GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms

GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms Haixu Liu

Lei Zhou

Yuhao Ren

Fudan University Shanghai, China hxliu26@m.fudan.edu.cn

Fudan University Shanghai, China zhoulei26@m.fudan.edu.cn

Fudan University Shanghai, China yhren24@m.fudan.edu.cn

Yumao Wu

Zhiang Wang

Fudan University Shanghai, China yumaowu@fudan.edu.cn

Fudan University Shanghai, China zhiangwang@fudan.edu.cn

arXiv:2608.16733v1 [cs.AR] 17 Aug 2026

Abstract Physical design algorithms operate within tightly coupled, multistage optimization flows, where stage-local gains may vanish or induce downstream degradation. Existing program-evolution frameworks often rely on stage-local objectives or undifferentiated multimetric feedback, which neither guarantee better final results nor identify which unmet requirement should guide the next iteration. We present GoalEvolve, a goal-driven framework that makes physical design algorithm evolution accountable for the final quality of results (QoR) of the complete flow. Given a multi-objective QoR target region, GoalEvolve converts unmet requirements into normalized target gaps, identifies the dominant bottleneck, and uses stage-resolved checkpoint evidence to locate the responsible stage. An LLM-based Teacher then narrows the search to a relevant algorithmic decision and source region, while parallel Student agents implement and validate hypotheses through full-flow evaluation. Local effects, optimization debt, and downstream retention are retained as mechanism evidence for subsequent evolution. Across eight ASAP7 designs, GoalEvolve improves post-route TNS by 30.67% on average and reduces leakage and dynamic power by 21.18% and 9.42% versus default OpenROAD. Relative to commercial-tool goals, it closes 62.20% of the normalized power gap on power-dominant designs, surpasses the TNS goals on both timing-dominant designs, and closes 32.48% of the equal-weight timing–power gap on joint designs. Across all three designs evaluated against Codex goal mode under matched budgets, GoalEvolve further improves TNS by 26.46% while reducing leakage and dynamic power by 12.38% and 0.76%, respectively.

Keywords physical design, electronic design automation, source-code evolution, large language models, post-placement optimization

1

Introduction

Physical design proceeds through a tightly coupled implementation flow consisting of floorplanning, placement, post-placement optimization, routing, and post-routing optimization, in which algorithmic decisions can propagate across stages. A common phenomenon is that an improvement achieved at one stage does not necessarily translate into better final QoR, and may even degrade the design after downstream processing. For example, an aggressive timing

transformation after placement may reduce local violations while increasing congestion, routing detours, or power, ultimately worsening post-route QoR. A stage-level decision is therefore valuable only if it preserves design validity and its benefit persists through the complete flow. This property imposes a stringent requirement on physical design algorithm evolution: optimizing an algorithm for a particular stage must account not only for its immediate objective, but also for its impact on the final multi-objective QoR of the entire implementation flow. The conventional development process follows an algorithm-first paradigm. Researchers typically begin with a perceived weakness, formulate an optimization strategy, implement the corresponding mechanism, and then evaluate the complete flow. This approach is effective when the relationship between the proposed mechanism and the target QoR is well understood. In many design-closure problems, however, the desired outcome is explicit while the algorithmic path toward it remains unclear. Stage logs and intermediate reports provide useful diagnostic evidence, but translating that evidence into the next source-level hypothesis still requires substantial manual analysis and domain expertise. Algorithm development therefore proceeds through repeated cycles of diagnosis, implementation, and validation, without an automated way to derive the next intervention directly from the remaining target gap. LLM agents make repository-scale source-code exploration and modification increasingly practical. General program-evolution systems combine program generation with automated evaluation [12, 15, 16, 20], while recent EDA systems extend this paradigm to logic synthesis and multiple stages of physical design [7, 9, 19, 21]. These studies show that LLM agents can iteratively improve EDA algorithms through execution feedback. Nevertheless, their control logic leaves two issues unresolved in tightly coupled physical design flows. First, when candidate selection is based on the objective of the modified stage, an apparent local gain may be lost or overturned by later stages and thus need not improve the full-flow outcome. Second, multiple reported metrics are often presented without an explicit priority. Such feedback can compare candidates, but does not indicate which remaining target deficit should govern the next source revision. As a result, the agent may alternate among competing objectives or modify mechanisms unrelated to the current bottleneck, leading to an unfocused search and unnecessary full-flow evaluations.

Haixu Liu, Lei Zhou, Yuhao Ren, Yumao Wu, and Zhiang Wang

Figure 1: Comparison of typical EDA evolution and GoalEvolve across three key dimensions. Unlike score-driven selection, GoalEvolve uses the remaining QoR gap to guide source edits and retain mechanism-level evidence. These limitations suggest that physical design algorithm evolution must be accountable for final full-flow QoR rather than for improvements observed only at the stage being modified. Under this full-flow accountability, QoR should serve not merely as a terminal fitness value, but as a control signal that determines what the evolution process should address next. Rather than asking whether a candidate is locally or globally better than its predecessor, the controller should identify the final QoR requirement with the largest unresolved target gap, locate where the gap is introduced or left unrepaired, and focus the next source modification on the corresponding stage and mechanism. This changes multi-objective evolution from an undirected search over aggregate improvements into a target-directed process focused on a specific unresolved finalQoR requirement in each iteration. Figure 1 summarizes this shift from score-driven selection to goal-gap-guided source evolution. Based on this principle, we present GoalEvolve, a goal-driven framework that evolves physical design algorithms toward an explicit multi-objective QoR target region. Given a QoR specification, GoalEvolve converts unmet final-QoR requirements into normalized target gaps: the dominant gap determines what to improve, while stage-resolved checkpoint evidence identifies the responsible stage by showing where the deficiency is introduced or left unrepaired. Guided by this diagnosis, an LLM-based Teacher narrows the search to the relevant algorithmic decision and bounded source region, while parallel Student agents implement and validate hypotheses. Stage contracts relate each candidate’s expected local effect to temporary optimization debt and specify the downstream evidence needed to verify that the benefit persists through the complete flow. Successful and failed experiments are retained as persistent mechanism evidence to refine promising mechanisms and avoid ineffective interventions. The same controller operates across

designs, while each algorithmic path adapts to design-specific targets and observed behavior. GoalEvolve thus provides a reusable methodology for deriving and revising optimization logic from explicit goals and full-flow evidence rather than improving a single optimization algorithm. The main contributions of this work are summarized as follows: • We introduce goal-driven physical design algorithm evolution toward explicit multi-objective QoR regions, formalized as targetset reachability over feasible program variants and evaluated by final full-flow QoR rather than stage-local gains. • We develop a bottleneck-directed loop that identifies the dominant unmet QoR requirement from normalized target gaps, uses stage-resolved checkpoints to locate the responsible stage, and narrows the next intervention to the relevant algorithmic decision and bounded source region. • We establish evidence-constrained hypotheses and persistent mechanism memory, retaining successful and failed experiments to guide subsequent evolution. • We instantiate GoalEvolve for OpenROAD post-placement optimization. Across eight ASAP7 designs, it improves post-route TNS by 30.67% and reduces leakage and dynamic power by 21.18% and 9.42% over default OpenROAD. Against commercial-tool targets, it closes 62.20% of the power gap on power-dominant designs and 32.48% of the joint timing–power gap, while surpassing TNS targets on both timing-dominant designs. Under matched budgets on three designs, it further improves TNS by 26.46% over Codex goal mode. • We will open-source the GoalEvolve implementation and experimental scripts to support reproducibility and future research. The remainder of this paper is organized as follows. Section 2 reviews related work on physical design optimization and LLM-based algorithm evolution. Section 3 presents the GoalEvolve framework for evolving physical design algorithms toward explicit QoR targets and its post-placement instantiation. Section 4 reports the experimental validation, and Section 5 concludes the paper.

2

Background and Related Work

This section traces the progression from expert-driven physical design algorithm development to LLM-based program evolution and repository-scale EDA agents. We first review how representative physical design algorithms rely on domain expertise for development and adaptation, and then examine how evolutionary and agentic systems generate, evaluate, and retain source variants.

2.1

Expert-Driven Algorithm Engineering

Recent physical design algorithms have largely advanced through expert-led revision of optimization models and control logic. RePlAce introduces constraint-oriented local-density penalties and dynamic step-size adaptation, whereas DREAMPlace maps analytical placement to PyTorch tensor operators and custom GPU kernels [4, 11]. Differentiable timing-driven placement models STA propagation as a differentiable computation to optimize TNS and WNS directly, while FusionSizer jointly optimizes cell locations and gate sizes through continuous relaxation [6, 8]. OpenPhySyn organizes physical synthesis transformations into violation-driven repair procedures, whereas CUGR combines a probabilistic resource

GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms

model with three-dimensional routing to improve detailed routability [1, 13]. RL-Sizer formulates sequential gate sizing as reinforcement learning driven by timing rewards, while DAGSizer uses directed timing graphs to predict discrete sizing assignments [3, 14]. Both methods require task-specific model training within predefined sizing spaces. These advances improve physical design optimization, but their development and adaptation still require substantial backend design expertise.

2.2

Agentic AI for Algorithm Evolution

The emergence of LLMs has opened a new path for general algorithm evolution by closing the loop among search-space exploration, code generation, and executable evaluation. FunSearch searches over implementations of a user-specified function within a fixed program scaffold, retains valid programs in island populations, and samples higher-scoring variants for subsequent prompts [16]. AlphaEvolve directly edits code and uses an evolutionary database to select parent programs according to feedback from multiple evaluators [15]. EoH co-evolves natural-language ideas and executable heuristics through fitness-based population updates, whereas ReEvo converts pairwise performance differences into immediate and accumulated reflections that guide crossover and elitist mutation [12, 20]. LLaMEA retains the best algorithm in a singleparent loop and feeds runtime fitness and errors back for mutation or redesign [17]. ShinkaEvolve improves sample efficiency through exploration-aware parent sampling, novelty filtering, and adaptive LLM selection [10]. Together, these systems demonstrate that LLM agents can sustain empirical algorithm evolution through execution feedback and structured retention, providing a practical foundation for extending this paradigm to EDA.

2.3

Agentic EDA and Source Evolution

Building on these advances, Agentic EDA extends program evolution to repository-scale tool development and design-flow optimization. Yao et al. use an LLM genetic flow to evolve three predefined components of global placement, selecting candidates by both placement quality and diversity [19]. AuDoPEDA combines repository graphs with literature-grounded planning to localize OpenROAD edits, then uses hard gates and staged flow evaluation to commit non-regressing patches while returning failures as planning counterexamples [7]. GR-Evolve externalizes router variants and QoR histories as versioned artifacts, then selects among bounded-search candidates using Pareto priorities over downstream routing QoR and runtime [9]. Self-Evolved ABC assigns major synthesis subsystems to specialized agents, while a central planner selects the next subsystem from multidimensional QoR feedback, merges improvements into a champion version, and rolls back regressions [21]. Existing work already uses structured QoR feedback to localize and revise source changes. However, we are not aware of prior work that formalizes the residual to a predefined end-of-flow QoR region as the control signal for assigning stage responsibility and generating the next source-level algorithm hypothesis. GoalEvolve addresses this gap by making the remaining target distance an explicit basis for subsequent evolution.

3

Our Approach

To move beyond algorithm-first development, we introduce GoalEvolve, a framework for goal-driven evolution of physical design algorithms. It couples two feedback loops: an optimization loop that translates the remaining target gap into a bounded source code experiment, and an evidence loop that converts completed experiments into persistent mechanism knowledge. The remaining goal gap therefore acts as an active control signal for deciding what evidence to inspect and which source mechanism to revise, rather than serving only as a terminal score. Figure 2 provides a structural overview, while Algorithm 1 summarizes the corresponding execution loop.

3.1

Goal-Guided Evolution Planning

GoalEvolve evaluates a program variant 𝑝 on a design 𝑑 against design-specific QoR targets. After orienting all metrics to a lower-isbetter form, with |TNS| used for TNS, we define the normalization scale, normalized target violation, and overall goal distance as follows:

𝑠𝑖 (𝑑) = max{|𝑞𝑖 (𝑝 0, 𝑑) − 𝑢𝑖 (𝑑)| , 𝜖𝑖 } ,   𝑞𝑖 (𝑝, 𝑑) − 𝑢𝑖 (𝑑) 𝑟𝑖 (𝑝, 𝑑) = , 𝑠𝑖 (𝑑) + 𝑚 ∑︁ 𝐷 𝐹 (𝑝, 𝑑) = 𝑤𝑖 𝑟𝑖 (𝑝, 𝑑),

(1) (2) (3)

𝑖=1

where [𝑥] + ≡ max(0, 𝑥), 𝑚 denotes the number of selected QoR metrics, and 𝑤𝑖 > 0 is the weight assigned to metric 𝑖. Here, 𝑝 0 denotes the baseline program, 𝑞𝑖 (𝑝, 𝑑) is the QoR value measured by the fixed evaluation flow, and 𝑢𝑖 (𝑑) is the corresponding inclusive upper target bound for design 𝑑. The positive 𝜖𝑖 prevents division by zero when the baseline value equals the target. Consequently, 𝐷 𝐹 (𝑝, 𝑑) = 0 if and only if all selected QoR targets are satisfied. A candidate is deemed goal-compliant only if it also passes all required validity checks. After each round, GoalEvolve identifies the dominant QoR bottleneck from the weighted target gaps and traces it through the white-box checkpoint trajectory. By mapping final metrics to their affecting stages, it compares expected and observed stage effects while accounting for unresolved optimization debt and downstream loss of earlier gains. A compact reflection prompt links the dominant gap to relevant checkpoint and object-level evidence, retrieving supporting artifacts by reference only when needed. This converts the global gap into a focused evidence request for the next source modification. The Teacher retrieves potential mechanisms from three complementary sources. OpenROAD Cards map stage behavior to implementation locations and preservation constraints. Paper Cards translate published methods into implementable mechanisms with expected effects and rejection criteria. Historical records from the Evolutionary Program Database in Section 3.3 help avoid ineffective mechanisms and reconsider promising ones. Guided by the diagnosis and retrieved evidence, the Teacher prioritizes mechanisms most likely to address the responsible stage,

Haixu Liu, Lei Zhou, Yuhao Ren, Yumao Wu, and Zhiang Wang

Figure 2: Overview of GoalEvolve. The Teacher converts QoR gaps and retrieved knowledge into targeted source hypotheses, while parallel Students evaluate candidates through checkpointed full-flow runs. Reviewed outcomes update mechanism evidence and parent selection for subsequent iterations. Algorithm 1 Core execution loop of GoalEvolve. Input: Initial program 𝑝 0 , design 𝑑 , frozen goal 𝐺 , fixed evaluation flow 𝐹 , OpenROAD Cards openroadCards, Paper Cards paperCards, and evaluation budget 𝐵 Output: Best feasible OpenROAD program 𝑝 best Variables: EPD[𝑝 ] stores the evaluation record and mechanism status of program 𝑝 ; pool retains feasible programs across rounds; parent is inherited by the next round, whereas 𝑝 best is the current champion; diagnosis, mechanisms, and hypotheses denote the identified bottleneck, retrieved algorithmic options, and planned branch modifications, respectively; ℎ denotes one hypothesis and child its implementation. 1: EPD ← ∅ 2: EPD[𝑝 0 ] ← Evaluate (𝑝 0 , 𝑑, 𝐹 ) 3: pool ← {𝑝 0 } ; parent ← 𝑝 0 ; 𝑝 best ← 𝑝 0 4: while Remaining (𝐵) and not Satisfy (EPD[𝑝 best ], 𝐺 ) do 5: diagnosis ← Diagnose (EPD[parent ], 𝐺, openroadCards) 6: mechanisms ← Retrieve (diagnosis, paperCards, EPD) 7: hypotheses ← Plan (diagnosis, mechanisms) 8: for all ℎ ∈ hypotheses in parallel do 9: child ← Implement (parent, ℎ) 10: EPD[child ] ← Evaluate (child, 𝑑, 𝐹, EPD[parent ] ) 11: EPD ← Update (EPD, ℎ, child ) 12: pool ← Retain (pool, child, EPD[child ] ) 13: end for 14: 𝑝 best ← Champion (pool, EPD) 15: parent ← Select (𝑝 best , pool, diagnosis, EPD) 16: openroadCards ← Refresh (openroadCards, parent, EPD[parent ] ) 17: end while 18: return 𝑝 best

balancing new exploration with refinement or integration supported by prior evidence. Each hypothesis links a concrete source modification to its expected stage response and final QoR effect, with a rejection criterion for retention. GoalEvolve thereby narrows an unmet QoR target to a responsible stage, candidate mechanism, and source implementation, which together define the next evolution target. Lines 5–7 of Algorithm 1 summarize this diagnosis– retrieval–planning sequence.

3.2

Controlled Evolution and Attribution

GoalEvolve evaluates source hypotheses through four controlled Student branches that start from the same parent version. Two Explorer branches implement distinct new ideas, one Enhancer strengthens a mechanism whose gains are promising but not yet

stable, and one Integrator combines previously validated mechanisms when their source modifications and expected stage effects are compatible. The common parent and evaluation flow provide a consistent reference for attributing each branch outcome to its assigned hypothesis. Within each branch, an LLM coding agent with direct repository access and command execution capabilities implements the assigned hypothesis and builds an isolated tool instance. When compilation fails or another implementation issue arises, the agent autonomously diagnoses the problem and revises the patch within a fixed repair budget, preventing an engineering error from prematurely rejecting the underlying mechanism. GoalEvolve introduces effect–debt analysis, which defines the immediate change in the target QoR metric as the local effect and degradation introduced in other metrics as optimization debt. Both quantities are measured against the common parent after the target stage, while the final comparison measures effect retention and debt repayment. GoalEvolve also tracks object-level netlist changes across checkpoints to identify operations that are later repeated or reversed and therefore require further evolution. These metric and object traces form an evidence signature that binds the source diff to observed behavior for subsequent mechanism selection. Lines 8–13 of Algorithm 1 summarize this controlled evolution-and-attribution process.

3.3

Mechanism Memory and Selection

GoalEvolve builds an Evolutionary Program Database (EPD), which stores all ideas proposed by the Teacher together with an idea tag identifying the optimization target, evaluation records, source patches, and other accumulated feedback. Each record is labeled as validated, promising, pending, or invalid according to its evaluation status and outcome, enabling the EPD to balance exploitation and exploration. For exploitation, compatible validated mechanisms are assigned to the Integrator, while the Enhancer can perform at most 𝐾rep bounded repairs on a promising record. The EPD also

GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms

retains programs based on distinct mechanisms even when they do not achieve the highest current scores, preventing evolution from being confined to a single path. In parallel, Explorers implement and evaluate newly proposed algorithmic ideas with no matching record in the database. Negative evaluation evidence suppresses repeated proposals and updates the contraindications in mechanism cards. As the database grows, compatibility with the responsible stage and current source state first narrows the candidate set, after which the LLM agent reasons over feedback from previous rounds to select the most promising mechanisms for enhancement or integration. The evidence accumulated in the EPD also guides checkpoint inheritance. During regular evolution, sibling experiments inherit the champion 𝑝 ∗ , defined as the feasible checkpoint with the smallest goal distance, while GoalEvolve retains a top-𝐾 portfolio containing 𝑝 ∗ and feasible alternatives from distinct mechanism families. A plateau is detected when the best goal distance fails to improve beyond a preset threshold for several consecutive rounds. GoalEvolve then samples the next parent 𝑐 from this portfolio according to   𝐷 𝐹 (𝑐) − 𝐷 𝐹 (𝑝 ∗ ) 𝑃 𝑗 (𝑐) ∝ exp − (1 + 𝛽𝑁𝑐 )(1 + 𝛾𝐴𝑐 ), 𝑇𝑗

(4)

where 𝑁𝑐 measures mechanism diversity and 𝐴𝑐 measures alignment with the current bottleneck: 𝑁𝑐 = 1 −

ℎ(𝜙𝑐 ) , 𝐻

𝐴𝑐 = 𝑀𝜏𝑏 ,𝜏𝑐 .

(5)

Here, ℎ(𝜙𝑐 ) counts how often the mechanism family 𝜙𝑐 was selected in the previous 𝐻 inheritance decisions. The entry 𝑀𝜏𝑏 ,𝜏𝑐 ∈ [0, 1] of a fixed tag compatibility matrix gives the compatibility between the candidate tag 𝜏𝑐 and the bottleneck tag 𝜏𝑏 , while 𝛽 and 𝛾 weight the diversity and alignment factors. At inheritance iteration 𝑗 after plateau detection, GoalEvolve normalizes 𝑃 𝑗 (𝑐) over the top-𝐾 portfolio and samples one checkpoint. The temperature 𝑇 𝑗 is gradually reduced according to a fixed schedule as 𝑗 increases. The champion is retained throughout this process, allowing GoalEvolve to explore another inheritance path without losing the best program found so far.

3.4

Post-Placement Instantiation

We instantiate GoalEvolve for post-placement timing and power optimization, where gate resizing, buffering, and VT reassignment improve a placed netlist, but routing-extracted RC parasitics may erode these gains. This gap between immediate improvement and downstream retention makes post-placement optimization a representative full-flow case study. All candidates start from the same placed netlist, while timing constraints, technology data, downstream routing, and the final evaluator remain fixed. The editable source scope is limited to Gate Resizer and Restructure mechanisms controlling candidate generation, scoring, scheduling, and commit decisions. The goal contract specifies post-route timing and power targets, while runtime is recorded as an observer metric. White-box telemetry and structural statistics, including buffer growth and VT composition, provide diagnostic evidence. Each full-flow evaluation records checkpoints after power reclaim, timing recovery, and supplemental repair. These observation

contracts expose local effects, optimization debt, and final retention, allowing the Teacher to prioritize the next stage. The initial curriculum applies power reclaim before timing recovery, while power-oriented or timing-oriented restructuring mechanisms become eligible only after cell-level optimization reaches a measured plateau. This instantiation maps GoalEvolve to a concrete source evolution task without imposing this stage sequence on the general framework.

4

Experiments

This section evaluates GoalEvolve’s post-route QoR improvement and progress toward frozen commercial-tool targets across eight ASAP7 designs. We then validate whether these gains arise from evolved source-level mechanisms and examine their transfer across designs. Finally, we compare GoalEvolve with Codex goal mode under matched formal-evaluation budgets and analyze the evolved JPEG mechanisms in detail.

4.1

Experimental Setup

All experiments are conducted on a Rocky Linux 8.10 server with two Intel Xeon Platinum 8462Y+ processors and 314 GiB of memory. We evaluate GoalEvolve on eight post-placement designs spanning approximately 20 K–313 K instances. All designs use the ASAP7 7 nm predictive process design kit and its 7.5-track standard-cell library [5, 18]. Our implementation is based on OpenROAD [2] commit 08f67ee5. Target construction is performed before evolution and is external to GoalEvolve. For each design, we use preliminary experiments with a commercial reference flow to characterize attainable post-placement repair opportunities and set its post-route TNS, leakage, and dynamic-power results as the frozen evolution targets. These targets are fixed before the first GoalEvolve or Codex goal mode run and reported in Table 1; runtime is recorded only as an observer metric. To ensure controlled evaluation, all candidate branches start from the same parent source snapshot and design checkpoint, but are built in isolated workspaces and evaluated with an identical checkpointed post-placement and global-routing flow. A GoalEvolve round comprises one Teacher and four coding agents, all using GPT-5.6 Terra with high reasoning effort. Evolution terminates when the predefined goal is reached or the full-flow evaluation budget is exhausted.

4.2

QoR Improvement and Goal Progress

Table 1 reports the OpenROAD baseline 𝐵, commercial-tool goal 𝐺, and final GoalEvolve result 𝐴. To characterize the repair opportunities implied by the commercial-tool targets, we derive baseline-togoal timing and total-power improvement potentials. Table 2 groups the eight designs into four power-dominant, two timing-dominant, and two joint timing–power cases based on these potentials. This grouping is used only for the result analysis below. We measure the fractions of the baseline-to-goal timing and total-power gaps closed by GoalEvolve using 𝐶𝑇 and 𝐶𝑃 , respectively, and use their equal-weight combination 𝐶 𝐽 = (𝐶𝑇 +𝐶𝑃 )/2 for joint timing–power

Haixu Liu, Lei Zhou, Yuhao Ren, Yumao Wu, and Zhiang Wang

Table 1: Frozen-contract baseline, goal, and recorded GoalEvolve result (Baseline/Goal/Achieved). Runtime is an observer metric with a recorded baseline but no frozen goal. Design AES Ariane JPEG MemPool NVDLA-A NVDLA-C NVDLA-M NVDLA-P

TNS (ns) −12.00 / −1,850.00 / −53.00 / −1,850.00 / −294.00 / −10.00 / −10.40 / −246.00 /

−12.44 / −7,568.43 / −48.77 / −3,680.33 / −203.23 / −55.58 / −13.99 / −198.18 /

−15.57 −688.54 −51.18 −2,714.69 −90.64 −7.25 −14.21 −163.49

96.3 / 17,900.0 / 174.0 / 3,070.0 / 321.0 / 17,300.0 / 61.5 / 306.0 /

𝑃leak (𝜇W) 35.0 / 17,600.0 / 80.0 / 1,210.0 / 46.3 / 16,500.0 / 31.3 / 66.6 /

Table 2: Baseline-to-goal improvement potentials and corresponding QoR profiles. Design

Timing potential

Total-power potential

Profile

AES Ariane JPEG MemPool NVDLA-A NVDLA-C NVDLA-M NVDLA-P

+3.54% +75.56% -8.67% +49.73% -44.66% +82.01% +25.66% -24.13%

+18.97% +2.64% +14.94% +33.26% +23.61% +0.25% +20.78% +8.83%

Power-dominant Timing-dominant Power-dominant Joint Power-dominant Timing-dominant Joint Power-dominant

29.1 17,935.1 114.5 3,059.5 285.3 17,259.4 38.3 256.4

Leakage power (mW)

|TNS| (ns)

90 80 70 60 50 0.0

2.5

5.0 7.5 10.0 12.5 15.0 evolution attempts

0.17 0.16 0.15 0.14 0.13 0.12 0.11

290 Dynamic power (mW)

best valid

final result

100

0.0

2.5

280 270 260 250

5.0 7.5 10.0 12.5 15.0 evolution attempts

0.0

2.5

5.0 7.5 10.0 12.5 15.0 evolution attempts

0

2

4 6 8 evolution attempts

NVDLA-M best valid

Leakage power (mW)

|TNS| (ns)

17 16 15 14 0

2

4 6 8 evolution attempts

10

44

0.060

final result

18

Dynamic power (mW)

19

0.055 0.050 0.045 0.040 0.035

0

2

4 6 8 evolution attempts

10

42 40 38 36 34

10

Figure 3: Timing and power trajectories across evolution attempts for JPEG (top) and NVDLA-M (bottom). cases:   |TNS𝐵 | − |TNS𝐴 | 𝐶𝑇 = min 1, . |TNS𝐵 | − |TNS𝐺 |   𝑃tot,𝐵 − 𝑃 tot,𝐴 𝐶𝑃 = min 1, . 𝑃tot,𝐵 − 𝑃 tot,𝐺

(6) (7)

Relative to the OpenROAD baseline, GoalEvolve improves postroute TNS by 30.67% on average while reducing leakage and dynamic power by 21.18% and 9.42%, respectively. The timing improvement is substantial on several large-gap designs: Ariane, NVDLA-C, and NVDLA-A each improve TNS by at least 55.40%. The three designs with TNS regressions incur at most 3.13 ns of degradation while still reducing leakage by 34.20–69.78% and dynamic power by 7.96–22.30%. Relative to the commercial-tool goals, GoalEvolve closes 62.20% of the normalized total-power gap on the four powerdominant designs and surpasses the commercial-tool TNS on three

𝑃 dyn (𝜇W) 350,000.0 / 623,000.0 / 250,000.0 / 185,000.0 / 126,000.0 / 583,000.0 / 35,300.0 / 36,400.0 /

335,607.1 588,058.6 270,427.7 249,586.4 144,228.6 584,086.0 39,473.3 38,231.5

Runtime (s) 32 / –/ 235 687 / –/ 378 187 / –/ 745 1,415 / –/ 489 166 / –/ 828 632 / –/ 124 46 / –/ 526 125 / –/ 1,074

of them. On the two timing-dominant designs, GoalEvolve surpasses the commercial-tool TNS on both while achieving 2.55% lower total power on average. For the two joint timing–power designs, it closes 32.48% of the equal-weight normalized timing–power gap. Figure 3 further shows the timing and power trajectories of JPEG and NVDLA-M, revealing the non-monotonic timing–power tradeoffs across successive evolution attempts. Together with the endpoint results, these trajectories show that GoalEvolve can navigate different QoR tradeoffs and make substantial progress toward the commercial-tool targets.

4.3 JPEG Encoder

431,903.7 / 640,100.0 / 293,826.0 / 275,930.0 / 164,679.0 / 583,700.0 / 44,538.5 / 39,694.0 /

Validation of Evolved Source Mechanisms

The repeated-baseline control is applied to the five designs for which GoalEvolve has substantially higher runtime than the default flow, allowing multiple baseline passes within the corresponding runtime budget. To test whether the gains arise merely from additional optimization time, we give the repeated baseline the largest integer number of default passes that fits within GoalEvolve’s recorded runtime, corresponding to 0.75–0.96× the GoalEvolve budget. Table 3 shows that GoalEvolve improves TNS by 3.09% on average while reducing leakage and dynamic power by 40.94% and 14.59%, respectively. Repeated execution of the existing optimization operators within a comparable runtime budget therefore does not reproduce the QoR gains of the evolved source. To further examine whether these evolved mechanisms are specific to the design on which they were discovered, we freeze the final AES-evolved OpenROAD source and replay it on the other seven designs using the baseline flow, without further source evolution. For this comparison, we compute 𝐷 𝐹 using Equation 3 with equal weights on TNS, leakage, and dynamic power. Table 4 shows that the transferred source improves TNS on all seven designs by 46.72% on average and reduces total power on six of them. Nevertheless, design-specific GoalEvolve achieves a smaller 𝐷 𝐹 on six of the seven designs. NVDLA-C is the only exception, where the transferred source achieves 𝐷 𝐹 = 0.8176 versus 0.8336 for design-specific evolution. These results indicate that the evolved source mechanisms exhibit useful cross-design transfer, while design-specific goal feedback remains important for approaching each frozen QoR target.

4.4

Comparison with Codex Goal Mode

To isolate the benefit of structured physical-design feedback, we compare GoalEvolve with Codex operating in goal mode on Ariane, NVDLA-M, and NVDLA-P. Both methods start from the same

GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms

Table 3: GoalEvolve (GE) vs. repeated baseline (RB). Design

RB passes

TNS (ns) GE/RB

𝑃 leak (𝜇W) GE/RB

𝑃dyn (mW) GE/RB

AES JPEG NVDLA-A NVDLA-M NVDLA-P

7 3 4 11 8

−15.57/−12.90 −51.18/−41.91 −90.64/−199.06 −14.21/−18.20 −163.49/−138.39

29.1/101.0 114.5/199.0 285.3/337.0 38.3/82.2 256.4/330.0

335.6/435.9 270.4/299.8 144.2/164.7 39.5/51.6 38.2/39.9

Table 4: Cross-design replay of the AES-evolved source. Positive Δ values indicate improvement; lower 𝐷 𝐹 is better. Design

ΔTNS (%)

Δ𝑃tot (%)

𝐷 𝐹 ,AES /𝐷 𝐹 ,GE

Ariane JPEG MemPool NVDLA-A NVDLA-C NVDLA-M NVDLA-P

+91.10 +10.01 +22.60 +64.75 +86.16 +8.23 +44.19

+7.86 +3.26 +11.06 +0.80 -0.05 +6.24 +1.84

0.373191/0.372333 0.525724/0.277710 0.732363/0.725688 0.637591/0.447106 0.817592/0.833560 0.751243/0.581600 0.579678/0.449609

Table 5: GoalEvolve (GE) versus Codex goal mode (CGM). Valid rounds/evals. (GE; CGM)

TNS (ns) GE / CGM

𝑃 dyn (mW) GE / CGM

𝑃 leak (𝜇 W) GE / CGM

Ariane

GE: 3 r, 12 evals. CGM: 12 evals.

−688.54 −2,548.99

588.1 594.0

17,935.1 18,000.0

NVDLA-M

GE: 10 r, 40 evals. CGM: 40 evals.

−14.21 −13.22

39.5 39.4

38.3 60.0

NVDLA-P

GE: 3 r, 12 evals. CGM: 12 evals.

−163.49 −189.81

38.2 38.8

256.4 258.0

Design

source snapshot, use GPT-5.6 Terra, and share the same evaluator and frozen QoR goals. Codex receives these goals in a naturallanguage prompt and iterates directly between source revision and full-flow evaluation, without GoalEvolve’s stage-aware diagnosis, mechanism memory, or evidence-guided planning. We match the number of valid formal evaluations exactly between the two methods, counting an evaluation only when the candidate completes the full flow and returns all required QoR metrics. Under these matched evaluation budgets, GoalEvolve achieves better QoR in seven of the nine timing–power comparisons in Table 5. Averaged across the three designs, GoalEvolve improves TNS by 26.46% relative to Codex goal mode while reducing leakage and dynamic power by 12.38% and 0.76%, respectively. GoalEvolve improves all three QoR metrics on Ariane and NVDLA-P. On NVDLAM, Codex achieves 0.99 ns better TNS and only 0.25% lower dynamic power, while GoalEvolve reduces leakage by 36.17%. These results indicate that GoalEvolve’s structured physical-design feedback produces higher-quality source revisions under the same budget of expensive full-flow evaluations.

4.5

Case Study: JPEG on ASAP7

On JPEG (ASAP7), GoalEvolve evolves a code-level, stage-aware power-recovery policy rather than merely retuning a Tcl schedule. The evolved flow coordinates three functional stages. First, an early forced power-reclaim stage aggressively explores power-saving cell changes before major timing recovery, with ties in utility stably

broken in favor of candidates with larger slack. Second, a bounded second-pass leakage-recovery stage immediately follows the initial reclaim to capture residual leakage-saving opportunities while enforcing explicit timing guards. Third, a timing–power tradeoff stage performs major timing recovery, then reuses restored slack for limited guarded power reduction before a final timing repair. The second-pass leakage-recovery stage also evolves the internal search and acceptance policy. Its main search uses a proportional move budget capped at 4,200 moves. Once this budget is exhausted, one or two bounded tail searches may examine at most 512 additional candidates each and retain at most 256 guard-passing moves. For guarded power-VT swaps, the implementation recomputes total cell leakage after parasitic and timing updates and rolls back the move if the measured leakage does not decrease or its timing budget is violated. The evolved source therefore combines slack-aware candidate ordering, staged timing–power coordination, bounded follow-up search, post-update benefit verification, and guarded rollback. At the final post-route endpoint, leakage decreases from 0.1740 to 0.1145 mW (34.2%) and dynamic power from 293.826 to 270.428 mW (8.0%), while TNS reaches −51.175 ns, surpassing the frozen −53 ns target.

5

Conclusion

GoalEvolve reframes physical design algorithm development as goal-directed source evolution under full-flow feedback. Remaining QoR gaps identify the stage and source mechanism to revise, while checkpoint evidence and mechanism memory favor effects that survive downstream interactions. Experiments show that GoalEvolve improves post-route QoR over default OpenROAD, makes substantial progress toward commercial-tool targets across heterogeneous timing–power profiles, demonstrates useful cross-design transfer of evolved mechanisms, and achieves better post-route QoR than Codex goal mode under matched full-flow evaluation budgets. These results establish goal-guided source evolution as a practical methodology for physical design.

Haixu Liu, Lei Zhou, Yuhao Ren, Yumao Wu, and Zhiang Wang

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