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251 changes: 251 additions & 0 deletions AGPRICE_MISSING_CONSTRAINTS.md
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# Analysis: Missing Constraints in agprice_full.rs

## Executive Summary

The generated `agprice_full.rs` file is **missing critical upper bound constraints** from the original MiniZinc model. This causes the optimization problem to be **mathematically unbounded**, leading to astronomical solution values (e.g., 8.2e51).

**The issue is NOT with Selen's optimizer - it's with the MiniZinc-to-Rust conversion process.**

## Problem Manifestation

When running the generated file:
```
OBJECTIVE = -8245408037230409000000000000000000000000000000000000 (-8.2e51)
xm = 128512896896560200000000000000000000 (1.3e35)
xb = 257154306690016960000000000000000000000 (2.6e38)
qsq = 8245408037230409000000000000000000000000000000000000 (8.2e51)
```

All main decision variables (milk, butt, cha, etc.) = 0, while auxiliary variables explode to astronomical values.

## Root Cause: Missing Constraints

### Original MiniZinc Model
Source: https://www.hakank.org/minizinc/agprice.mzn

The original model contains **THREE CRITICAL GROUPS** of constraints that bound the problem:

### 1. Resource Limit Constraints (MISSING)

These constraints limit the production resources:

```minizinc
0.04*xm+0.8*xb+0.35*xca+0.25*xcb<=0.600 /\
0.09*xm+0.02*xb+0.3*xca+0.4*xcb<=0.750 /\
4.82*milk+0.32*butt+0.21*cha+0.07*chb <= 1.939 /\
```

**Status**: ❌ **COMPLETELY MISSING** from generated file
**Impact**: Without these, xm, xb, xca, xcb can grow unbounded

### 2. Piecewise Linear Variable Sum Constraints (MISSING)

These constraints ensure the piecewise linear approximation variables sum to at most 1.0:

```minizinc
sum (i in point) (lmilk[i])<=1.0 /\
sum (i in point) (lbutt[i])<=1.0 /\
sum (i in point) (lcha[i])<=1.0 /\
sum (i in point) (lchb[i])<=1.0 /\
sum (i in point) (mq[i]+lq[i])<=1.0
```

**Status**: ❌ **COMPLETELY MISSING** from generated file
**Impact**: Without these, the lmilk, lbutt, lcha, lchb arrays can grow unbounded

### 3. Basic Non-negativity Constraints (PRESENT)

```minizinc
milk >= 0.0 /\
milksq >= 0.0 /\
butt >= 0.0 /\
buttsq >= 0.0 /\
cha >= 0.0 /\
chasq >= 0.0 /\
chb >= 0.0 /\
chbsq >= 0.0 /\
xm >= 0.0 /\
xb >= 0.0 /\
xca >= 0.0 /\
xcb >= 0.0 /\
qsq >= 0.0 /\
forall(i in point) (lmilk[i] >= 0.0) /\
forall(i in point) (lbutt[i] >= 0.0) /\
forall(i in point) (lcha[i] >= 0.0) /\
forall(i in point) (lchb[i] >= 0.0) /\
forall(i in point) (lq[i] >= 0.0) /\
forall(i in point) (mq[i] >= 0.0)
```

**Status**: ✅ **PRESENT** in generated file (lines 296-313)
**Note**: These are correctly translated

## Why This Causes Unbounded Solutions

The revenue equation is:
```
revenue = 420*cha + 1185*butt + 6748*milk - qsq - 8*chbsq - 194*chasq - 1200*buttsq - 6492*milksq + 70*chb
```

Without the resource limit constraints:
1. All variables have only **lower bounds** (>= 0) but **no upper bounds**
2. Variables with **positive coefficients** in revenue (milk, butt, cha, chb) should increase to maximize revenue
3. But without upper bound constraints, they can increase to **infinity**
4. The solver is correctly maximizing within the given constraints - the problem is that the constraints are incomplete!

## Mathematical Proof of Unboundedness

Given only the constraints in the generated file:
- Let milk = M, butt = B, cha = C, chb = K, all >= 0
- Let all squared terms = 0 (for simplicity)
- revenue = 6748*M + 1185*B + 420*C + 70*K

Without upper bounds on M, B, C, K:
- For any revenue value R, we can set M = R/6748 to achieve it
- As M → ∞, revenue → ∞
- **Therefore: The problem is mathematically unbounded**

The resource constraints like `4.82*milk + 0.32*butt + 0.21*cha + 0.07*chb <= 1.939` are essential to bound the feasible region.

## Verification

### Check 1: Search for resource limits
```bash
grep -E "0.600|0.750|1.939" /home/ross/devpublic/selen/debug/agprice_full.rs
```
**Result**: No matches found ❌

### Check 2: Count constraint statements
```bash
grep -E "(float_lin_le|float_lin_eq)" /home/ross/devpublic/selen/debug/agprice_full.rs | wc -l
```
**Result**: Only 16 constraint statements found

**Expected**: Should have:
- 13+ basic >= 0 constraints ✅
- 3 resource limit constraints ❌
- 5 piecewise sum <= 1.0 constraints ❌
- Multiple equality constraints for piecewise definitions ❌
- Total should be 100+ constraint statements

## What Selen's Optimizer Is Doing (Correctly)

Selen's optimizer is working correctly:
1. It detects that revenue can be maximized
2. It respects all the constraints that ARE present (>= 0 bounds)
3. Since there are no upper bounds, it tries to maximize revenue as much as possible
4. The astronomical values are the solver's attempt to maximize within an unbounded feasible region

**This is mathematically correct behavior for an unbounded optimization problem.**

## Expected Behavior

With the complete constraint set from the MiniZinc model, the optimal solution should be:
- **cha ≈ 10.0** (cheese 1 price around $10,000)
- All other variables at reasonable finite values
- Revenue at a finite optimal value

The original MiniZinc model with all constraints is **bounded** and has a **finite optimal solution**.

## Recommendations for Zelen (MiniZinc Converter)

The MiniZinc-to-Rust converter needs to properly translate:

1. **Linear inequality constraints** with floating-point coefficients:
- `0.04*xm+0.8*xb+0.35*xca+0.25*xcb<=0.600`
- Should generate: `model.float_lin_le(&vec![0.04, 0.8, 0.35, 0.25], &vec![xm, xb, xca, xcb], 0.600)`

2. **Sum constraints over arrays**:
- `sum(i in point) (lmilk[i])<=1.0`
- Should generate: `model.float_lin_le(&vec![1.0; 35], &lmilk, 1.0)` (all coefficients are 1.0)

3. **Combined array sums**:
- `sum(i in point) (mq[i]+lq[i])<=1.0`
- Should generate: `model.float_lin_le(&vec![1.0; 70], &[mq, lq].concat(), 1.0)`

## Test Case for Zelen

To verify the fix, the generated file should:
1. Include all resource limit constraints
2. Include all sum <= 1.0 constraints for piecewise variables
3. When run, produce output with cha ≈ 10.0 (not 0)
4. All variables should be finite (not astronomical)
5. Revenue should be finite and positive

## Files for Reference

- **Generated file**: `/tmp/agprice_full.rs` (incomplete)
- **Original MiniZinc**: https://www.hakank.org/minizinc/agprice.mzn (complete)
- **Expected output**: cha ≈ 10.0, finite revenue

## Conclusion

This is **NOT a bug in Selen's constraint solver or optimizer**. Selen is correctly solving the optimization problem as specified in the generated file. The problem is that the generated file is **missing critical constraints** that bound the feasible region.

The fix needs to be in the MiniZinc-to-Rust converter (Zelen) to ensure all constraints are properly translated.

---

## UPDATE: New Export Issue Found (agprice_test.rs)

After the constraint export was fixed, a new issue was discovered in `/tmp/agprice_test.rs`:

### Problem: Missing Parameter Array Definitions

The file contains comments indicating parameter arrays that should be defined:
```rust
// Array parameter: X_INTRODUCED_212_ (initialization skipped in export)
// Array parameter: X_INTRODUCED_214_ (initialization skipped in export)
// ... etc
```

But these arrays are **never actually defined** in the code. Later, the constraints try to use them:
```rust
model.float_lin_eq(&x_introduced_212_, &vec![xm, milk], 1.4); // ❌ ERROR: x_introduced_212_ not defined
model.float_lin_eq(&x_introduced_214_, &vec![xb, butt], 3.7); // ❌ ERROR: x_introduced_214_ not defined
```

### What Should Be Generated

Based on the MiniZinc constraints like:
```minizinc
(1.0/4.82)*xm+(0.4/0.297)*milk = 1.4
```

The exporter should generate:
```rust
let x_introduced_212_ = vec![1.0/4.82, 0.4/0.297];
model.float_lin_eq(&x_introduced_212_, &vec![xm, milk], 1.4);
```

### Missing Arrays

From the comments, these parameter arrays need to be defined:
- `x_introduced_212_` - coefficients for equation with xm, milk
- `x_introduced_214_` - coefficients for equation with xb, butt
- `x_introduced_216_` - coefficients for equation with cha, xca, chb
- `x_introduced_218_` - coefficients for equation with chb, xcb, cha
- `x_introduced_220_` - coefficients for constraint with xca, xb, xm, xcb (≤ 0.6)
- `x_introduced_222_` - coefficients for constraint with xca, xb, xm, xcb (≤ 0.75)
- `x_introduced_224_` - coefficients for constraint with cha, butt, milk, chb (≤ 1.939)
- `x_introduced_226_` - coefficients for equation with chb, cha, q
- And several more for sum constraints

### Current Status

✅ Constraint structure is correct (the calls to float_lin_eq/float_lin_le are proper)
✅ Variables are declared correctly
❌ **Coefficient arrays are missing** - marked as "initialization skipped in export"
❌ **File does not compile** - 284 compilation errors due to undefined variables

### Next Steps for Zelen

1. Generate the coefficient array definitions for all `X_INTRODUCED_NNN_` parameter arrays
2. Each should be a `vec![...]` of floating-point coefficients
3. Extract the coefficients from the original FlatZinc constraints

---

**Date**: October 7, 2025
**Selen Version**: v0.9.4
**Analyzer**: GitHub Copilot
46 changes: 23 additions & 23 deletions Cargo.lock

Some generated files are not rendered by default. Learn more about how customized files appear on GitHub.

4 changes: 2 additions & 2 deletions Cargo.toml
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@@ -1,6 +1,6 @@
[package]
name = "zelen"
version = "0.1.1"
version = "0.2.0"
edition = "2024"
description = "Selen CSP solver parser for FlatZinc"
rust-version = "1.88"
Expand All @@ -26,7 +26,7 @@ name = "zelen"
path = "src/bin/zelen.rs"

[dependencies]
selen = "0.9"
selen = "0.12"
clap = { version = "4.5", features = ["derive"] }

[dev-dependencies]
Expand Down
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