HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

Feijie Wu; Hugo Barbalho; Konstantina Mellou; Marco Molinaro; Jing Gao; Ishai Menache; Xinzhi Zhang; Sirui Li

cs.CLSep 28, 2026

HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

Authors: Feijie Wu, Hugo Barbalho, Konstantina Mellou, Marco Molinaro, Jing Gao, Ishai Menache, Xinzhi Zhang, Sirui Li

Organizations: Purdue University · Microsoft Research

Abstract

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

Figures & tables

Step	Component	Subgoal	Implementation details	Time budget
1	Euclidean tour construction	Produce feasible and diverse incumbents	Build a small portfolio of nearest-neighbor and insertion tours; retain a diverse elite set	$9$ s
2	Local tour improvement	Rapidly reduce tour length with cheap moves	Apply candidate-restricted 2-opt and Or-opt descent; perturb and restart only after stagnation	$20$ s
3	Candidate-edge restricted MIP	Escape local minima through nonlocal edge changes	Warm-start Gurobi on a sparse graph containing proximity, incumbent, elite, and repair arcs	$32$ s
4	Large-neighborhood search	Repair costly regions missed by the sparse global search	Fix most of the incumbent, destroy a long-edge or geographic region, and use Gurobi to reconnect that region exactly	$42$ s
5	Residual anytime primal portfolio	Use the residual budget on the most productive search mode	Adaptively select among Gurobi LNS micro-repair, Gurobi sparse-MIP retry, and heuristic local-search restart using same-run progress	Remaining time

Table 1: An example plan for the traveling salesperson problem.

	Mean gap (%)		Beat Gurobi
Method	Train	Test	Train	Test
OpenEvolve	$+0.71$	$+0.41^{\ddagger}$	$5/11$	$4/11$
AdaEvolve	$-0.15$	$+0.91$	$7/11$	$\mathbf{7/11}$
EvoX	$+1.22$	$+2.24$	$5/11$	$4/11$
HeurEvo	$\mathbf{-2.22}$	$\mathbf{-1.45}$	$\mathbf{8/11}$	$\mathbf{7/11}$

Table 2: Average synthetic performance. ‡ The OpenEvolve test mean excludes OP, whose reported test value has incomplete evaluation coverage.

	Mean gap (%)		Beat Gurobi
Method	Train	Test	Train	Test
OpenEvolve	$+0.71$	$+0.41^{\ddagger}$	$5/11$	$4/11$
AdaEvolve	$-0.15$	$+0.91$	$7/11$	$\mathbf{7/11}$
EvoX	$+1.22$	$+2.24$	$5/11$	$4/11$
HeurEvo	$\mathbf{-2.22}$	$\mathbf{-1.45}$	$\mathbf{8/11}$	$\mathbf{7/11}$

Table 2: Average synthetic performance. ‡ The OpenEvolve test mean excludes OP, whose reported test value has incomplete evaluation coverage.

Method

C-CVRP

RCPS

PFSS

MIS

Train

Val

Test

Train

Val

Test

Train

Val

Test

Train

Val

Test

Train

Val

Test

EoH (GLS)

–

-2.65

-2.61

-2.20

–

ReEvo (ACO)

+4.16

+1.32

+7.40

+6.58

+9.77

+8.28

–

RefineEvo (ACO)

–

+5.06

+9.59

+8.18

–

OpenEvolve

+16.65

+16.10

+22.61^{\ddagger}

+1.93

+4.57

+2.96

+0.64

\mathbf{-0.57}

+1.74

-0.48

+0.41

-0.27

\mathbf{-0.04}

+0.39

\mathbf{+0.14}

AdaEvolve

+16.92

+15.73

+21.75

-1.77

-0.84

-1.62

+1.49

+1.21

+0.70

-2.19

-1.84

\mathbf{-2.21}

+0.15

+0.29

+0.45

Table 3: Representative synthetic objective gaps (%). Since AHD methods do not introduce a host function or an initial heuristic solution for the selected problems, their results are left blank. ‡ Incomplete evaluation coverage; excluded from the OpenEvolve test mean.

Method	comp12-2idx $\downarrow$	comp21-2idx $\downarrow$	graphdraw- grafo2 $\downarrow$	graphdraw- mainerd $\downarrow$	opm2-z12-s8 $\uparrow$	sct32 $\downarrow$
AdaEvolve	366.20	100.40	85061.30	47940.40	58057.20	-3.01
HeurEvo	327.00	103.20	82003.10	45681.00	58519.40	-2.77

Table 4: Training objectives on MIPLIB.

Method	Circle packing-rectangle $\uparrow$		Min-max distance ratio $\downarrow$			Hexagon packing $\downarrow$
Method	$n=21$	$n=26$	$n=16,d=2$	$n=21,d=2$	$n=22,d=2$	$n=11$	$n=12$	$n=14$
SOTA	2.3658323759	2.6393205590	12.8892299	17.77499	19.05398	3.9245008973	3.9416420675	4.2689949573
AdaEvolve	2.3642481267	2.6355313151	12.8892299077	17.7749805542	19.0539845098	3.9326758559	3.9416423004	4.2723920772
HeurEvo	2.36 58323759	2.63 93205 643	12.889229 1072	17.7749 80 3417	19.0539 769136	3.9 245011309	3.941642 06 25	4.2 689950806

Table 5: Nonlinear objectives versus reported best values. Underline indicates the part better than AdaEvolve; Bold indicates the part better than the reported best-known value.

Variant	Averaged performance			OP			C-CVRP			RCPS			PFSS
Variant	Train	Val	Test	Train	Val	Test	Train	Val	Test	Train	Val	Test	Train	Val	Test
Fixed plan	$-1.19$	$+0.06$	$+0.25$	$+1.94$	$+8.1$	$+7.97$	$-3.15$	$-2.3$	$-3.26$	$+1.39$	$+1.8$	$+0.39$	$-0.83$	$-1.0$	$-0.50$
Component only	$-1.45$	$-0.38$	$+0.08$	$-1.67$	$+0.9$	$+3.86$	$-3.09$	$-2.4$	$-3.47$	$+1.37$	$+1.2$	$+1.61$	$-0.79$	$-0.3$	$-0.69$
Always-plan	$-1.67$	$-0.36$	$-0.27$	$+0.45$	$+8.0$	$+8.12$	$-2.84$	$-2.0$	$-2.95$	$+0.50$	$\mathbf{0.0}$	$+0.43$	$-1.52$	$-1.6$	$-1.67$
Always-plan + component	$-1.89$	$-1.38$	$-0.70$	$-2.67$	$\mathbf{-8.9}$	$\mathbf{-2.39}$	$-3.20$	$-2.6$	$-3.62$	$\mathbf{-0.35}$	$\mathbf{0.0}$	$+0.43$	$-1.16$	$-0.9$	$-0.93$
Adaptive plan only	$-1.35$	$-1.01$	$-0.21$	$-0.87$	$-3.8$	$+3.76$	$-2.48$	$-2.2$	$-3.00$	$+0.87$	$+0.1$	$+0.65$	$-1.48$	$-1.0$	$-0.64$

Table 6: Component ablation of HeurEvo .

Variant	Average gap (%)
Variant	Train	Val	Test
Single island	$-1.31$	$-0.98$	$-0.75$
Shared plan	$-1.76$	$-1.24$	$-1.23$
Partitioned library	$-1.41$	$-1.69$	$\mathbf{-1.57}$
HeurEvo (Ours)	$\mathbf{-2.22}$	$\mathbf{-2.22}$	$-1.45$

Table 7: Island initialization ablation.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

	Symbol	Description	Value
Search budget and initialization
	$K$	Number of islands (one initial plan per island)	5
	–	Validated seed programs generated per plan	1
	$M_{\mathrm{dbg}}$	Debugging attempts per generation call	3
	$B$	Per-instance execution budget (seconds)	120
Island scheduling (Eqs. C1, C3)

Appendix

Table A8: Hyperparameters of HeurEvo. Symbols follow Appendix C ; a dash marks a quantity the analysis does not name. Values describe the default configuration; the ablation studies vary the specified components.

Method	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
EoH (Constr.)	–	–	–	+3.53	–	–	–	–	–	–	–
EoH (GLS)	–	–	+0.68	–	–	–	–	-2.65	–	–	–
ReEvo (ACO)	+6.58	+9.66	+8.60	+1.14	+4.16	–	–	–	–	–	–
ReEvo (Constr.)	–	–	+16.02	–	–	–	–	–	–	–	–
ReEvo (GLS)	–	–	-0.83	–	–	–	–	–	–	–	–
RefineEvo (ACO)	+5.06	+9.10	+9.60	–	–	–	–	–	–	–	–

Appendix

Table A9: Full synthetic training gaps (%).

Method	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
EoH (Constr.)	–	–	–	+3.30	–	–	–	–	–	–	–
EoH (GLS)	–	–	+0.60	–	–	–	–	-2.20	–	–	–
ReEvo (ACO)	+8.28	+13.30	+9.96	+1.56	+7.40	–	–	–	–	–	–
ReEvo (Constr.)	–	–	+15.37	–	–	–	–	–	–	–	–
ReEvo (GLS)	–	–	-0.79	–	–	–	–	–	–	–	–
RefineEvo (ACO)	+8.18	+12.26	+12.72	–	–	–	–	–	–	–	–

Appendix

Table A10: Full synthetic test gaps (%).

Problem	$n$	$d$	Best result source	Reported reference	AdaEvolve	HeurEvo
Circle packing (rectangle) $\uparrow$	21	–	EinsteinArena a	2.3658323759185156	2.3642481267	2.36 58323759
Circle packing (rectangle) $\uparrow$	26	–	Lai b	2.639320558987759336	2.6355313151	2.63 93205 643
Circle packing (rectangle) $\uparrow$	27	–	Dutton / Lai b,c	2.691523360671018652	2.6834410277	2.68 91174195
Circle packing (square) $\uparrow$	26	–	Packomania d	2.635983084919	2.6359830484	2.6359775049
Circle packing (square) $\uparrow$	32	–	Berthold et al. (2026a) d	2.939572771205	2.9395727706	2.9395727706
Distance ratio $\downarrow$	14	3	Sun–Samanta e	4.165	4.1657834746	4.16578 20926

Appendix

Table A11: Complete nonlinear training objectives. For HeurEvo , Underline indicates the part better than AdaEvolve, and Bold indicates the part better than the reported best-known value.

Method	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
Fixed plan	-3.15	-2.25	+1.23	+0.45	+1.94	+1.47	-12.29	-0.83	+1.39	-1.19	+0.19
Adaptive plan only	-2.48	-0.68	+1.11	+0.45	-0.87	+1.43	-12.32	-1.48	+0.87	-1.18	+0.27
Component only	-3.09	-2.47	+1.98	+0.40	-1.67	+1.30	-12.28	-0.79	+1.37	-1.08	+0.35
Earlier full configuration	-3.04	-1.82	+1.45	+0.45	-0.75	+1.45	-12.32	-1.15	+0.82	-1.83	+0.23
Always-plan + component	-3.20	-1.78	+0.40	+0.45	-2.67	+1.47	-12.32	-1.16	-0.35	-1.69	+0.11
Always-plan	-2.84	-2.04	-0.23	+0.10	+0.45	+1.44	-12.23	-1.52	+0.50	-1.89	-0.12

Appendix

Table A12: Synthetic ablation training gaps (%).

Method	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
Fixed plan	-3.26	-1.81	+2.53	+0.69	+7.97	+2.66	-6.30	-0.50	+0.39	-0.86	+1.20
Adaptive plan only	-3.00	-1.81	+2.44	+0.69	+3.76	+2.01	-6.57	-0.64	+0.65	-0.79	+0.90
Component only	-3.47	-1.59	+4.17	+0.69	+3.86	+1.62	-6.41	-0.69	+1.61	-0.70	+1.79
Earlier full configuration	-3.45	-1.06	+1.78	+0.69	+7.04	+1.98	-6.42	-0.89	+0.57	-1.54	+0.57
Always-plan + component	-3.62	+0.09	+1.97	+0.69	-2.39	+1.82	-6.19	-0.93	+0.43	-1.08	+1.52
Always-plan	-2.95	-1.96	+0.18	+0.38	+8.12	+2.03	-6.17	-1.67	+0.43	-1.44	+0.11

Appendix

Table A13: Synthetic ablation test gaps (%).

Variant	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
Single island	-2.88	+3.10	-0.92	+0.49	-0.06	+1.05	-7.07	-2.65	-0.57	-1.32	+0.10
Shared plan	-2.69	-1.93	-0.98	+0.62	-0.97	+1.55	-6.61	-2.35	+1.21	-1.41	-0.10
Partitioned library	-1.88	-1.94	-0.93	+0.49	-3.98	+1.17	-6.74	-1.86	-1.78	-1.23	+0.10
HeurEvo (Ours)	-3.36	-3.19	-0.82	+0.45	-3.80	+1.40	-11.60	-2.25	+0.12	-1.32	-0.04

Appendix

Table A14: Island ablation validation gaps (%). Bold indicates the lowest gap in each column, including ties.

Variant	C-CVRP	U-CVRP	TSP	BP	OP	Decap	JSS	PFSS	RCPS	Max-Cut	MIS
Single island	-4.87	+2.09	-0.79	+0.50	+4.18	+1.20	-6.90	-2.31	+0.29	-1.60	0.00
Shared plan	-4.55	-2.96	-0.84	+0.50	+3.85	+1.06	-7.46	-2.05	+0.58	-1.42	-0.26
Partitioned library	-3.58	-3.74	-0.78	+0.50	-1.46	+1.45	-6.90	-1.52	+0.29	-1.51	-0.07
HeurEvo (Ours)	-4.38	-3.48	-0.70	+0.69	-1.94	+1.90	-5.52	-1.85	0.00	-0.85	+0.14

Appendix

Table A15: Island ablation test gaps (%). Bold indicates the lowest gap in each column, including ties.

Collection	Tasks	Train	Val.	Test	Total
Synthetic Problems	11	55	22	44	121
MIPLIB-Derived Problems	6	30	–	–	30
Total	17	85	22	44	151

Appendix

Table B16: Instances used in the reported experiments. Dashes indicate splits outside the reported evaluation.

Task	Definition, generation details, and references
Clustered CVRP	Minimize total distance while serving each customer exactly once using exactly 22 depot-return routes, each carrying at most 55 demand units. There are 120 customers in four Gaussian clusters with coordinate standard deviation 0.08, clipped to the unit square. The depot is at $(0.1,0.1)$ ; customer demands are uniform integers from 1 to 13. Each customer independently chooses a cluster center uniformly from $(0.25,0.25)$ , $(0.75,0.30)$ , $(0.35,0.78)$ , and $(0.78,0.75)$ before its coordinates are sampled. This is our custom clustered generator for the CVRP of Dantzig & Ramser (1959) , not a reproduction of a published instance set.
Uniform CVRP	Minimize total distance with complete single-visit service, depot-return routes, and vehicle capacity 50. The 200 customers are sampled uniformly from the unit square, with a depot at $(0.5,0.5)$ and demands uniform on the integers 1–9. The fleet size is fixed for each instance and ranges from 20 to 22 vehicles: $K=\max\!\left(\left\lceil\frac{\sum_{i}q_{i}}{50}\right\rceil+1,K_{\mathrm{FFD}}\right),$ where $K_{\mathrm{FFD}}$ is the number of capacity-50 bins obtained by first-fit decreasing on the demands. Coordinates, demands, depot, and capacity follow the ACO benchmark sampling of ReEvo Ye et al. (2024) ; the exact fleet-size constraint and integer distances are our adaptations.
Decap-Placement Proxy	Minimize capacitor cost subject to placing at most one capacitor type at each site and meeting every target’s required cumulative synthetic effect. A $30\times 30$ grid supplies 900 sites and 900 targets. Four types give 3,600 site–type choices; effects decay with distance inside a type-specific radius. Type $k$ contributes $e_{k}/(1+d_{st})$ when the Euclidean grid distance $d_{st}\leq\rho_{k}$ , and zero otherwise. The four $(\mathrm{cost},e_{k},\rho_{k})$ tuples are $(1.0,1.4,1.25)$ , $(2.1,2.6,2.25)$ , $(3.8,4.3,3.5)$ , and $(6.4,7.0,5.25)$ . Before rounding, target $t$ requires $0.22m_{t}F_{t}$ , where $F_{t}$ is the strongest-type all-site coverage and $m_{t}=0.90+0.20\lVert p_{t}-(14.5,14.5)\rVert_{2}/(14.5\sqrt{2})$ . Target-weight jitter is uniform on $[-0.06,0.06]$ but cancels against inversely scaled base requirements, up to rounding. This covering proxy is inspired by ReEvo’s application Ye et al. (2024) , not its electrical simulator or data distribution; see Section B.2 for the diversity qualification.
Job-Shop Scheduling	job_shop_scheduling . Minimize makespan while preserving each job’s operation order and preventing machine conflicts. Operations cannot be interrupted. There are 100 jobs and 20 machines (2,000 operations). Every job visits every machine once in a random order, with processing times uniform on the integers 1–99. This follows Taillard’s random-permutation and processing-time recipe Taillard (1993) , with fresh seeds; the scheduling formulation follows Manne (1960) .
Max-Cut	max_cut . Partition the vertices into two sets to maximize the number of crossing edges Goemans & Williamson (1995) . Each graph has 2,000 vertices and 10,882–11,072 edges. Our hybrid generator combines Barabási–Albert-style preferential attachment Barabási & Albert (1999) , initialized with a five-vertex clique and attachment parameter 4, with an independent Erdős–Rényi $G(n,p)$ edge overlay at $p=0.0015$ Erdős & Rényi (1959) ; Gilbert (1959) . Duplicate edges are merged; all stored edge weights equal one. This is our custom combination of the two graph models.
Maximum Independent Set	maximum_independent_set . Maximize the cardinality of a vertex subset containing no adjacent pair. Each preferential-attachment graph has 1,500 vertices and 11,964 edges, uses attachment parameter 8, and starts from a nine-vertex clique. We follow the preferential-attachment principle of Barabási & Albert (1999) with this explicit initialization and use the unweighted independent-set objective Nemhauser & Trotter (1975) .

Appendix

Table B17: Synthetic problem definitions and generation settings.

Problem ID	Definition and instance configuration
comp12-2idx	Coursescheduling. Schedule all required lectures into available periods while avoiding course conflicts and respecting the number of rooms. Minimize penalties for room-capacity shortfalls, insufficient teaching-day spread, and isolated curriculum lectures. There are 88 courses, 218 lectures, six days with six periods each, 11 rooms, 146 curricula, and 519 course-conflict pairs.
comp21-2idx	Coursescheduling. Solve the same time-assignment problem and three-part penalty objective, with a different timetable, room inventory, and curriculum structure. Room capacities are represented by capacity thresholds and penalized shortfalls. There are 94 courses, 327 lectures, five days with five periods each, 18 rooms, 78 curricula, and 302 conflict pairs.
graphdraw-grafo2	Graphdrawing. Place entities at integer coordinates inside their permitted windows, enforcing size-dependent non-overlap and consistent directional relations. Minimize weighted connection-distance terms plus deviation from preferred anchors. This is the entity-placement phase of graph drawing, with 67 entities, 73 connections, and 2,211 entity pairs. All edge weights equal 122.
graphdraw-mainerd	Graphdrawing. Solve the same entity-placement problem on a smaller graph, with placement windows, pairwise separations, directional consistency, and centering terms. There are 31 entities, 33 connections, and 465 entity pairs. All edge weights equal 126.
opm2-z12-s8	Mining-projectselection. Select mining blocks/projects to maximize total net present value. Selecting a project requires selecting its predecessors, and the total use of each resource must respect its capacity. There are 10,800 binary project decisions, eight resources, and 319,500 dependency arcs. Every resource has capacity 3,704,832.
sct32	PCBassembly-lineconfiguration. Assign each operation’s full workload across eligible workstation options, using binary decisions on discrete lanes and fractional assignments where permitted. Minimize staffing cost minus weighted checkpoint performance and discrete-routing rewards, subject to capacities, checkpoint constraints, priority-token eligibility and budget, and policy checks. There are 552 operations, ten workstation options, seven board variants, 27 checkpoints, 67 policy checks, and a priority-token budget of six.

Appendix

Table B18: MIPLIB-derived problem definitions.

Problem	Variables	Linear constraints	Key instance parameters
C-CVRP	14,640	14,522	120 customers; 22 vehicles; capacity 55
U-CVRP	40,400	40,202	200 customers; 20–22 vehicles; capacity 50
OP	250,498	250,501	500 nodes; travel budget 8,944
TSP	122,499	122,152	350 nodes
JSSP	101,001	201,900	100 jobs; 20 machines; 2,000 operations
PFSSP	12,000	4,081	100 jobs; 20 machines

Appendix

Table B19: Formulation sizes before presolve for 11 synthetic and six MIPLIB-derived tasks. Ranges cover synthetic instances; “varies” marks MIPLIB constraint counts affected by perturbation.

Problem Name	Size Configurations
circle_packing_square	$n\in\{26,32\}$
circle_packing_rectangle	$n\in\{21,26,27\}$
distance_ratio	$d=2,\ n\in\{16,21,22\}$ ; $d=3,\ n=14$
hexagon_packing	$n\in\{11,12,14,15,16\}$

Appendix

Table B20: Nonlinear problem names and size configurations.

Annotation	Description
$\mathcal{A},\mathcal{A}_{j}$	Shared Program Database of retained, validated programs.
$\mathcal{A}_{j}^{(k)}$	All retained programs from island $k$ , including earlier plans.
$\mathcal{A}_{j}^{(k,\mathrm{par})},\mathcal{C}_{j}^{(k)}$	Parent-eligible programs under the current plan generation.
$\mathcal{A}_{j}^{(k,\mathrm{ins})}$	Available inspiration programs for island $k$ .
$\mathcal{D},B$	Training set and per-instance execution budget.
$f(G;d),F(G)$	Instance fitness and average training fitness; larger is better.

Appendix

Table C1: Annotations

Call category	Operators
System functions	SelectIsland , SelectCode , RestartIsland , UpdateState , SelectComponents
Agent-response calls	ImprovePlan , CodePlan , ImproveCode , Interpret , ImproveComponents

Appendix

Table C2: System functions and agent-response calls.

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Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · The Hong Kong University of Science and Technology

Automated Heuristic Design Multi-Agent Evolution Particle Swarm Optimization Ensemble

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May 7, 2026cs.NE

CoupleEvo: Evolving Heuristics for Coupled Optimization Problems Using Large Language Models

Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design approaches are limited to single-problem settings. In this paper, we propose CoupleEvo. CoupleEvo proposes three evolutionary coordination strategies to evolve heuristics for coupled optimization problems: the sequential strategy evolves heuristics for one subproblem after the other; the iterative strategy alternates the evolution of heuristics for different subproblems over successive generations; and the integrated strategy evolves heuristics for all problems simultaneously. The approach is evaluated on two representative coupled optimization problems. Experimental results show that decomposition-based strategies (sequential and iterative) provide more stable convergence and higher solution quality, while the integrated evolution strategy suffers from increased search complexity and variability. These findings highlight the importance of coordinating evolutionary search across interdependent subproblems and demonstrate the potential of LLM-driven heuristic design for complex coupled optimization problems. The code is available: https://github.com/tb-git-kit-research/CoupleEvo.

Thomas Bömer, Bastian Amberg, Max Disselnmeyer +1

Karlsruhe Institute of Technology Karlsruhe, Germany

Automated Heuristic Design Evolutionary Search Heuristics

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