Change how multiple objectives are stored

Author: odow

README.md

@@ -10,13 +10,13 @@ It is heavily inspired by [MathOptInterface](https://github.com/JuliaOpt/MathOpt
 MathOptFormat is a generic file format for mathematical optimization problems
 encoded in the form
 
-       min/max: fᵢ(x)       i=1,2,…,I
-    subject to: gⱼ(x) ∈ Sⱼ  j=1,2,…,J
+       min/max: f₀(x)
+    subject to: fᵢ(x) ∈ Sᵢ  i=1,2,…,I
 
-where `x ∈ ℝᴺ`, `fᵢ: ℝᴺ → ℝ`, and `gⱼ: ℝᴺ → ℝᴹʲ`, and `Sⱼ ⊆ ℝᴹʲ`.
+where `x ∈ ℝᴺ`, `fᵢ: ℝᴺ → ℝᴹⁱ`, and `Sᵢ ⊆ ℝᴹⁱ`.
 
-The functions `fᵢ` and `gⱼ`, and sets `Sⱼ` supported by MathOptFormat are
-defined in the [MathOptFormat schema](#the-schema).
+The functions `fᵢ` and sets `Sᵢ` supported by MathOptFormat are defined in the
+[MathOptFormat schema](#the-schema).
 
 The current list of supported functions and sets is not exhaustive. It is
 intended that MathOptFormat will be extended in future versions to support
@@ -32,19 +32,19 @@ consider the following linear program:
 
 Encoded in our standard form, we have
 
-    f₁(x) = 2x + 1
-    g₁(x) = x
+    f₀(x) = 2x + 1
+    f₁(x) = x
     S₁    = [1, ∞)
 
 Encoded into the MathOptFormat file format, this example becomes:
 ```json
 {
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{"name": "x"}],
-    "objectives": [{
+    "objective": {
         "sense": "min",
         "function": {
             "head": "ScalarAffineFunction",
@@ -53,7 +53,7 @@ Encoded into the MathOptFormat file format, this example becomes:
             ],
             "constant": 1
         }
-    }],
+    },
     "constraints": [{
         "name": "x >= 1",
         "function": {"head": "SingleVariable", "variable": "x"},
@@ -88,14 +88,15 @@ required keys at the top level:
    variable. It is illegal to have two variables with the same name. These names
    will be used later in the file to refer to each variable.
 
- - `"objectives"`
+ - `"objective"`
 
-   A list of JSON objects, with one element for each objective in the model.
-   Each object has two required keys:
+   A JSON objects describing the objective of the model. It has one required
+   keys:
 
     - `"sense"`
 
-      A string which must be `"min"` or `"max"`.
+      A string which must be `"min"`, `"max"`, or `"feasibility"`. If the sense
+      is `min` or `max`, a second key `"function"`, must be defined:
 
     - `"function"`
 
@@ -163,8 +164,8 @@ adding to this documentation, clarifying edits should be made to the
 
 The list of functions supported by MathOptFormat are contained in the
 `#/definitions/scalar_functions` and `#/definitions/vector_functions` fields of
-the schema. Scalar functions are functions for which `Mj=1`, while vector
-functions are functions for which `Mj≥1`.
+the schema. Scalar functions are functions for which `Mi=1`, while vector
+functions are functions for which `Mi≥1`.
 
 Here is a summary of the functions defined by MathOptFormat.
 

examples/biobjective.mof.json

@@ -1,35 +1,39 @@
 {
-    "description": "The problem: [min{2x - y + 1}, max{y}]",
+    "description": "The problem: [min{2x - y + 1, -y}]",
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{
         "name": "x"
     }, {
         "name": "y"
     }],
-    "objectives": [{
+    "objective": {
         "sense": "min",
         "function": {
-            "head": "ScalarAffineFunction",
+            "head": "VectorAffineFunction",
             "terms": [{
+                "output_index": 1,
+                "scalar_term": {
                     "coefficient": 2,
                     "variable": "x"
-                },
-                {
+                }
+            }, {
+                "output_index": 1,
+                "scalar_term": {
                     "coefficient": -1,
                     "variable": "y"
                 }
-            ],
-            "constant": 1
-        }
-    }, {
-        "sense": "max",
-        "function": {
-            "head": "SingleVariable",
-            "variable": "y"
+            }, {
+                "output_index": 2,
+                "scalar_term": {
+                    "coefficient": -1,
+                    "variable": "y"
+                }
+            }],
+            "constants": [1, 0]
         }
-    }],
+    },
     "constraints": []
 }

examples/milp.mof.json

@@ -2,7 +2,7 @@
     "description": "The problem: min{x | x + y >= 1, x ∈ [0, 1], y ∈ {0, 1}}",
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{
         "name": "x",
@@ -11,13 +11,13 @@
         "name": "y",
         "primal_start": 1.0
     }],
-    "objectives": [{
+    "objective": {
         "sense": "min",
         "function": {
             "head": "SingleVariable",
             "variable": "x"
         }
-    }],
+    },
     "constraints": [{
         "name": "x + y >= 1",
         "function": {

examples/nlp.json

@@ -2,14 +2,14 @@
     "description": "The problem: min{2x + sin(x)^2 + y}.",
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{
         "name": "x"
     }, {
         "name": "y"
     }],
-    "objectives": [{
+    "objective": {
         "sense": "min",
         "function": {
             "head": "ScalarNonlinearFunction",
@@ -55,6 +55,6 @@
                 }]
             }]
         }
-    }],
+    },
     "constraints": []
 }

examples/quadratic.mof.json

@@ -2,14 +2,14 @@
     "description": "The problem: min{x^2 + x * y + y^2}",
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{
         "name": "x"
     }, {
         "name": "y"
     }],
-    "objectives": [{
+    "objective": {
         "sense": "min",
         "function": {
             "description": "Note that the format is `a'x + 0.5 x' Q x + c`.",
@@ -33,6 +33,6 @@
             ],
             "constant": 0
         }
-    }],
+    },
     "constraints": []
 }

examples/vector.json

@@ -2,14 +2,16 @@
     "description": "The problem: min{0 | [1 2; 3 4][x, y] + [5, 6] ∈ R+.",
     "version": {
         "major": 0,
-        "minor": 3
+        "minor": 4
     },
     "variables": [{
         "name": "x"
     }, {
         "name": "y"
     }],
-    "objectives": [],
+    "objective": {
+        "sense": "feasibility"
+    },
     "constraints": [{
         "function": {
             "head": "VectorAffineFunction",

mof.schema.json

@@ -3,15 +3,15 @@
     "$id": "https://github.com/odow/MathOptFormat/blob/master/mof.schema.json",
     "title": "The schema for MathOptFormat",
     "type": "object",
-    "required": ["version", "variables", "objectives", "constraints"],
+    "required": ["version", "variables", "objective", "constraints"],
     "properties": {
         "version": {
             "description": "The version of MathOptFormat that this schema validates against.",
             "type": "object",
             "required": ["minor", "major"],
             "properties": {
                 "minor": {
-                    "const": 3
+                    "const": 4
                 },
                 "major": {
                     "const": 0
@@ -48,21 +48,30 @@
             },
             "uniqueItems": true
         },
-        "objectives": {
-            "description": "An array of objectives in the model.",
-            "type": "array",
-            "items": {
-                "type": "object",
-                "required": ["sense", "function"],
+        "objective": {
+            "description": "The objective of the model.",
+            "type": "object",
+            "required": ["sense"],
+            "oneOf": [{
                 "properties": {
                     "sense": {
                         "enum": ["min", "max"]
                     },
                     "function": {
-                        "$ref": "#/definitions/scalar_functions"
+                        "oneOf": [{
+                            "$ref": "#/definitions/scalar_functions"
+                        }, {
+                            "$ref": "#/definitions/vector_functions"
+                        }]
                     }
                 }
-            }
+            }, {
+                "properties": {
+                    "sense": {
+                        "const": "feasibility"
+                    }
+                }
+            }]
         },
         "constraints": {
             "description": "An array of constraints in the model. Scalar-valued functions can only be paired with scalar-sets, and the same applies for vector-valued functions and sets.",