oximo 0.3.0

A Rust algebraic modeling library for solving optimization problems
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232

//! Integration tests for the GAMS backend.
//!
//! These tests shell out to a GAMS installation and are therefore
//! compiled and run only when `--features gams` is passed.  Each test
//! mirrors the corresponding HiGHS test in `solve.rs` so that regressions
//! are caught on both backends.
//!
//! Run with:
//! ```
//! cargo test -p oximo --features gams --test solve_gams
//! ```

#![cfg(feature = "gams")]

use std::time::Duration;

use oximo::gams::{GamsCplexOptions, GamsHighsOptions, GamsHighsSolver, GamsSolverConfig};
use oximo::prelude::*;
use oximo::solvers::Gams;

#[test]
fn gams_lp_canonical() {
    let m = Model::new("lp");
    variable!(m, x >= 0.0);
    variable!(m, 0.0 <= y <= 4.0);
    constraint!(m, c1, x + 2.0 * y <= 14.0);
    constraint!(m, c2, 3.0 * x - y >= 0.0);
    constraint!(m, c3, x - y <= 2.0);
    objective!(m, Max, 3.0 * x + 4.0 * y);

    let opts = GamsOptions::default().time_limit(Duration::from_secs(60));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Optimal);
    assert!((result.objective().unwrap() - 34.0).abs() < 1e-4, "obj={:?}", result.objective());
    assert!((result.value_of(x).unwrap() - 6.0).abs() < 1e-4);
    assert!((result.value_of(y).unwrap() - 4.0).abs() < 1e-4);
}

#[test]
fn gams_lp_duals_and_reduced_costs() {
    // max x  s.t.  x <= 5,  x >= 0
    // Optimal: x = 5, dual of (x <= 5) = +/-1.0, reduced cost of x = 0.
    let m = Model::new("lp_dual");
    variable!(m, x >= 0.0);
    let c = constraint!(m, cap, x <= 5.0);
    objective!(m, Max, x);

    let opts = GamsOptions::default().time_limit(Duration::from_secs(30));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Optimal);
    assert!((result.objective().unwrap() - 5.0).abs() < 1e-6);

    let d = result.dual_of(c).expect("dual missing for cap constraint");
    assert!((d.abs() - 1.0).abs() < 1e-6, "dual={d}");

    // Only one variable in the model -> VarId(0).
    let rc = result.reduced_costs.get(&VarId(0)).copied().expect("reduced cost missing for x");
    assert!(rc.abs() < 1e-6, "reduced_cost(x)={rc}");
}

#[test]
fn gams_nlp_duals_at_local_point() {
    // min exp(x)  s.t.  x >= 1
    // Optimum: x = 1, obj e. KKT: exp(x) = lambda => dual of (x >= 1) = +/-e,
    // reduced cost of x = 0.
    let m = Model::new("nlp_dual");
    variable!(m, -10.0 <= x <= 10.0);
    let cap = constraint!(m, cap, x >= 1.0);
    objective!(m, Min, x.exp());

    let opts = GamsOptions::default().time_limit(Duration::from_secs(30));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert!(
        matches!(result.status, SolverStatus::Optimal | SolverStatus::Feasible),
        "status={:?}",
        result.status
    );
    assert!((result.objective().unwrap() - std::f64::consts::E).abs() < 1e-5);
    assert!((result.value_of(x).unwrap() - 1.0).abs() < 1e-5);

    let dual = result.dual_of(cap).expect("dual missing for cap");
    assert!((dual.abs() - std::f64::consts::E).abs() < 1e-5, "dual={dual}");
    let rc = result.reduced_costs.get(&VarId(0)).copied().expect("reduced cost missing for x");
    assert!(rc.abs() < 1e-5, "reduced_cost(x)={rc}");
}

#[test]
fn gams_mip_duals_at_fixed_point() {
    // max 2a + 3b  s.t.  a + b <= 1,  a, b binary.
    // GAMS MIP links re-solve with integers fixed, so `.m` carries
    // the duals of the fixed problem at the optimum (0, 1).
    // The exact split between constraint duals and reduced costs is
    // solver-dependent. We assert presence, not values.
    let m = Model::new("mip_dual");
    variable!(m, a, Bin);
    variable!(m, b, Bin);
    let cap = constraint!(m, cap, a + b <= 1.0);
    objective!(m, Max, 2.0 * a + 3.0 * b);

    let opts = GamsOptions::default().time_limit(Duration::from_secs(30));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Optimal);
    assert!((result.objective().unwrap() - 3.0).abs() < 1e-6);
    assert!(result.dual_of(cap).is_some(), "dual missing for cap");
    assert!(!result.reduced_costs.is_empty(), "reduced costs missing");
}

#[test]
fn gams_knapsack_milp() {
    let weights = [3.0, 4.0, 2.0, 5.0, 1.0, 6.0, 7.0, 2.0];
    let values = [10.0, 12.0, 5.0, 14.0, 3.0, 18.0, 22.0, 6.0];
    let n = weights.len();

    let m = Model::new("knapsack");
    variable!(m, x[i in 0..n], Bin);
    constraint!(m, cap, sum!(weights[i] * x[i] for i in 0..n) <= 15.0);
    objective!(m, Max, sum!(values[i] * x[i] for i in 0..n));

    let opts = GamsOptions::default().time_limit(Duration::from_secs(60));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Optimal);
    assert!((result.objective().unwrap() - 47.0).abs() < 1e-4, "obj={:?}", result.objective());
}

#[test]
fn gams_infeasible_returns_status() {
    let m = Model::new("infeas");
    variable!(m, 0.0 <= x <= 1.0);
    constraint!(m, c1, x >= 5.0);
    objective!(m, Min, x);

    let opts = GamsOptions::default().time_limit(Duration::from_secs(30));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Infeasible);
}

#[test]
fn gams_mip_gap_option() {
    let weights = [3.0, 4.0, 2.0, 5.0, 1.0];
    let values = [10.0, 12.0, 5.0, 14.0, 3.0];
    let n = weights.len();
    let m = Model::new("ks");
    variable!(m, x[i in 0..n], Bin);
    constraint!(m, cap, sum!(weights[i] * x[i] for i in 0..n) <= 8.0);
    objective!(m, Max, sum!(values[i] * x[i] for i in 0..n));

    let result = Gams::new().solve(&m, &GamsOptions::default().mip_gap(0.5)).unwrap();
    assert!(
        matches!(result.status, SolverStatus::Optimal | SolverStatus::Feasible),
        "unexpected status: {:?}",
        result.status
    );
    assert!(result.objective().unwrap() > 0.0);
}

/// Exercises the typed-options path: a `highs.opt` file is written with
/// `solver = simplex` and GAMS picks it up via `model.optfile = 1`.
///
/// Requires GAMS with HiGHS available as a sub-solver.
#[test]
fn gams_highs_opt_file_simplex() {
    let m = Model::new("lp");
    variable!(m, x >= 0.0);
    variable!(m, 0.0 <= y <= 4.0);
    constraint!(m, c1, x + 2.0 * y <= 14.0);
    constraint!(m, c2, 3.0 * x - y >= 0.0);
    constraint!(m, c3, x - y <= 2.0);
    objective!(m, Max, 3.0 * x + 4.0 * y);

    let opts = GamsOptions::default().solver(GamsSolverConfig::Highs(GamsHighsOptions {
        solver: Some(GamsHighsSolver::Simplex),
        ..Default::default()
    }));
    let result = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(result.status, SolverStatus::Optimal);
    assert!((result.objective().unwrap() - 34.0).abs() < 1e-4, "obj={:?}", result.objective());
}

#[test]
fn gams_multi_optima_returns_single_best() {
    // A MILP with several optimal solutions. Without a sub-solver pool option the
    // GAMS bridge returns one optimum: exactly one valid point.
    let m = Model::new("multi");
    let items = Set::range(0..4usize);
    variable!(m, x[i in items], Bin);
    constraint!(m, cap, sum!(x[i] for i in items) <= 2.0);
    objective!(m, Max, sum!(x[i] for i in items));

    let opts = GamsOptions::default().time_limit(Duration::from_secs(60));
    let r = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(r.status, SolverStatus::Optimal);
    assert_eq!(r.result_count(), 1);
    assert!((r.objective().unwrap() - 2.0).abs() < 1e-4);
    let chosen: f64 = (0..4).filter_map(|i| r.value_of_idx(&x, i)).sum();
    assert!((chosen - 2.0).abs() < 1e-4, "best is not an optimum: sum={chosen}");
}

#[test]
fn gams_reads_cplex_solution_pool() {
    // Same multi-optima MILP. When the user enables CPLEX's `solnpool`, the
    // sub-solver writes a pool of GDX files into the run directory.
    // The GAMS backend reads them back and surfaces every point, best first.
    // Requires a GAMS install with a licensed CPLEX.
    let m = Model::new("multi");
    let items = Set::range(0..4usize);
    variable!(m, x[i in items], Bin);
    constraint!(m, cap, sum!(x[i] for i in items) <= 2.0);
    objective!(m, Max, sum!(x[i] for i in items));

    let cfg = GamsSolverConfig::Cplex(GamsCplexOptions {
        raw: vec![
            "solnpool oximo_pool.gdx".into(),
            "solnpoolpop 2".into(),
            "populatelim 20".into(),
        ],
        ..Default::default()
    });
    let opts = GamsOptions::default().solver(cfg).time_limit(Duration::from_secs(60));
    let r = Gams::new().solve(&m, &opts).unwrap();
    assert_eq!(r.status, SolverStatus::Optimal);
    assert!(r.result_count() > 1, "expected a solution pool, got {}", r.result_count());

    assert!((r.objective().unwrap() - 2.0).abs() < 1e-4);
    let mut prev = f64::INFINITY;
    for s in &r.solutions {
        let chosen: f64 = (0..4).filter_map(|i| s.value_of_idx(&x, i)).sum();
        assert!(chosen <= 2.0 + 1e-6, "infeasible pool point: sum={chosen}");
        let obj = s.objective.expect("pool point has an objective");
        assert!(obj <= prev + 1e-9, "pool not ordered best-first");
        prev = obj;
    }
}