solve_highs_problem
Solve linear or mixed-integer programming problems using HiGHs solver by defining variables, objectives, and constraints. Obtain solutions for optimization tasks with support for dense/sparse matrices and multiple algorithms.
Instructions
Solve a HiGHs linear/mixed-integer programming problem.
This tool takes a HiGHs optimization problem defined with variables, objective,
and constraints, and returns a solution if one exists.
HiGHs is a high-performance linear programming solver that supports:
- Linear programming (LP)
- Mixed-integer programming (MIP)
- Both dense and sparse constraint matrices
- Various solver algorithms (simplex, interior point, etc.)
Example problem structure:
{
"problem": {
"sense": "minimize",
"objective": {
"linear": [1.0, 2.0, 3.0]
},
"variables": [
{"name": "x1", "lb": 0, "ub": 10, "type": "cont"},
{"name": "x2", "lb": 0, "ub": null, "type": "cont"},
{"name": "x3", "lb": 0, "ub": 1, "type": "bin"}
],
"constraints": {
"dense": [
[1, 1, 0],
[0, 1, 1]
],
"sense": ["<=", ">="],
"rhs": [5, 3]
}
},
"options": {
"time_limit": 60.0,
"output_flag": false
}
}
Args:
problem: The HiGHs problem definition with variables, objective, and constraints
Returns:
A list of TextContent containing the solution or an error message
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| problem | Yes |
Input Schema (JSON Schema)
{
"$defs": {
"HiGHSConstraintSense": {
"description": "Constraint directions in HiGHs.",
"enum": [
"<=",
">=",
"="
],
"title": "HiGHSConstraintSense",
"type": "string"
},
"HiGHSConstraints": {
"description": "Constraint specification for HiGHs.",
"properties": {
"dense": {
"anyOf": [
{
"items": {
"items": {
"type": "number"
},
"type": "array"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "2D array where each row is a constraint",
"title": "Dense"
},
"rhs": {
"description": "Right-hand side values",
"items": {
"type": "number"
},
"title": "Rhs",
"type": "array"
},
"sense": {
"description": "Constraint directions",
"items": {
"$ref": "#/$defs/HiGHSConstraintSense"
},
"title": "Sense",
"type": "array"
},
"sparse": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSSparseMatrix"
},
{
"type": "null"
}
],
"default": null,
"description": "Sparse matrix representation"
}
},
"required": [
"sense",
"rhs"
],
"title": "HiGHSConstraints",
"type": "object"
},
"HiGHSObjective": {
"description": "Objective function specification for HiGHs.",
"properties": {
"linear": {
"description": "Coefficients for each variable",
"items": {
"type": "number"
},
"title": "Linear",
"type": "array"
}
},
"required": [
"linear"
],
"title": "HiGHSObjective",
"type": "object"
},
"HiGHSOptions": {
"description": "Options for HiGHs solver.",
"properties": {
"dual_feasibility_tolerance": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Default: 1e-7",
"title": "Dual Feasibility Tolerance"
},
"highs_debug_level": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "0-4: debug verbosity",
"title": "Highs Debug Level"
},
"infinite_bound": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Default: 1e20",
"title": "Infinite Bound"
},
"infinite_cost": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Default: 1e20",
"title": "Infinite Cost"
},
"ipm_iteration_limit": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "IPM max iterations",
"title": "Ipm Iteration Limit"
},
"ipm_optimality_tolerance": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Default: 1e-8",
"title": "Ipm Optimality Tolerance"
},
"log_to_console": {
"anyOf": [
{
"type": "boolean"
},
{
"type": "null"
}
],
"default": null,
"description": "Console logging",
"title": "Log To Console"
},
"mip_abs_gap": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Absolute gap tolerance",
"title": "Mip Abs Gap"
},
"mip_detect_symmetry": {
"anyOf": [
{
"type": "boolean"
},
{
"type": "null"
}
],
"default": null,
"description": "Detect symmetry",
"title": "Mip Detect Symmetry"
},
"mip_feasibility_tolerance": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "MIP feasibility tolerance",
"title": "Mip Feasibility Tolerance"
},
"mip_max_nodes": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "Max branch-and-bound nodes",
"title": "Mip Max Nodes"
},
"mip_rel_gap": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Relative gap tolerance",
"title": "Mip Rel Gap"
},
"output_flag": {
"anyOf": [
{
"type": "boolean"
},
{
"type": "null"
}
],
"default": null,
"description": "Enable solver output",
"title": "Output Flag"
},
"parallel": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSParallel"
},
{
"type": "null"
}
],
"default": null,
"description": "Parallel option"
},
"pdlp_iteration_limit": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "PDLP max iterations",
"title": "Pdlp Iteration Limit"
},
"pdlp_scaling": {
"anyOf": [
{
"type": "boolean"
},
{
"type": "null"
}
],
"default": null,
"description": "PDLP scaling",
"title": "Pdlp Scaling"
},
"presolve": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSPresolve"
},
{
"type": "null"
}
],
"default": null,
"description": "Presolve option"
},
"primal_feasibility_tolerance": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Default: 1e-7",
"title": "Primal Feasibility Tolerance"
},
"random_seed": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "Random seed for reproducibility",
"title": "Random Seed"
},
"simplex_dual_edge_weight_strategy": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "-1 to 2: pricing",
"title": "Simplex Dual Edge Weight Strategy"
},
"simplex_iteration_limit": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "Max iterations",
"title": "Simplex Iteration Limit"
},
"simplex_scale_strategy": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "0-5: scaling strategy",
"title": "Simplex Scale Strategy"
},
"simplex_strategy": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "0-4: algorithm strategy",
"title": "Simplex Strategy"
},
"solution_file": {
"anyOf": [
{
"type": "string"
},
{
"type": "null"
}
],
"default": null,
"description": "Solution file path",
"title": "Solution File"
},
"solver": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSSolver"
},
{
"type": "null"
}
],
"default": null,
"description": "Solver algorithm"
},
"threads": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "Number of threads (0=automatic)",
"title": "Threads"
},
"time_limit": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Time limit in seconds",
"title": "Time Limit"
},
"write_solution_style": {
"anyOf": [
{
"type": "integer"
},
{
"type": "null"
}
],
"default": null,
"description": "Solution format style",
"title": "Write Solution Style"
},
"write_solution_to_file": {
"anyOf": [
{
"type": "boolean"
},
{
"type": "null"
}
],
"default": null,
"description": "Write solution to file",
"title": "Write Solution To File"
}
},
"title": "HiGHSOptions",
"type": "object"
},
"HiGHSParallel": {
"description": "Parallel options for HiGHs.",
"enum": [
"off",
"choose",
"on"
],
"title": "HiGHSParallel",
"type": "string"
},
"HiGHSPresolve": {
"description": "Presolve options for HiGHs.",
"enum": [
"off",
"choose",
"on"
],
"title": "HiGHSPresolve",
"type": "string"
},
"HiGHSProblem": {
"description": "Complete HiGHS optimization problem.",
"properties": {
"options": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSOptions"
},
{
"type": "null"
}
],
"default": null,
"description": "Solver options"
},
"problem": {
"$ref": "#/$defs/HiGHSProblemSpec",
"description": "Problem specification"
}
},
"required": [
"problem"
],
"title": "HiGHSProblem",
"type": "object"
},
"HiGHSProblemSpec": {
"description": "Problem specification for HiGHs.",
"properties": {
"constraints": {
"$ref": "#/$defs/HiGHSConstraints",
"description": "Constraint specifications"
},
"objective": {
"$ref": "#/$defs/HiGHSObjective",
"description": "Objective function"
},
"sense": {
"$ref": "#/$defs/HiGHSSense",
"description": "Optimization sense"
},
"variables": {
"description": "Variable specifications",
"items": {
"$ref": "#/$defs/HiGHSVariable"
},
"title": "Variables",
"type": "array"
}
},
"required": [
"sense",
"objective",
"variables",
"constraints"
],
"title": "HiGHSProblemSpec",
"type": "object"
},
"HiGHSSense": {
"description": "Optimization sense for HiGHs problems.",
"enum": [
"minimize",
"maximize"
],
"title": "HiGHSSense",
"type": "string"
},
"HiGHSSolver": {
"description": "Solver options for HiGHs.",
"enum": [
"simplex",
"choose",
"ipm",
"pdlp"
],
"title": "HiGHSSolver",
"type": "string"
},
"HiGHSSparseMatrix": {
"description": "Sparse matrix representation for constraints.",
"properties": {
"cols": {
"description": "Column indices of non-zero coefficients (0-indexed)",
"items": {
"type": "integer"
},
"title": "Cols",
"type": "array"
},
"rows": {
"description": "Row indices of non-zero coefficients (0-indexed)",
"items": {
"type": "integer"
},
"title": "Rows",
"type": "array"
},
"shape": {
"description": "[num_constraints, num_variables]",
"maxItems": 2,
"minItems": 2,
"prefixItems": [
{
"type": "integer"
},
{
"type": "integer"
}
],
"title": "Shape",
"type": "array"
},
"values": {
"description": "Non-zero coefficient values",
"items": {
"type": "number"
},
"title": "Values",
"type": "array"
}
},
"required": [
"rows",
"cols",
"values",
"shape"
],
"title": "HiGHSSparseMatrix",
"type": "object"
},
"HiGHSVariable": {
"description": "Variable specification for HiGHs.",
"properties": {
"lb": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Lower bound (optional, defaults to 0)",
"title": "Lb"
},
"name": {
"anyOf": [
{
"type": "string"
},
{
"type": "null"
}
],
"default": null,
"description": "Variable name (optional, defaults to x1, x2, etc.)",
"title": "Name"
},
"type": {
"anyOf": [
{
"$ref": "#/$defs/HiGHSVariableType"
},
{
"type": "null"
}
],
"default": null,
"description": "Variable type (optional, defaults to 'cont')"
},
"ub": {
"anyOf": [
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Upper bound (optional, defaults to +∞, except binary gets 1)",
"title": "Ub"
}
},
"title": "HiGHSVariable",
"type": "object"
},
"HiGHSVariableType": {
"description": "Variable types in HiGHs.",
"enum": [
"cont",
"int",
"bin"
],
"title": "HiGHSVariableType",
"type": "string"
}
},
"properties": {
"problem": {
"$ref": "#/$defs/HiGHSProblem"
}
},
"required": [
"problem"
],
"title": "solve_highs_problem_toolArguments",
"type": "object"
}