with the DIDS algorithm and a stochastic blackbox with SAA.
  • Figure 4: Data profiles on Problem ${\sf solar 3}$ with 20 different problem instances.
  • Figure 5: Occurrence (%) of last used fidelities in ${\sf solar 3}$ evaluations.
  • ...and 4 more figures

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Lemma 4
  • proof
  • ...and 4 more