Pareto front find

pareto-front-find · version 1.0.0 · Optimization & voting · free, no key needed

Find stable nondominated row indices and a domination witness for every excluded row using exact rational criteria.

Use when you need to: find the pareto front · find nondominated alternatives · filter dominated rows.

Decide before calling

Read the versioned contract and the supported scope below. Reuse pareto-front-find@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use pareto-front-find@1.0.0 for find the pareto front. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• find the pareto front
• find nondominated alternatives
• filter dominated rows
• compare mixed objectives exactly
• return pareto domination witnesses
• optimize minimize and maximize criteria
• compute a skyline over rational values

Not supported

• rank alternatives into a total order or choose one preferred row
• approximate floating-point, missing, infinite, or nonnumeric criterion values
• compute Pareto layers beyond the first nondominated front

Behavior

• Canonical rationals are 0, signed base-10 integers without leading zero, or reduced p/q with a positive denominator greater than 1; -0, zero fractions, and /1 are invalid.
• A row dominates another when it is no worse on every criterion and strictly better on at least one, respecting minimize and maximize directions.
• Equal and duplicate rows do not dominate each other; duplicates of a nondominated point all remain nondominated.
• Indices and excluded records follow input order; dominated_by is the lowest input index that directly dominates the excluded row.
• Exact BigInt cross multiplication is used with bounded O(rows squared times criteria) work; no approximation is performed.

Input

• criteria (array of object, required): min items 1; max items 16
• rows (array of array of string, required): min items 1; max items 128; each min items 1; each max items 16; each each min length 1; each each max length 128; each each pattern ^(0|-?[1-9][0-9]*(/[1-9][0-9]*)?)$

Output

• nondominated_indices (array of integer, required): max items 128; each min 0; each max 127
• excluded (array of object, required): max items 128

Limits

• max rows: 128
• max criteria: 16
• max rational bytes: 128
• max dominance checks: 16256

Example

Request input:

{
  "criteria": [
    {
      "direction": "minimize"
    },
    {
      "direction": "maximize"
    }
  ],
  "rows": [
    [
      "1",
      "1"
    ],
    [
      "2",
      "3"
    ],
    [
      "3",
      "2"
    ],
    [
      "2",
      "1"
    ]
  ]
}

Response:

{
  "result": {
    "nondominated_indices": [
      0,
      1
    ],
    "excluded": [
      {
        "index": 2,
        "dominated_by": 1
      },
      {
        "index": 3,
        "dominated_by": 0
      }
    ]
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "pareto-front-find",
  "version": "1.0.0",
  "input": {
    "criteria": [
      {
        "direction": "minimize"
      },
      {
        "direction": "maximize"
      }
    ],
    "rows": [
      [
        "1",
        "1"
      ],
      [
        "2",
        "3"
      ],
      [
        "3",
        "2"
      ],
      [
        "2",
        "1"
      ]
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/pareto-front-find/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"criteria":[{"direction":"minimize"},{"direction":"maximize"}],"rows":[["1","1"],["2","3"],["3","2"],["2","1"]]}'

The machine-readable contract is at /v1/tools/pareto-front-find/versions/1.0.0.

CLI

node cli.mjs run pareto-front-find 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Knapsack 01 solve: Solve bounded 0/1 knapsack exactly and return the optimum value, weight, and lexicographically smallest index list.
• Assignment hungarian solve: Solve a bounded rectangular integer minimum-cost assignment with explicit unmatched costs.
• Vote condorcet winner: Compute weighted pairwise counts, a strict Condorcet winner, and the generalized Smith set.
• Rank borda aggregate: Aggregate weighted complete or partial rankings into exact Borda scores, rank groups, and audit contributions.
• Round robin schedule generate: Generate a deterministic single or double round-robin schedule with ordered rounds, home/away assignments, and byes.