AlgoEvo: Self-Evolving Agentic Search for Automated Algorithm Discovery

1 INTRODUCTION

• Prior LLM-driven discovery spans population search, island models, MCTS, and localized code edits, then extends from single objectives to Pareto trade-offs and multi-component systems.The cited examples include EoH, FunSearch, MEoH, E2OC, and MOTIF.Source: §1 · p. 1
• Existing frameworks embed LLMs in rigid, expert-predefined pipelines, leaving them as passive code samplers and limiting interactive debugging and structural refactoring.Paradigm-specific coupling fragments frameworks, while scalar feedback can discard execution details needed to understand success or failure.Source: §1 · pp. 1–2
• AlgoEvo replaces predefined prompt completion with an autonomous agent that dynamically inspects, diagnoses, edits, and evaluates code based on runtime feedback.Its design skill hub decouples paradigm-specific knowledge so one workflow can handle single-heuristic, multi-objective, and multi-component tasks.Source: §1 · p. 2
• A hierarchical experience bank turns search trajectories into structured cards and a task-level tree, retrieving relevant insights to guide later iterations and transfer experience across tasks.The framework also reports continual self-improvement and cross-task knowledge transfer.Source: §1 · p. 2
• Within 7% of the evaluation budget, AlgoEvo matches or surpasses the strongest baseline on all six tasks, by up to 8.8%.The experiments span single-heuristic, multi-objective, and multi-component algorithm-design tasks.Source: §1 · p. 2

2 AUTOMATED ALGORITHM DISCOVERY

• Automated algorithm discovery synthesizes executable code or heuristic programs for optimization tasks, spanning single heuristics, multi-objective strategies, and interacting operators.Candidate programs are searched in a task-specific space and guided by evaluations.Source: §2 · p. 3
• An optimization domain is characterized by an instance space, a solution space, and a task objective; each instance has a feasible subset of solutions.The underlying optimization problem is stated for an instance and its feasible set.Source: §2 · p. 3
• A solver uses designable strategies, and the induced algorithm space is the product of their strategy spaces; K=1 denotes single-heuristic design and K>1 denotes jointly optimized multi-component design.Strategies may include scoring rules, construction policies, neighborhood operators, or penalty-update mechanisms.Source: §2 · p. 3
• Algorithm performance is reduced to a scalar measure, such as an objective value or hypervolume, with smaller values treated as better.The discovery objective is subject to a computational budget bounding evaluation and discovery resources.Source: §2 · p. 3

3 ALGOEVO: SELF-EVOLVING AGENTIC ALGORITHM DISCOVERY

• The framework combines a design skill, a matched or created experience tree, agent-driven search, evaluation summaries, and cross-task skill refinement.The agent dynamically inspects, modifies, evaluates, and diagnoses algorithms using runtime feedback.Source: §3 · p. 3

3.1 AGENTIC SEARCH LOOP

• At each step, the agent chooses whether and when to inspect code, modify a strategy, diagnose, or evaluate, interleaving targeted analysis and edits rather than following a fixed cycle.The agent observes the discovery state and processes feedback until the budget is exhausted or it terminates.Source: §3.1 · pp. 3–4

3.2 DESIGN SKILL HUB

• Design skills declare strategy roles, code interfaces, valid-modification principles, and evaluation conventions, specializing the same search engine without changing its loop.The hub selects a matching skill at task initialization and refines it only after task completion, not within a task.Source: §3.2 · pp. 4–5

3.3 HIERARCHICAL EXPERIENCE BANK

• Evaluations are distilled into experience cards recording design context, modification, reward, and rationale; cards from one task form a tree whose edges encode derived-from relationships.The bank has three levels: cards, a task-level tree, and cross-task consolidation.Source: §3.3 · p. 5
• Card selection uses an upper confidence bound conditioned on the current situation, while backpropagated rewards update ancestor cards to favor design directions with strong descendants.The situation can include stagnation, bottleneck, coupling, or sparse front; the parameter c controls the exploration-exploitation trade-off.Source: §3.3 · p. 5

3.4 EXPERIENCE ACCUMULATION AND SELF-EVOLUTION

• At evaluation, the agent creates and attaches an experience card; diagnosis or retrieval uses relevant experiences, and accumulated trees eventually support cross-task skill refinement.Once a skill owns at least µ experience trees, salient patterns are summarized to refine it for later tasks.Source: §3.4 · pp. 5–6

4.1 EXPERIMENTAL SETUP

• The benchmark covers six tasks across three paradigms, compared with each paradigm’s strongest method using shared instance splits, evaluation entries, three seeds, and 500 evaluations per seed.The tasks include TSP and CVRP, Bi-TSP and Bi-FJSP, and CVRP-DR and FJSP 4-Ops; multi-objective quality is reported on training instances.Source: §4.1 · p. 6

4.2 MAIN RESULTS

• On TSP and CVRP, AlgoEvo leads the strongest LLM-AHD baseline by 4–7% and nearest-neighbour on TSP by 12.3%.It finds its best incumbent by about 35 evaluations, compared with the 500-evaluation cap used by baselines.Source: §4.2 · p. 7
• On both multi-objective tasks, AlgoEvo attains the best training HV; it also has the best Bi-TSP IGD but trails MEoH on Bi-FJSP front proximity.Its front reaches low-objective corners missed by baselines, while the MOEA/D front collapses to a point.Source: §4.2 · p. 7
• AlgoEvo leads both CVRP-DR splits and the held-out FJSP four-operator co-design result, improving on expert operators there while using most of the budget.Unlike the four other tasks, these multi-component tasks draw on most of the evaluation allowance.Source: §4.2 · p. 8

4.3 ANALYSIS AND DISCUSSION

• Within-task experience reuse accompanies fixed-budget gains: TSP tour length improves from 4.8928 to 4.7995 and Bi-FJSP HV from 0.1549 to 0.1862 across rounds.Warm-started runs also consistently improve over cold starts while reducing variance.Source: §4.3 · p. 8, Table 2 · p. 8, Table 3 · p. 8
• Transferring CVRP design patterns to CVRP-DR lowers mean cost from 10.314 to 9.816, below the cold-start baseline of 10.791.The transferred edge-scoring rules are reused within the target task’s constructor.Source: §4.3 · p. 9, Table 4 · p. 9
• AlgoEvo reaches final quality within tens of evaluations while baselines use their full budgets; across CVRP-DR seeds, the diagnosis-driven trajectory reaches the best cost.The agent continues proposing changes to the harness limit, and few proposals improve on the incumbent.Source: Figure 3 · p. 8, §4.3 · p. 9, Figure 4 · p. 9

4.4 METHOD SKILLS FOR AUTOMATED ALGORITHM DESIGN

• Method skills distilled from six established approaches match or exceed their native frameworks’ solution quality while requiring substantially fewer evaluations.AlgoEvo uses the skills without importing the methods’ native search procedures.Source: §4.4 · p. 9

5 CONCLUSION

• Across six representative combinatorial optimization benchmarks, AlgoEvo achieves state-of-the-art solution quality using as little as 7% of the standard evaluation budget.The conclusion also reports intra-task experience accumulation and cross-task knowledge transfer in complex algorithmic co-design.Source: §5 · p. 10
• A design skill hub decouples paradigm-specific knowledge, while a hierarchical experience bank organizes discovery trajectories to support a unified engine across three design settings.The settings are single-heuristic, multi-objective, and multi-component tasks.Source: §5 · p. 10
• AlgoEvo replaces rigid, expert-predefined pipelines with adaptive, knowledge-accumulating search.The conclusion characterizes this as a state-aware search control process.Source: §5 · p. 10

LLM-based Automated Algorithm and Heuristic Design

• LLM-based algorithm-design approaches generate and refine ideas, but their search procedures and multi-component coordination policies remain tied to fixed protocols.Examples span evolutionary search, iterative refinement, Monte Carlo tree search, and multi-objective design.Source: A RELATED WORK · p. 15

Agentic Coding and Program Synthesis

• General coding agents optimize correctness against static specifications, while algorithm discovery must address optimization bottlenecks, search trajectories, and generalization across instances.AlgoEvo treats code as the implementation medium and optimization feedback across problem instances as the state signal for structural redesign.Source: A RELATED WORK · p. 15

Skill-based and Experience-driven Agents

• Generic skill and memory structures can degrade or propagate errors, while algorithm design involves structural coupling and nonlinear performance trends.AlgoEvo's design skills encode execution mechanisms, applicable conditions, principles, and characteristic failure or convergence patterns.Source: A RELATED WORK · p. 16

Positioning of AlgoEvo

• AlgoEvo's agentic loop chooses inspection, diagnosis, modification, or evaluation according to the current optimization state rather than a prescribed cycle.This addresses the gap that existing LLM-based discovery searches candidate programs under fixed protocols rather than searching the design process itself.Source: A RELATED WORK · p. 16
• The design skill hub uses paradigm-specific contracts to let one engine span single-heuristic, multi-objective, and multi-component tasks.The cited gap is that coding agents lack an algorithm representation and cross-component coordination is absent or governed by static rules.Source: A RELATED WORK · p. 16
• The hierarchical experience bank stores situation-conditioned design decisions in a task-level tree and consolidates validated patterns into transferable skills.This is presented as a domain-specific alternative to generic skill and memory structures that may not capture algorithm-design semantics.Source: A RELATED WORK · p. 16

B.1 TASK SPECIFICATION AND INITIALIZATION

• Each task fixes its initial code, editable units, evaluator, and evaluation budget; supporting multi-objective or multi-component design changes the task specification, not the core loop.Initialization activates the best-matching skill and retrieves or creates an experience tree indexed by skill, problem, and evaluator.Source: §B.1 · pp. 16–17

B.2 DISCOVERY STATE, ACTIONS, AND DIAGNOSIS

• Evaluation alone produces candidates and consumes the evaluation budget; the returned algorithm is the best evaluated incumbent, not necessarily the latest one.Rewards apply only when an evaluated candidate updates the incumbent; analytical actions do not receive reward.Source: §B.2 · pp. 17–18
• Counterfactual unit and joint-unit probes estimate performance attribution and coupling, helping categorize bottlenecks or interactions and guide situation-matched experience retrieval.Neutralizing a pair and applying inclusion-exclusion estimates coupling; strong coupling suggests redesigning the units together, and these probes do not consume evaluation budget.Source: §B.2 · pp. 18–19

B.3 DESIGN SKILL HUB

• The design skill hub supplies paradigm-specific guidance without changing the agentic search loop, and new paradigms require adding skills rather than restructuring the architecture.Skills can be refined across tasks after accumulating at least µ experience trees (µ = 2 by default), grounding updates in cross-task patterns.Source: §B.3 · pp. 19–21

B.4 HIERARCHICAL EXPERIENCE BANK

• The experience bank stores design decisions as structured cards in task-level trees, retrieves cards using situation-conditioned UCB, and promotes cross-task patterns into skills.Evaluation outcomes become validated or avoid cards; post-task reflections capture effective paths and practices to avoid, while skill refinement occurs after the tree threshold is met.Source: §B.4 · pp. 21–22

B.5 CONCRETE ARTIFACTS AND PROMPTS

• The method distinguishes paradigm skills, which specify design settings and unit interfaces, from method skills, which convey an established algorithm’s methodology without importing its native search loop.A single system prompt supplies the method and task, followed by the active skill, retrieved experience cards, and knowledge state.Source: §B.5 · pp. 22, 23, 25
• A reference code artifact selects the unvisited node minimizing distance from the current node multiplied by 1 + angle(j).The artifact also lists random selection as a strategy to avoid, with five failed attempts.Source: §B.5 · p. 25
• The system prompt combines the stated method and task with the active skill, retrieved experience cards, and current knowledge state.An example knowledge state records a greedy heuristic score of 7.231 and an improvement to 6.892 after adding 2-opt.Source: §B.5 · pp. 25–26

[SKILL ACTIVATION]

• Skill activation selects and justifies the single most appropriate registered design skill given the problem description and objectives.Source: [SKILL ACTIVATION] · p. 26

[EXPERIENCE TREE MATCHING]

• Experience-tree matching searches by skill, problem, and evaluator, loading a matching tree or creating an empty one when none exists.Source: [EXPERIENCE TREE MATCHING] · p. 26

[EXPERIENCE CARD SUMMARIZATION]

• After each evaluation, the agent summarizes an experience card with problem, situation, mode, unit, skill, design pattern, and empirical evidence.Reference code and metrics are optional card fields.Source: [EXPERIENCE CARD SUMMARIZATION] · p. 26

[SKILL REFINEMENT]

• Skill refinement summarizes recurring patterns from its experience trees and updates the skill document without overwriting paradigm-level guidance.Source: [SKILL REFINEMENT] · p. 26

C.1 BENCHMARK TASKS AND INSTANCE SETS

• Six tasks span single-heuristic, multi-objective, and multi-component design, each with training instances for discovery and a disjoint test set for generalization.All comparative methods use identical instance splits.Source: §C.1 · p. 26, Table 8 · p. 26

C.2 METRICS

• Single-objective performance is mean training-set objective, while multi-objective evaluation reports normalized HV and IGD, compared within each problem.Higher HV and lower IGD indicate better convergence and diversity; reported metrics are normalized over evaluated solutions.Source: §C.2 · p. 27

C.3 BASELINE DETAILS

• For multi-component tasks, Synergy weights edits toward stagnating components, while Rotating-EoH cycles through components and keeps only improving changes.Neither baseline measures cross-component coupling, which AlgoEvo probes diagnostically.Source: §C.3 · pp. 27–28
• Baselines include rule-based heuristics and search methods for each design paradigm, evaluated under a shared protocol with controlled sampling budgets and environments.Search-based baselines retain their published hyperparameters; instance pools, splits, code templates, and evaluation routines are fixed.Source: §C.3 · pp. 27–28

C.4 ANTI-CHEATING SETTINGS

• Runs discard invalid candidates and errors, verify evaluation counts against generated individuals, reject objective calls that bypass the evaluator, and isolate run state.Evaluation counters are checked at both the instance layer and the shared evaluation entry point.Source: §C.4 · p. 28

D DESIGN SPACE AND TASK INSTANTIATION

• The design space fixes the solver, instance handling, feasibility checks, and objective evaluation, varying only predefined algorithmic units across six tasks.Table 9 summarizes the unit configuration.Source: D DESIGN SPACE AND TASK INSTANTIATION · p. 28, Table 9 · p. 28

Evolvable Unit: Next-Node Scoring Function

• For TSP, the evolvable unit is the scoring rule that selects the next unvisited city; construction and termination remain fixed..Source: D DESIGN SPACE AND TASK INSTANTIATION · p. 29, Evolvable Unit: Next-Node Scoring… · p. 29

Evolvable Unit: Capacity-Aware Next-Node Selection

• For CVRP, the designed component selects customers and depot-return timing, while the fixed evaluator enforces vehicle-load constraints and filters infeasible choices..Source: Evolvable Unit: Next-Node Scoring… · p. 29, Evolvable Unit: Capacity-Aware… · p. 29

Evolvable Unit: Bi-Objective Next-City Selection

• For Bi-TSP, one constructive rule is evaluated against two distance objectives, producing Pareto archives through multi-objective feedback..Source: Evolvable Unit: Capacity-Aware… · p. 29, Evolvable Unit: Bi-Objective Next-City… · p. 29

Evolvable Unit: Operation Dispatching Rule

• For Bi-FJSP, the evolvable priority dispatching rule sets task order while the fixed evaluator enforces precedence and machine eligibility..Source: Evolvable Unit: Bi-Objective Next-City… · p. 29, Evolvable Unit: Operation Dispatching… · p. 29

Evolvable Units: Destroy-and-Repair Components (F1/F2/F3)

• CVRP-DR jointly designs construction, destruction, and repair in sequence; each stage shapes the next, requiring coordinated rather than isolated tuning.The procedure constructs an initial solution, removes high-badness customers, reinserts them, and applies fixed local improvement.Source: Evolvable Unit: Operation Dispatching… · p. 29, Evolvable Units: Destroy-and-Repair… · pp. 29–30
• FJSP 4-Ops jointly optimizes priority and machine-assignment crossover and mutation operators through a shared chromosome and decoding mechanism.Unlike CVRP-DR's sequential pipeline, its components interact through a shared representation.Source: Evolvable Units: Destroy-and-Repair… · p. 30

E.1 CONVERGENCE UNDER THE EVALUATION BUDGET

• Single-heuristic and multi-objective tasks reach competitive designs within a small fraction of budget, while multi-component tasks need longer trajectories amid larger spaces and component interactions.Figure 10 tracks best-so-far performance against evaluation budget across all six tasks.Source: §E.1 · p. 30, Figure 10 · p. 31

E.2 PARETO ARCHIVES ON MULTI-OBJECTIVE TASKS

• AlgoEvo's multi-objective archives cover a wider objective-space region and yield non-dominated solutions closer to optimal trade-off frontiers.Figure 11 includes evaluated candidates across three seeds alongside final archives.Source: §E.2 · p. 31, Figure 11 · p. 32

E.3 ABLATION OF KNOWLEDGE MECHANISMS

• On CVRP-DR, removing the experience bank or design skill hub causes a larger performance drop than omitting situation-triggered injection.The ablation indicates persistent memory and reusable abstractions are primary performance drivers, while injection mainly refines knowledge-selection efficiency; values may vary from the primary benchmark batch.Source: §E.3 · p. 32, Table 10 · p. 32

F.1 METHOD SKILLS AND METHODOLOGICAL TRANSFER

• On TSP and Bi-TSP, the agent inspects code, implements a candidate, and conditions revisions on evaluation feedback, following the workflow encoded in the skill rather than random rewriting.Figure 12 traces action types and best-so-far quality over evaluations.Source: §F.1 · pp. 32–33, Figure 12 · p. 33
• Method skills distilled from six established methods yield solution quality comparable to or exceeding native counterparts, with stronger average TSP performance using fewer evaluations and improved Bi-TSP archive quality and stability.Bi-TSP evaluation reductions are less pronounced; Figure 14 shows per-seed comparisons.Source: §F.1 · pp. 32–33, Table 11 · p. 33

F.2 REPRESENTATIVE DIAGNOSIS-GUIDED DESIGN TRAJECTORY

• In a representative CVRP-DR trajectory, component attribution identifies the destroyer bottleneck, then interaction analysis detects operator coupling and shifts search from isolated edits to joint design..Source: §F.2 · p. 34, Table 12 · p. 34

F.3 VARIATION IN SEARCH BEHAVIOR

• Across three CVRP-DR runs, the diagnosis-intensive run performs best in this sample, but larger samples are needed to establish a definitive link between operation mix and outcome.The runs allocate effort differently across code modification and diagnostic analysis.Source: §F.3 · p. 35, Table 13 · p. 35

• Mean performance improves from 4.961 to 4.808 with warm starts, accompanied by reduced cross-seed variance.Source: §F.4 · p. 35, Figure 17 · p. 36
• Every warm-started seed outperforms its cold-started counterpart after initialization with a transferred design yielding a tour length of 5.017.Source: §F.4 · p. 35
• Previously discovered algorithms serve as effective starting points for subsequent search rather than being discarded after task completion.Source: §F.4 · p. 36

Hand-Designed Situation Awareness

• Hand-designed categorical probes may miss failure modes outside their predefined categories; learned situation awareness is proposed as a more adaptive alternative.Source: §F.5 · p. 36

Skill Overfitting

• Skills distilled from prior outcomes may overfit aligned problem distributions and limit zero-shot transfer to different domains; held-out validation is proposed to mitigate this.Source: §F.5 · p. 36

Rigid Evaluation and Anti-Cheating Boundaries

• Strict harnesses and sandbox boundaries can suppress unconventional but valid structural exploration; future protocols could support verifiable open-ended exploration.Source: §F.5 · p. 36