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From Feasible to Practical: Pareto-Optimal Synthesis Planning

Friedrich Hastedt, Dongda Zhang, Antonio del Rio Chanona

arXiv:2605.07521v2cs.AI

TL;DR

Retrosynthesis planning often focuses on finding a single feasible route, although chemists may need to balance economic, sustainability, and other objectives. MORetro∗ searches for Pareto fronts using scalarization and informed sampling, and reports improved front quality and diversity across datasets and single-step models while largely preserving success rates.

  • Problem

    Retrosynthesis search must navigate many possible transformations, and finding routes that also optimize economic and sustainability costs is challenging.

    Source: §1 · p. 1

  • Method

    MORetro∗ uses weight scalarization and Bayesian optimization-informed sampling to search for Pareto fronts under user-defined objectives, with optimality bounds for a fixed single-step model.

    Source: §1 · pp. 1–2, §6 · p. 9

  • Results

    Across multiple datasets and single-step models, MORetro∗ improves Pareto-front quality and chemical diversity over single-objective and fixed-weight baselines while largely preserving success rates.

    Source: §6 · p. 9

  • Takeaways & Limitations

    By incorporating practical objectives into planning, MORetro∗ offers a flexible foundation for decision-making and scale-up of industrial chemical synthesis.

    Source: §6 · p. 9

    MORetro∗ assumes additive reaction costs, its practical heuristics are not provably admissible, and the study fixes the number of Pareto objectives at three.

    Source: §5 · p. 9

Abstract

from arXiv · show

Current computer-aided synthesis planning (CASP) methods often treat retrosynthesis as solved once a single feasible route is identified, focusing primarily on convergence or shortest-path metrics. This view is misaligned with real-world practice, where chemists must balance competing objectives such as cost, sustainability, toxicity, and overall yield. To address this, we formulate synthesis planning as a multi-objective search problem and introduce MORetro*, an algorithm that generates a Pareto front of synthesis routes to explicitly capture trade-offs among user-defined criteria. MORetro* uses weighted scalarization and BO-informed sampling to efficiently navigate the combinatorial search space and prioritize promising trade-offs. Building on multi-objective A*-search, we provide optimality guarantees showing that, for a fixed single-step model, MORetro* recovers the true Pareto front under admissibility. Across multiple retrosynthesis benchmarks, MORetro* produces diverse, high-quality Pareto fronts, uncovering solutions overlooked by single-objective approaches and better aligning CASP outputs with industrial decision-making.

1. Introduction

Retrosynthesis seeks routes from target molecules to commercially available building blocks, but the search becomes harder when routes must also optimize economic and sustainability costs. MORetro∗ searches for Pareto-optimal routes across user-defined objectives, combining weight sampling with optimality bounds and practical reaction objectives.

1. Introduction

  • Finding a route is difficult because each intermediate could lead to hundreds of transformations, and optimizing economic and sustainability costs adds further complexity.Chemists may need diverse pathways to match personal financial and sustainability interests.Source: §1 · p. 1
  • Separating route generation from post-hoc objective analysis can cause promising synthesis routes to be missed.Post-hoc analysis may also add relevant reaction conditions such as temperature and agents.Source: §1 · p. 1
  • MORetro∗ extends single-objective Retro∗ through weight-based scalarization and weight-sampling strategies to explore the high-dimensional objective space.A lower bound supports Pareto-optimality guarantees and early pruning of dominated intermediate molecules.Source: §1 · p. 2
  • MORetro∗ incorporates predicted reaction conditions, including temperature and reagents, to define and optimize industrially relevant sustainability and scalability objectives.The objectives also include toxicity, sustainability, and scale-up potential.Source: §1 · p. 2
  • MORetro∗ returns Pareto fronts for arbitrary numbers of user-defined objectives and outperforms single-objective baselines in front quality and diversity, independent of the single-step model.The approach uses weight scalarization and sampling.Source: §1 · p. 2
  • The method derives optimality bounds that guarantee recovery of all Pareto-optimal routes for a given single-step model.The guarantee is conditioned on the fixed single-step model.Source: §1 · p. 2

2. Background

Prior synthesis-planning work largely targets finding a valid route, while multi-objective retrosynthesis and Pareto-optimal search raise distinct coverage and graph-structure challenges. The paper frames planning over AND-OR graphs and additive route costs, with routes ending in commercially available building blocks.

2.1. Related Work

  • Earlier retrosynthesis methods primarily seek any valid route; MO-MCTS introduced multi-objective planning but lacks Pareto-optimality guarantees and systematic front coverage.The paper notes that direct comparison is difficult because the original MO-MCTS concerns terminal objectives.Source: §2.1 · pp. 2–3
  • Multi-objective path-search methods such as NAMOA∗ handle standard OR graphs, whereas retrosynthesis AND-OR graphs require all reactant children of a reaction node to be solved jointly.The paper introduces an AND-OR pruning mechanism generalizing NAMOA∗-style admissibility.Source: §2.1 · p. 3
  • Retrosynthesis objectives can use predicted reaction conditions to assess greenness, toxicity, and sustainability, while prices and separability metrics inform scale-up and economic feasibility.The passage also identifies route length and building-block count as simpler objectives.Source: §2.1 · p. 3

2.2. Problem Setting

  • The single-step predictor proposes reactant sets and transformation rules, and a condition predictor augments each reaction with reagents and temperature.Molecules are OR nodes, while reactions are AND nodes requiring all reactants to be solved.Source: §2.2 · p. 3
  • A valid synthesis route ends when all terminal reactants are commercially available building blocks; route cost is the sum of its reaction costs, and Pareto optimality is defined by component-wise non-domination.The objective vector has a non-negative cost for each dimension.Source: §2.2 · p. 3

3. Methods

MORetro* extends Retro* to multi-objective retrosynthesis using vector-valued costs and weight-scalarized searches over a shared search graph. It combines practical reaction objectives and weight-sampling strategies with a bound-based guarantee for Pareto-front recovery and safe pruning.

3.1. A∗Search for Multi-Objective Synthesis Planning

  • The A* formulation combines path cost with estimated future synthesis cost, using objective-specific reaction costs and heuristic estimates for each molecule.The heuristic estimates molecule synthesis cost independently of the current search graph, while the reaction number conditions that estimate on reactions already in the graph.Source: §3.1 · pp. 3–4

3.2. Overview of MORetro∗

  • MORetro* runs separate scalarized searches for sampled weight vectors over a shared AND-OR DAG, where molecules are OR nodes and reactions are AND nodes.The graph is directed and acyclic; weights are periodically resampled, and the search returns the accumulated Pareto front.Source: §3.2 · pp. 4–5

3.3. Weight Sampling Strategies

  • After a grid or Sobol warm-up, solution-informed Bayesian optimization samples weights to maximize expected information gain from observed hypervolume improvements.For batch sampling, the method uses GIBBON, which approximates joint information gain while promoting diversity.Source: §3.3 · pp. 5–6

3.4. Proposed Objectives for Synthesis Planning

  • The proposed objectives measure sustainability, toxicity, and scale-up potential, while an additional guiding objective steers search toward purchasable building blocks but is excluded from Pareto analysis.Sustainability combines reaction temperature and atom economy; toxicity accounts for catalyst and solvent hazards; scale-up potential uses the product–reactant logP difference as a proxy for separability.Source: §3.4 · p. 6

3.5. Optimality Guarantee for the Pareto Front

  • Under the stated lower-bound, feasible-route, and termination conditions, the search returns the true Pareto front and can safely prune unexpanded molecules that cannot belong to one.Relaxing bound dominance to ε-dominance gives a guarantee of recovering the ε-Pareto front.Source: §3.5 · p. 6

4. Experiments

The experiments compare MORetro* with single-objective and fixed-weight baselines across datasets and single-step models. On USPTO-190, MORetro* improves Pareto-front quality and diversity, largely preserves success rates, and can reduce search through Vbound pruning.

4.2. Results

  • MORetro* improves HV by approximately 5–8% over Retro* and Fixed, with all HV improvements statistically significant (p < 0.01).It also produces the largest average number of unique Pareto-optimal routes.Source: Table 1 · p. 7, §4.2 · p. 8

4.1. Experimental Setup

  • The evaluation uses USPTO-190, Pistachio-reachable, and ChEMBL targets, with template-based and template-free single-step models.Three single-step models are evaluated; all methods receive a budget of 300 single-step expansions and use building blocks from eMolecules.Source: §4.1 · p. 7

4.2. Results

  • Pareto-front quality is assessed primarily with HV and R2, while dominance coverage measures how many baseline or MORetro* solutions are dominated.Higher HV and lower R2 indicate better performance under the stated evaluation; molecules without a route are excluded from R2 analysis.Source: §4.2 · pp. 7–8
  • MORetro* fails on only 2–3 more of 190 targets than Retro*, while Fixed solves up to 25% fewer targets.MORetro* adaptively samples weights, while Fixed assigns a constant guidance weight of 0.4.Source: Table 2 · p. 8, §4.2 · p. 8
  • MORetro* consistently achieves higher chemical diversity than both baselines, measured using route-pair dissimilarity and the fraction of pairs exceeding 0.5 dissimilarity.The comparison uses average maximum dissimilarity and diversity fraction.Source: Table 3 · p. 8, §4.2 · p. 8
  • Exact Vbound pruning reduces the search space by an average of 54%, while ε-Vbound reduces it by 60% on average.With exact Vbound, 21% of molecules have 90% of open nodes pruned; ε-Vbound certifies ε-PFs without PF-quality deterioration for 32 molecules, using 265 single-step calls on average.Source: Table 4 · p. 9, §4.2 · p. 9
  • BO sampling outperforms Sobol across Pareto-front quality, success rate, and diversity; against grid sampling, its gains vary across experiments.BO shows clear HV and success-rate gains in two experiments and comparable performance in the others.Source: §4.2 · p. 9

5. Limitations and Future Outlook

MORetro* is currently limited to additive reaction costs and three Pareto objectives; the authors identify objective robustness, chemical accuracy, and the success-rate gap as areas for future work.

5. Limitations and Future Outlook

  • The additive-cost assumption limits objectives to those decomposable per reaction or molecule.The study fixes the number of Pareto objectives at three and identifies scaling to more diverse objectives as future work.Source: §5 · p. 9
  • Practical heuristics are not provably admissible, so the pruning bound falls back to zero and reduces pruning efficiency.Constructing tight admissible lower bounds remains an open challenge.Source: §5 · p. 9
  • Broader industrial adoption will require work on objective robustness and chemical accuracy, while adaptive strategies may address the remaining success-rate gap to single-objective search.Source: §5 · p. 9

6. Conclusion

MORetro* combines weight scalarization with Bayesian optimization-informed sampling to recover high-quality Pareto fronts under a fixed expansion budget. The study reports improved front quality and chemical diversity across datasets and single-step models, while largely preserving success rates.

6. Conclusion

  • Across multiple datasets and single-step models, MORetro* improves Pareto-front quality and chemical diversity over single-objective and fixed-weight baselines while largely preserving success rates.The conclusion frames the approach as a foundation for decision-making, discovery, and industrial synthesis scale-up.Source: §6 · p. 9

A. Single-Step Retrosynthesis and Condition Prediction Models

B. Proof of Theorem 3.4

The proof establishes that the multi-objective algorithm returns the true Pareto front when it terminates under the bound-dominance criterion. Its admissibility argument extends the single-objective Retro* lower-bound reasoning component-wise to multiple objectives.

B. Proof of Theorem 3.4

B.1. Connection to single-objective Retro*

  • In single-objective Retro*, an admissible heuristic guarantees an optimal solution and makes the route cost estimate a lower bound for routes through a molecule [Chen et al., 2020].Source: §B.1 · p. 13

B.2. Multi-objective admissibility of Vbound

  • The multi-objective bound is component-wise admissible: frontier estimates are admissible by assumption, and recursive computation extends that property through the search graph.Source: §B.2 · p. 13

B.3. Proof of Theorem 3.4

The proof establishes soundness and completeness of the discovered Pareto front using a component-wise admissible bound. The accompanying appendices define the objectives and describe the search and weight-sampling procedures.

B.3. Proof of Theorem 3.4

  • Completeness follows because any undiscovered Pareto-optimal route would be dominated by a discovered route under the termination bound, contradicting its Pareto optimality.The proof also states that explicitly constructed, non-dominated routes are Pareto-optimal.Source: §B.3 · p. 14

C. Objective Functions

  • The objectives include sustainability from temperature and atom economy, toxicity from hazardous agents, and scale-up costs informed by separation difficulty and predicted molecule prices.The SAScore is used as a proxy for remaining reactions toward building blocks; the guidance cost uses single-step reaction likelihood.Source: C. Objective Functions · pp. 14–16

D. Search Hyperparameters

  • The single-step retrosynthesis model returns K = 25 candidate reactions per molecule, except for PDVN where K = 50, and the reaction condition predictor proposes two likely conditions per reaction.Source: D. Search Hyperparameters · p. 16

D.1. Bayesian Optimization.

  • Bayesian optimization begins with weights emphasizing guidance, then selects batches from refined-grid or Sobol candidates; age-dependent utility decay discourages repeated sampling near weights that no longer improve the front.The warm-up retains weights with guidance weight at least 0.5.Source: §D.1 · pp. 16–17

D.2. Grid Sampling

  • Grid sampling draws weight vectors from a coarse grid over the objective simplex at resolution 0.33.The grid strategy uses a weight-iteration budget of 16 and five parallel weights per iteration.Source: §D.2 · p. 17

D.3. Sobol (Random)

  • Sobol sampling draws weights from a Sobol sequence, with 32 samples plus four extreme points and five parallel weights per iteration.Its weight-iteration budget is 10.Source: §D.3 · p. 17

E.1. Diverse Datasets

This section extends evaluation to ChEMBL and Pistachio-reachable datasets using G2E and NeuralSym models. It presents comparisons of multi-objective performance, success rate, chemical diversity, and per-molecule unique solutions.

E.1. Diverse Datasets

  • The evaluation also tests G2E and NeuralSym on the ChEMBL and Pistachio-reachable datasets.Findings are presented in the referenced tables, but their values are not supplied here.Source: §E.1 · p. 18
  • The ChEMBL and Pistachio-reachable evaluations cover multi-objective performance, success rate, and chemical diversity, with Table 5 also spanning three single-step models.The supplied passages identify the comparison scope but do not provide table values.Source: Table 5 · p. 18, Table 6 · p. 18, Table 7 · p. 18
  • MORetro* with BO sampling is compared against Fixed and single-objective Retro* baselines.The passage does not state which method performs better.Source: §E.1 · p. 18
  • Figure 6 reports per-molecule normalized numbers of unique solutions across all investigated datasets.The caption does not specify comparative outcomes.Source: Figure 6 · p. 18

E.2.1. RESULTS FOR ADDITIONAL (FIXED) WEIGHTS

This merged section reports additional fixed-weight results, compares sampling strategies, and describes the reward adaptation used for MO-MCTS with additive objectives.

E.2.1. RESULTS FOR ADDITIONAL (FIXED) WEIGHTS

  • Table 8 reports additional USPTO-190 fixed-weight results, including hypervolume mean ± standard deviation and front-dominance percentages.Each weight vector fixes scalarization coefficients for four objectives; the table caption defines Baseline Dom. and Self Dom. as percentages of one front dominated by the other.Source: Table 8 · p. 19

E.2.2. IMPACT OF SAMPLING STRATEGIES

  • Sampling strategies are compared on success rate and Pareto-front quality, with Table 9 R2 calculations excluding molecules without solutions across all methods.The excluded molecules differ because the BO comparison uses different methods than the main-body comparison.Source: §E.2.2 · p. 19, Table 9 · p. 19, Table 10 · p. 20

E.3.2. PRELIMINARY RESULTS

The preliminary comparison finds the MO-MCTS re-implementation is not competitive under a fixed budget, while the following toxicity prompt specifies a structured assessment procedure.

E.3.2. PRELIMINARY RESULTS

  • Under the fixed budget NB = 300, the MO-MCTS re-implementation is not competitive, which the authors attribute to rollout budget drain and high variance when estimating multiple objectives.No hyperparameter tuning was performed for MO-MCTS.Source: §E.3.2 · p. 20, Table 11 · p. 20

F. Toxicity Assessment Prompt Template

  • The task assigns a toxicity score in [0, 1] to a molecular structure given in SMILES notation, using priority-ordered checks: custom reference studies, acute-toxicity data, environmental impact and persistence, then regulatory hazard classifications.Source: F. Toxicity Assessment Prompt Template · p. 21

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