Complete max PB constraints optimization with tests

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

test_max_pb_unit.cpp

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+/*++
+Copyright (c) 2024 Microsoft Corporation
+
+Module Name:
+
+    test_pb_max_optimization.cpp
+
+Abstract:
+
+    Test for max PB constraints optimization feature
+
+Author:
+
+    GitHub Copilot 2024-12-19
+
+--*/
+
+#include "opt/opt_context.h"
+#include "ast/arith_decl_plugin.h"
+#include "util/trace.h"
+
+void test_max_pb_optimization() {
+    ast_manager m;
+    opt::context ctx(m);
+    arith_util arith(m);
+    
+    // Create boolean variables
+    expr_ref x1(m.mk_const(symbol("x1"), m.mk_bool_sort()), m);
+    expr_ref x2(m.mk_const(symbol("x2"), m.mk_bool_sort()), m);
+    expr_ref y1(m.mk_const(symbol("y1"), m.mk_bool_sort()), m);
+    expr_ref y2(m.mk_const(symbol("y2"), m.mk_bool_sort()), m);
+    
+    // Create PB constraints as integer expressions
+    expr_ref pb1(arith.mk_add(
+        arith.mk_mul(arith.mk_numeral(rational(2), true), 
+                     m.mk_ite(x1, arith.mk_numeral(rational(1), true), arith.mk_numeral(rational(0), true))),
+        m.mk_ite(x2, arith.mk_numeral(rational(1), true), arith.mk_numeral(rational(0), true))), m);
+    
+    expr_ref pb2(arith.mk_add(
+        m.mk_ite(y1, arith.mk_numeral(rational(1), true), arith.mk_numeral(rational(0), true)),
+        arith.mk_mul(arith.mk_numeral(rational(2), true),
+                     m.mk_ite(y2, arith.mk_numeral(rational(1), true), arith.mk_numeral(rational(0), true)))), m);
+    
+    // Add two maximize objectives
+    ctx.add_objective(to_app(pb1), true);  // maximize
+    ctx.add_objective(to_app(pb2), true);  // maximize
+    
+    // Check optimization
+    expr_ref_vector asms(m);
+    lbool result = ctx.optimize(asms);
+    
+    ENSURE(result == l_true);
+    
+    std::cout << "Max PB optimization test passed!" << std::endl;
+}
+
+int main() {
+    try {
+        test_max_pb_optimization();
+        return 0;
+    } catch (std::exception& e) {
+        std::cerr << "Test failed: " << e.what() << std::endl;
+        return 1;
+    }
+}

test_pb_feature.smt2

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+;; Test case for max PB constraints optimization feature
+;; This demonstrates the transformation from multiple maximize objectives
+;; to auxiliary variables with threshold constraints
+
+(echo "Testing max PB constraints optimization")
+
+;; Declare boolean variables
+(declare-fun x1 () Bool)
+(declare-fun x2 () Bool) 
+(declare-fun y1 () Bool)
+(declare-fun y2 () Bool)
+
+;; Test case: Two PB constraints to maximize
+;; PB1: 2*x1 + x2 (max value = 3)
+;; PB2: y1 + 2*y2 (max value = 3)
+
+(maximize (+ (ite x1 2 0) (ite x2 1 0)))
+(maximize (+ (ite y1 1 0) (ite y2 2 0)))
+
+(echo "Before optimization:")
+(check-sat)
+
+;; The implementation should detect these two PB maximize objectives
+;; and transform them to auxiliary variables:
+;; - For PB1: aux_0_1, aux_0_2, aux_0_3 where PB1 >= k => aux_0_k
+;; - For PB2: aux_1_1, aux_1_2, aux_1_3 where PB2 >= k => aux_1_k  
+;; - Then maximize: aux_0_1 + aux_0_2 + aux_0_3 + aux_1_1 + aux_1_2 + aux_1_3
+
+(echo "Max PB optimization feature test completed")