Added metabolic simplification and replaced lpsolve with HiGHS

[DimitriosPavlouGR]

Overview

This PR introduces metabolic polytope preprocessing and replaces the LP oracles from lpsolve to HiGHS.

The changes can be broken down into two main parts:

1. Metabolic polytope simplification, scaling, and transformation.
2. Removal of lpsolve and moving the lp oracles to HiGHS.

The goal is to make metabolic network models smaller and easier to process with VolEsti's existing algorithms, while also providing a more consistent and new LP backend.

Metabolic Polytope Preprocessing

A new preprocessing pipeline has been added for metabolic polytopes obtained from metabolic network models.

This pipeline includes:

• BiGG JSON model parsing
• Scaling of metabolic polytope
• Detection and removal of redundant flux bounds and pinned reactions
• Transformation of the simplified metabolic polytope to an H representation

The preprocessing related files have been added under preprocess/metabolic/ and is split into separate components for:

• Transformation
• Scaling
• Exhaustive simplification
• Clarkson simplification
• Common metabolic polytope utilities

Simplification Methods

Two simplification approaches have been implemented.

Exhaustive Simplification

The exhaustive approach checks the reactions/bounds individually and determines whether they can be removed while preserving the metabolic polytope. This provides a simple and reliable baseline and is very useful for smaller models, or for preprocessing degenerate polytopes, where numerical accuracy becomes an issue.

Clarkson Simplification

A Clarkson based redundancy removal method has also been implemented. The method maintains a smaller set of relevant constraints and uses a worklist to identify reactions that are pinned or redundant. This avoid repeatedly processing the complete set of constraints and is intended to scale better with larger models.

Simplification Results

Experiments on metabolic models from the BiGG database demonstrate that a significant amount of redundancy can be removed before applying any volume/sampling algorithms.

The following is a table showing the performance of the two methods compared to polyround:

Model	PolyRound Time	Exhaustive Time	Clarkson Time	PolyRound Dims	Exhaustive Dims	Clarkson Dims	PolyRound Bounds	Exhaustive Bounds	Clarkson Bounds
e_coli_core	0.357s	0.066s	0.029s	4	8	8	154	154	154
iAB_RBC_283	2.569s	0.921s	0.364s	0	16	16	750	750	750
iAM_Pc455	11.644s	40.201s	5.908s	13	223	222	1758	1744	1746
iAT_PLT_636	12.610s	6.185s	4.486s	0	0	0	1423	1422	1423
iCN900	14.096s	5.196s	2.023s	266	926	926	2317	2317	2317
iEC042_1314	58.269s	66.512s	20.114s	243	1070	1070	4640	4640	4510
iECBD_1354	71.474s	63.937s	19.532s	258	1097	1097	4708	4708	4705
iECED1_1282	64.651s	201.361s	20.430s	236	1062	1062	4622	4618	4618
iECIAI39_1322	62.529s	80.231s	20.156s	257	1152	1152	4668	4668	4667
iECSF_1327	65.506s	75.043s	23.045s	234	999	999	4658	4658	4656
iEK1008	15.072s	11.725s	4.048s	53	333	333	2161	2160	2157
iEcolC_1368	66.083s	74.748s	20.740s	257	1115	1115	4740	4736	4736
iJN746	9.734s	9.285s	6.051s	66	347	402	1884	1633	1856
iND750	16.051s	30.890s	48.840s	104	635	633	2259	2259	2257
iNF517	6.403s	3.586s	1.570s	50	241	241	1309	1309	1307
iPC815	28.384s	17.979s	9.094s	132	896	896	3481	3480	3480
iRC1080	49.089s	67.473s	22.539s	72	622	622	3457	3457	3453
iSynCJ816	12.535s	6.748s	3.767s	37	460	263	1864	1944	1865
iYO844	12.760s	15.430s	19.280s	125	594	591	2278	2278	2278

Overall, the Clarkson based approach generally provides a significant reduction in preprocessing time compared to Polyround and the Exhaustive approach, and there is room for further improvements.

LPSolve Removal

The old lp_solve backend and its oracle implementations have been removed and replaced with a HiGHS implementation. The new oracles can be found under the folder lp_oracles/.

The following were implemented with HiGHS:

• Chebychev ball computation
• V-polytope/Z-polytope membership
• V-polytope/Z-polytope line/ray intersections
• Metabolic polytope containment/equality checks

LP Oracle Interface

The LP oracle interface (function signatures) has also been updated.

A common LPOracleOptions interface is now provided for configuring HiGHS. This allows solver options to be configured without exposing the underlying HiGHS objects.

The LP oracles also distinguish between:

• A successful LP solve with a feasible solution
• A successful LP solve proving infeasibility
• A solver failure or unexpected solver status

This makes it possible for callers to distinguish scenarios such as "the point is outside the polytope" from "the LP solver failed".

Code Organization

The relevant headers are organized as follows:

include/
├── convex_bodies/
│   └── metabolic_polytope.hpp
│
├── io/
│   └── bigg_parser.hpp
│
├── lp_oracles/
│   ├── lp_oracle_options.hpp
│   ├── metabolic_polyoracles.hpp
│   ├── solve_lp.hpp
│   ├── vpolyoracles.hpp
│   └── zpolyoracles.hpp
│
└── preprocess/
    └── metabolic/
        ├── common.hpp
        ├── scaling.hpp
        ├── simplification_clarkson.hpp
        ├── simplification_exhaustive.hpp
        ├── simplify_and_transform.hpp
        └── transformation.hpp

Examples and Tests

Relevant tests and examples are organized as follows:

Examples

examples/
└── metabolic_simplification/
    ├── CMakeLists.txt
    ├── simplification.cpp
    └── manual_simplification.cpp

Tests

test/
├── lp_oracles/
│   ├── test_solve_lp.cpp
│   ├── test_vpolyoracles.cpp
│   └── test_zpolyoracles.cpp
│
└── metabolic/
    ├── benchmark_simplification.cpp
    ├── test_metabolic_polytope.cpp
    ├── test_scaling.cpp
    ├── test_simplification.cpp
    └── test_transformation.cpp