647 lines
22 KiB
C++
647 lines
22 KiB
C++
// Copyright 2010-2021 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "ortools/sat/encoding.h"
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#include <algorithm>
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#include <cstdint>
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#include <deque>
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#include <queue>
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#include <vector>
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#include "ortools/base/logging.h"
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#include "ortools/sat/boolean_problem.pb.h"
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#include "ortools/sat/pb_constraint.h"
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#include "ortools/sat/sat_base.h"
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#include "ortools/sat/sat_parameters.pb.h"
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#include "ortools/sat/sat_solver.h"
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#include "ortools/util/strong_integers.h"
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namespace operations_research {
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namespace sat {
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EncodingNode::EncodingNode(Literal l)
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: for_sorting_(l.Variable()),
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child_a_(nullptr),
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child_b_(nullptr),
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literals_(1, l) {}
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void EncodingNode::InitializeFullNode(int n, EncodingNode* a, EncodingNode* b,
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SatSolver* solver) {
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CHECK(literals_.empty()) << "Already initialized";
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CHECK_GT(n, 0);
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const BooleanVariable first_var_index(solver->NumVariables());
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solver->SetNumVariables(solver->NumVariables() + n);
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for (int i = 0; i < n; ++i) {
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literals_.push_back(Literal(first_var_index + i, true));
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if (i > 0) {
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solver->AddBinaryClause(literal(i - 1), literal(i).Negated());
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}
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}
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lb_ = a->lb_ + b->lb_;
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ub_ = lb_ + n;
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depth_ = 1 + std::max(a->depth_, b->depth_);
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child_a_ = a;
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child_b_ = b;
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for_sorting_ = first_var_index;
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}
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void EncodingNode::InitializeLazyNode(EncodingNode* a, EncodingNode* b,
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SatSolver* solver) {
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CHECK(literals_.empty()) << "Already initialized";
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const BooleanVariable first_var_index(solver->NumVariables());
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solver->SetNumVariables(solver->NumVariables() + 1);
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literals_.emplace_back(first_var_index, true);
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child_a_ = a;
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child_b_ = b;
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ub_ = a->ub_ + b->ub_;
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lb_ = a->lb_ + b->lb_;
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depth_ = 1 + std::max(a->depth_, b->depth_);
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// Merging the node of the same depth in order seems to help a bit.
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for_sorting_ = std::min(a->for_sorting_, b->for_sorting_);
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}
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void EncodingNode::InitializeLazyCoreNode(Coefficient weight, EncodingNode* a,
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EncodingNode* b) {
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CHECK(literals_.empty()) << "Already initialized";
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child_a_ = a;
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child_b_ = b;
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ub_ = a->ub_ + b->ub_;
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weight_ = weight;
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weight_lb_ = a->lb_ + b->lb_;
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lb_ = weight_lb_ + 1;
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depth_ = 1 + std::max(a->depth_, b->depth_);
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// Merging the node of the same depth in order seems to help a bit.
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for_sorting_ = std::min(a->for_sorting_, b->for_sorting_);
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}
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bool EncodingNode::IncreaseCurrentUB(SatSolver* solver) {
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if (current_ub() == ub_) return false;
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literals_.emplace_back(BooleanVariable(solver->NumVariables()), true);
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solver->SetNumVariables(solver->NumVariables() + 1);
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if (literals_.size() > 1) {
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solver->AddBinaryClause(literals_.back().Negated(),
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literals_[literals_.size() - 2]);
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}
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return true;
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}
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Coefficient EncodingNode::Reduce(const SatSolver& solver) {
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int i = 0;
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while (i < literals_.size() &&
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solver.Assignment().LiteralIsTrue(literals_[i])) {
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++i;
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++lb_;
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}
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literals_.erase(literals_.begin(), literals_.begin() + i);
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while (!literals_.empty() &&
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solver.Assignment().LiteralIsFalse(literals_.back())) {
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literals_.pop_back();
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ub_ = lb_ + literals_.size();
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}
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if (weight_lb_ >= lb_) return Coefficient(0);
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const Coefficient result = Coefficient(lb_ - weight_lb_) * weight_;
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weight_lb_ = lb_;
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return result;
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}
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void EncodingNode::ApplyWeightUpperBound(Coefficient gap, SatSolver* solver) {
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CHECK_GT(weight_, 0);
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const Coefficient num_allowed = (gap / weight_);
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const Coefficient new_size =
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std::max(Coefficient(0), Coefficient(weight_lb_ - lb_) + num_allowed);
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if (size() <= new_size) return;
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for (int i = new_size.value(); i < size(); ++i) {
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solver->AddUnitClause(literal(i).Negated());
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}
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literals_.resize(new_size.value());
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ub_ = lb_ + literals_.size();
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}
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Literal EncodingNode::GetAssumption(SatSolver* solver) {
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CHECK(!HasNoWeight());
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const int index = weight_lb_ - lb_;
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CHECK_GE(index, 0) << "Not reduced?";
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while (index >= literals_.size()) {
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CHECK_NE(solver, nullptr);
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IncreaseNodeSize(this, solver);
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}
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return literals_[index].Negated();
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}
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void EncodingNode::IncreaseWeightLb() {
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CHECK_LT(weight_lb_ - lb_, literals_.size());
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weight_lb_++;
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}
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bool EncodingNode::HasNoWeight() const {
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return weight_ == 0 || weight_lb_ >= ub_;
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}
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std::string EncodingNode::DebugString(
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const VariablesAssignment& assignment) const {
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std::string result;
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absl::StrAppend(&result, "depth:", depth_);
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absl::StrAppend(&result, " [", lb_, ",", lb_ + literals_.size(), "]");
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absl::StrAppend(&result, " ub:", ub_);
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absl::StrAppend(&result, " weight:", weight_.value());
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absl::StrAppend(&result, " weight_lb:", weight_lb_);
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absl::StrAppend(&result, " values:");
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const size_t limit = 20;
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int value = 0;
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for (int i = 0; i < std::min(literals_.size(), limit); ++i) {
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char c = '?';
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if (assignment.LiteralIsTrue(literals_[i])) {
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c = '1';
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value = i + 1;
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} else if (assignment.LiteralIsFalse(literals_[i])) {
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c = '0';
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}
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result += c;
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}
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absl::StrAppend(&result, " val:", lb_ + value);
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return result;
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}
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EncodingNode LazyMerge(EncodingNode* a, EncodingNode* b, SatSolver* solver) {
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EncodingNode n;
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n.InitializeLazyNode(a, b, solver);
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solver->AddBinaryClause(a->literal(0).Negated(), n.literal(0));
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solver->AddBinaryClause(b->literal(0).Negated(), n.literal(0));
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solver->AddTernaryClause(n.literal(0).Negated(), a->literal(0),
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b->literal(0));
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return n;
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}
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void IncreaseNodeSize(EncodingNode* node, SatSolver* solver) {
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if (!node->IncreaseCurrentUB(solver)) return;
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std::vector<EncodingNode*> to_process;
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to_process.push_back(node);
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// Only one side of the constraint is mandatory (the one propagating the ones
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// to the top of the encoding tree), and it seems more efficient not to encode
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// the other side.
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//
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// TODO(user): Experiment more.
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const bool complete_encoding = false;
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while (!to_process.empty()) {
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EncodingNode* n = to_process.back();
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EncodingNode* a = n->child_a();
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EncodingNode* b = n->child_b();
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to_process.pop_back();
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// Note that since we were able to increase its size, n must have children.
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// n->GreaterThan(target) is the new literal of n.
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CHECK(a != nullptr);
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CHECK(b != nullptr);
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const int target = n->current_ub() - 1;
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// Add a literal to a if needed.
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// That is, now that the node n can go up to it new current_ub, if we need
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// to increase the current_ub of a.
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if (a->current_ub() != a->ub()) {
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CHECK_GE(a->current_ub() - 1 + b->lb(), target - 1);
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if (a->current_ub() - 1 + b->lb() < target) {
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CHECK(a->IncreaseCurrentUB(solver));
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to_process.push_back(a);
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}
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}
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// Add a literal to b if needed.
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if (b->current_ub() != b->ub()) {
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CHECK_GE(b->current_ub() - 1 + a->lb(), target - 1);
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if (b->current_ub() - 1 + a->lb() < target) {
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CHECK(b->IncreaseCurrentUB(solver));
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to_process.push_back(b);
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}
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}
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// Wire the new literal of n correctly with its two children.
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for (int ia = a->lb(); ia < a->current_ub(); ++ia) {
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const int ib = target - ia;
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if (complete_encoding && ib >= b->lb() && ib < b->current_ub()) {
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// if x <= ia and y <= ib then x + y <= ia + ib.
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solver->AddTernaryClause(n->GreaterThan(target).Negated(),
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a->GreaterThan(ia), b->GreaterThan(ib));
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}
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if (complete_encoding && ib == b->ub()) {
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solver->AddBinaryClause(n->GreaterThan(target).Negated(),
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a->GreaterThan(ia));
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}
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if (ib - 1 == b->lb() - 1) {
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solver->AddBinaryClause(n->GreaterThan(target),
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a->GreaterThan(ia).Negated());
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}
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if ((ib - 1) >= b->lb() && (ib - 1) < b->current_ub()) {
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// if x > ia and y > ib - 1 then x + y > ia + ib.
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solver->AddTernaryClause(n->GreaterThan(target),
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a->GreaterThan(ia).Negated(),
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b->GreaterThan(ib - 1).Negated());
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}
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}
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// Case ia = a->lb() - 1; a->GreaterThan(ia) always true.
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{
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const int ib = target - (a->lb() - 1);
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if ((ib - 1) == b->lb() - 1) {
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solver->AddUnitClause(n->GreaterThan(target));
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}
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if ((ib - 1) >= b->lb() && (ib - 1) < b->current_ub()) {
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solver->AddBinaryClause(n->GreaterThan(target),
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b->GreaterThan(ib - 1).Negated());
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}
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}
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// case ia == a->ub; a->GreaterThan(ia) always false.
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{
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const int ib = target - a->ub();
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if (complete_encoding && ib >= b->lb() && ib < b->current_ub()) {
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solver->AddBinaryClause(n->GreaterThan(target).Negated(),
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b->GreaterThan(ib));
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}
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if (ib == b->ub()) {
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solver->AddUnitClause(n->GreaterThan(target).Negated());
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}
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}
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}
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}
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EncodingNode FullMerge(Coefficient upper_bound, EncodingNode* a,
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EncodingNode* b, SatSolver* solver) {
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EncodingNode n;
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const int size =
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std::min(Coefficient(a->size() + b->size()), upper_bound).value();
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n.InitializeFullNode(size, a, b, solver);
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for (int ia = 0; ia < a->size(); ++ia) {
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if (ia + b->size() < size) {
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solver->AddBinaryClause(n.literal(ia + b->size()).Negated(),
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a->literal(ia));
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}
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if (ia < size) {
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solver->AddBinaryClause(n.literal(ia), a->literal(ia).Negated());
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} else {
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// Fix the variable to false because of the given upper_bound.
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solver->AddUnitClause(a->literal(ia).Negated());
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}
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}
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for (int ib = 0; ib < b->size(); ++ib) {
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if (ib + a->size() < size) {
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solver->AddBinaryClause(n.literal(ib + a->size()).Negated(),
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b->literal(ib));
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}
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if (ib < size) {
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solver->AddBinaryClause(n.literal(ib), b->literal(ib).Negated());
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} else {
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// Fix the variable to false because of the given upper_bound.
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solver->AddUnitClause(b->literal(ib).Negated());
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}
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}
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for (int ia = 0; ia < a->size(); ++ia) {
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for (int ib = 0; ib < b->size(); ++ib) {
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if (ia + ib < size) {
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// if x <= ia and y <= ib, then x + y <= ia + ib.
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solver->AddTernaryClause(n.literal(ia + ib).Negated(), a->literal(ia),
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b->literal(ib));
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}
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if (ia + ib + 1 < size) {
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// if x > ia and y > ib, then x + y > ia + ib + 1.
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solver->AddTernaryClause(n.literal(ia + ib + 1),
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a->literal(ia).Negated(),
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b->literal(ib).Negated());
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} else {
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solver->AddBinaryClause(a->literal(ia).Negated(),
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b->literal(ib).Negated());
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}
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}
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}
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return n;
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}
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EncodingNode* MergeAllNodesWithDeque(Coefficient upper_bound,
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const std::vector<EncodingNode*>& nodes,
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SatSolver* solver,
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std::deque<EncodingNode>* repository) {
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std::deque<EncodingNode*> dq(nodes.begin(), nodes.end());
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while (dq.size() > 1) {
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EncodingNode* a = dq.front();
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dq.pop_front();
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EncodingNode* b = dq.front();
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dq.pop_front();
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repository->push_back(FullMerge(upper_bound, a, b, solver));
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dq.push_back(&repository->back());
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}
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return dq.front();
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}
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namespace {
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struct SortEncodingNodePointers {
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bool operator()(EncodingNode* a, EncodingNode* b) const { return *a < *b; }
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};
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} // namespace
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EncodingNode* LazyMergeAllNodeWithPQAndIncreaseLb(
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Coefficient weight, const std::vector<EncodingNode*>& nodes,
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SatSolver* solver, std::deque<EncodingNode>* repository) {
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std::priority_queue<EncodingNode*, std::vector<EncodingNode*>,
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SortEncodingNodePointers>
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pq(nodes.begin(), nodes.end());
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while (pq.size() > 2) {
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EncodingNode* a = pq.top();
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pq.pop();
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EncodingNode* b = pq.top();
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pq.pop();
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repository->push_back(LazyMerge(a, b, solver));
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pq.push(&repository->back());
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}
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CHECK_EQ(pq.size(), 2);
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EncodingNode* a = pq.top();
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pq.pop();
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EncodingNode* b = pq.top();
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pq.pop();
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repository->push_back(EncodingNode());
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EncodingNode* n = &repository->back();
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n->InitializeLazyCoreNode(weight, a, b);
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solver->AddBinaryClause(a->literal(0), b->literal(0));
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return n;
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}
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std::vector<EncodingNode*> CreateInitialEncodingNodes(
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const std::vector<Literal>& literals,
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const std::vector<Coefficient>& coeffs, Coefficient* offset,
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std::deque<EncodingNode>* repository) {
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CHECK_EQ(literals.size(), coeffs.size());
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*offset = 0;
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std::vector<EncodingNode*> nodes;
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for (int i = 0; i < literals.size(); ++i) {
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// We want to maximize the cost when this literal is true.
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if (coeffs[i] > 0) {
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repository->emplace_back(literals[i]);
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nodes.push_back(&repository->back());
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nodes.back()->set_weight(coeffs[i]);
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} else {
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repository->emplace_back(literals[i].Negated());
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nodes.push_back(&repository->back());
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nodes.back()->set_weight(-coeffs[i]);
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// Note that this increase the offset since the coeff is negative.
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*offset -= coeffs[i];
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}
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}
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return nodes;
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}
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std::vector<EncodingNode*> CreateInitialEncodingNodes(
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const LinearObjective& objective_proto, Coefficient* offset,
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std::deque<EncodingNode>* repository) {
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*offset = 0;
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std::vector<EncodingNode*> nodes;
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for (int i = 0; i < objective_proto.literals_size(); ++i) {
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const Literal literal(objective_proto.literals(i));
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// We want to maximize the cost when this literal is true.
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if (objective_proto.coefficients(i) > 0) {
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repository->emplace_back(literal);
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nodes.push_back(&repository->back());
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nodes.back()->set_weight(Coefficient(objective_proto.coefficients(i)));
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} else {
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repository->emplace_back(literal.Negated());
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nodes.push_back(&repository->back());
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nodes.back()->set_weight(Coefficient(-objective_proto.coefficients(i)));
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// Note that this increase the offset since the coeff is negative.
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*offset -= objective_proto.coefficients(i);
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}
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}
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return nodes;
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}
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namespace {
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bool EncodingNodeByWeight(const EncodingNode* a, const EncodingNode* b) {
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return a->weight() < b->weight();
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}
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bool EncodingNodeByDepth(const EncodingNode* a, const EncodingNode* b) {
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return a->depth() < b->depth();
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}
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} // namespace
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std::vector<Literal> ReduceNodesAndExtractAssumptions(
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Coefficient upper_bound, Coefficient stratified_lower_bound,
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Coefficient* lower_bound, std::vector<EncodingNode*>* nodes,
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SatSolver* solver) {
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// Remove the left-most variables fixed to one from each node.
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// Also update the lower_bound. Note that Reduce() needs the solver to be
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// at the root node in order to work.
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solver->Backtrack(0);
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for (EncodingNode* n : *nodes) {
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*lower_bound += n->Reduce(*solver);
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}
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// Fix the nodes right-most variables that are above the gap.
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// If we closed the problem, we abort and return and empty vector.
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if (upper_bound != kCoefficientMax) {
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const Coefficient gap = upper_bound - *lower_bound;
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if (gap < 0) return {};
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for (EncodingNode* n : *nodes) {
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n->ApplyWeightUpperBound(gap, solver);
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}
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}
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// Remove the empty nodes.
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nodes->erase(std::remove_if(nodes->begin(), nodes->end(),
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[](EncodingNode* a) { return a->HasNoWeight(); }),
|
|
nodes->end());
|
|
|
|
// Sort the nodes.
|
|
switch (solver->parameters().max_sat_assumption_order()) {
|
|
case SatParameters::DEFAULT_ASSUMPTION_ORDER:
|
|
break;
|
|
case SatParameters::ORDER_ASSUMPTION_BY_DEPTH:
|
|
std::sort(nodes->begin(), nodes->end(), EncodingNodeByDepth);
|
|
break;
|
|
case SatParameters::ORDER_ASSUMPTION_BY_WEIGHT:
|
|
std::sort(nodes->begin(), nodes->end(), EncodingNodeByWeight);
|
|
break;
|
|
}
|
|
if (solver->parameters().max_sat_reverse_assumption_order()) {
|
|
// TODO(user): with DEFAULT_ASSUMPTION_ORDER, this will lead to a somewhat
|
|
// weird behavior, since we will reverse the nodes at each iteration...
|
|
std::reverse(nodes->begin(), nodes->end());
|
|
}
|
|
|
|
// Extract the assumptions from the nodes.
|
|
std::vector<Literal> assumptions;
|
|
for (EncodingNode* n : *nodes) {
|
|
if (n->weight() >= stratified_lower_bound) {
|
|
assumptions.push_back(n->GetAssumption(solver));
|
|
}
|
|
}
|
|
return assumptions;
|
|
}
|
|
|
|
Coefficient ComputeCoreMinWeight(const std::vector<EncodingNode*>& nodes,
|
|
const std::vector<Literal>& core) {
|
|
Coefficient min_weight = kCoefficientMax;
|
|
int index = 0;
|
|
for (int i = 0; i < core.size(); ++i) {
|
|
for (; index < nodes.size() &&
|
|
nodes[index]->GetAssumption(nullptr) != core[i];
|
|
++index) {
|
|
}
|
|
CHECK_LT(index, nodes.size());
|
|
min_weight = std::min(min_weight, nodes[index]->weight());
|
|
}
|
|
return min_weight;
|
|
}
|
|
|
|
Coefficient MaxNodeWeightSmallerThan(const std::vector<EncodingNode*>& nodes,
|
|
Coefficient upper_bound) {
|
|
Coefficient result(0);
|
|
for (EncodingNode* n : nodes) {
|
|
CHECK_GT(n->weight(), 0);
|
|
if (n->weight() < upper_bound) {
|
|
result = std::max(result, n->weight());
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
bool ProcessCore(const std::vector<Literal>& core, Coefficient min_weight,
|
|
std::deque<EncodingNode>* repository,
|
|
std::vector<EncodingNode*>* nodes, SatSolver* solver) {
|
|
// Backtrack to be able to add new constraints.
|
|
solver->ResetToLevelZero();
|
|
if (core.size() == 1) {
|
|
return solver->AddUnitClause(core[0].Negated());
|
|
}
|
|
|
|
// Remove from nodes the EncodingNode in the core, merge them, and add the
|
|
// resulting EncodingNode at the back.
|
|
int index = 0;
|
|
int new_node_index = 0;
|
|
std::vector<EncodingNode*> to_merge;
|
|
for (int i = 0; i < core.size(); ++i) {
|
|
// Since the nodes appear in order in the core, we can find the
|
|
// relevant "objective" variable efficiently with a simple linear scan
|
|
// in the nodes vector (done with index).
|
|
for (; (*nodes)[index]->GetAssumption(nullptr) != core[i]; ++index) {
|
|
CHECK_LT(index, nodes->size());
|
|
(*nodes)[new_node_index] = (*nodes)[index];
|
|
++new_node_index;
|
|
}
|
|
CHECK_LT(index, nodes->size());
|
|
to_merge.push_back((*nodes)[index]);
|
|
|
|
// Special case if the weight > min_weight. we keep it, but reduce its
|
|
// cost. This is the same "trick" as in WPM1 used to deal with weight.
|
|
// We basically split a clause with a larger weight in two identical
|
|
// clauses, one with weight min_weight that will be merged and one with
|
|
// the remaining weight.
|
|
if ((*nodes)[index]->weight() > min_weight) {
|
|
(*nodes)[index]->set_weight((*nodes)[index]->weight() - min_weight);
|
|
(*nodes)[new_node_index] = (*nodes)[index];
|
|
++new_node_index;
|
|
}
|
|
++index;
|
|
}
|
|
for (; index < nodes->size(); ++index) {
|
|
(*nodes)[new_node_index] = (*nodes)[index];
|
|
++new_node_index;
|
|
}
|
|
nodes->resize(new_node_index);
|
|
nodes->push_back(LazyMergeAllNodeWithPQAndIncreaseLb(min_weight, to_merge,
|
|
solver, repository));
|
|
return !solver->IsModelUnsat();
|
|
}
|
|
|
|
bool ProcessCoreWithNewEncoding(const std::vector<Literal>& core,
|
|
Coefficient min_weight,
|
|
std::deque<EncodingNode>* repository,
|
|
std::vector<EncodingNode*>* nodes,
|
|
SatSolver* solver) {
|
|
// Backtrack to be able to add new constraints.
|
|
solver->ResetToLevelZero();
|
|
|
|
if (core.size() == 1) {
|
|
return solver->AddUnitClause(core[0].Negated());
|
|
}
|
|
|
|
std::vector<EncodingNode*> new_nodes;
|
|
std::vector<EncodingNode*> to_merge;
|
|
|
|
// Preconditions.
|
|
for (EncodingNode* n : *nodes) {
|
|
CHECK_GT(n->size(), 0);
|
|
}
|
|
|
|
// Remove from nodes the EncodingNode in the core, merge them, and add the
|
|
// resulting EncodingNode at the back.
|
|
int index = 0;
|
|
for (int i = 0; i < core.size(); ++i) {
|
|
// Since the nodes appear in order in the core, we can find the
|
|
// relevant "objective" variable efficiently with a simple linear scan
|
|
// in the nodes vector (done with index).
|
|
CHECK_LT(index, nodes->size());
|
|
for (; (*nodes)[index]->GetAssumption(nullptr) != core[i]; ++index) {
|
|
CHECK_LT(index, nodes->size());
|
|
new_nodes.push_back((*nodes)[index]);
|
|
}
|
|
CHECK_LT(index, nodes->size());
|
|
|
|
// We have a node from the core.
|
|
// We will distinguish its first literal.
|
|
EncodingNode* n = (*nodes)[index];
|
|
const Literal lit = n->GetAssumption(nullptr).Negated();
|
|
n->IncreaseWeightLb();
|
|
++index;
|
|
CHECK_GT(n->size(), 0);
|
|
|
|
// TODO(user): For node with same depth, the sorting order is not the same
|
|
// if we create a new node or reuse one. Experiment what is the best order.
|
|
repository->emplace_back(lit);
|
|
EncodingNode* new_bool_node = &repository->back();
|
|
new_bool_node->set_depth(n->depth());
|
|
CHECK_GT(new_bool_node->size(), 0);
|
|
to_merge.push_back(new_bool_node);
|
|
if (n->weight() > min_weight) {
|
|
new_bool_node->set_weight(n->weight() - min_weight);
|
|
new_nodes.push_back(new_bool_node);
|
|
}
|
|
|
|
if (!n->HasNoWeight()) {
|
|
new_nodes.push_back(n);
|
|
}
|
|
}
|
|
|
|
for (; index < nodes->size(); ++index) {
|
|
new_nodes.push_back((*nodes)[index]);
|
|
}
|
|
|
|
new_nodes.push_back(LazyMergeAllNodeWithPQAndIncreaseLb(min_weight, to_merge,
|
|
solver, repository));
|
|
*nodes = new_nodes;
|
|
return !solver->IsModelUnsat();
|
|
}
|
|
|
|
} // namespace sat
|
|
} // namespace operations_research
|