org.chocosolver.solver.constraints.nary.flow.PropMinCostMaxFlow Maven / Gradle / Ivy
/*
* This file is part of choco-solver, http://choco-solver.org/
*
* Copyright (c) 2022, IMT Atlantique. All rights reserved.
*
* Licensed under the BSD 4-clause license.
*
* See LICENSE file in the project root for full license information.
*/
package org.chocosolver.solver.constraints.nary.flow;
import org.chocosolver.solver.constraints.Propagator;
import org.chocosolver.solver.constraints.PropagatorPriority;
import org.chocosolver.solver.exception.ContradictionException;
import org.chocosolver.solver.variables.IntVar;
import org.chocosolver.solver.variables.events.PropagatorEventType;
import org.chocosolver.util.ESat;
import org.chocosolver.util.objects.IntCircularQueue;
import org.chocosolver.util.tools.ArrayUtils;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.List;
/**
*
*
* @author Charles Prud'homme
* @since 06/01/2022
*/
public class PropMinCostMaxFlow extends Propagator {
private final int offset;
private final int[] starts;
private final int[] ends;
private final int[] balances;
private final int[] weights;
private final IntVar[] flows;
private final IntVar cost;
private final Residual g;
private final BitSet toCheck;
public PropMinCostMaxFlow(int[] starts, int[] ends, int[] balances, int[] weights, IntVar[] flows, IntVar cost, int offset) {
super(ArrayUtils.append(flows, new IntVar[]{cost}), PropagatorPriority.QUADRATIC, true);
this.offset = offset;
this.starts = starts;
this.ends = ends;
this.balances = balances;
this.weights = weights;
this.flows = flows;
this.cost = cost;
this.g = new Residual();
this.toCheck = new BitSet(flows.length);
}
@Override
public void propagate(int evtmask) throws ContradictionException {
if (PropagatorEventType.isFullPropagation(evtmask)) {
toCheck.clear();
toCheck.set(0, flows.length);
}
g.refresh(-1, 0);
int minCost = minCostFlow(-1, 0);
if (minCost == -1) {
toCheck.clear();
this.fails();
}
this.cost.updateLowerBound(minCost, this);
int maxcost = this.cost.getUB();
try {
for (int i = toCheck.nextSetBit(0); i > -1; i = toCheck.nextSetBit(i + 1)) {
updateFlow4(i, maxcost);
}
} finally {
toCheck.clear();
}
}
private void updateFlow0(int i, int minCost, int maxcost) throws ContradictionException {
int l = flows[i].getLB();
int u = flows[i].getUB();
int m = u;
g.refresh(i, m);
int c = minCostFlow(i, m);
if (c > maxcost || c == -1) {
while (l <= u) {
m = (l + u) >>> 1;
g.refresh(i, m);
c = minCostFlow(i, m);
if (c == -1) {
u = m - 1;
} else if (c > maxcost) {
u = m - 1;
} else if (c < maxcost) {
l = m + 1;
} else break;
}
flows[i].updateUpperBound(m, this);
}
}
private void updateFlow1(int i, int minCost, int maxcost) throws ContradictionException {
int c;
int l;
do {
l = flows[i].getLB();
g.refresh(i, l);
c = minCostFlow(i, l);
} while ((c == -1 || c < minCost) && flows[i].updateLowerBound(l + 1, this));
int u;
do {
u = flows[i].getUB();
g.refresh(i, u);
c = minCostFlow(i, u);
} while ((c == -1 || c > maxcost) && flows[i].updateUpperBound(u - 1, this));
}
private void updateFlow4(int i, int maxcost) throws ContradictionException {
int l = flows[i].getLB();
int u = flows[i].getUB();
int m = u;
g.refresh(i, m);
int c = minCostFlow(i, m);
if (c > maxcost || c == -1) {
while (l <= u) {
m = (l + u) >>> 1;
g.refresh(i, m);
c = minCostFlow(i, m);
if (c == -1) {
u = m - 1;
} else if (c > maxcost) {
u = m - 1;
} else if (c < maxcost) {
l = m + 1;
} else break;
}
flows[i].updateUpperBound(m, this);
if (l == u + 1) {
u = flows[i].getUB();
g.refresh(i, u);
c = minCostFlow(i, u);
if (c == -1 || c > maxcost) {
flows[i].updateUpperBound(u - 1, this);
}
}
}
}
@Override
public void propagate(int idxVarInProp, int mask) throws ContradictionException {
if (idxVarInProp < flows.length) {
toCheck.set(idxVarInProp);
} else {
toCheck.set(0, flows.length);
}
forcePropagate(PropagatorEventType.CUSTOM_PROPAGATION);
}
////////////////////////
private final static class Edge {
final int id;
final int from;
final int to;
int capacity;
int flow;
final int cost;
final int rId;
public Edge(int id, int from, int to, int capacity, int cost, int rId) {
this.id = id;
this.from = from;
this.to = to;
this.capacity = capacity;
this.cost = cost;
this.rId = rId;
}
@Override
public String toString() {
return "E#" + id + ": (" + from + "," + to + ") ca=" + capacity + ", co=" + cost + " -- " + rId;
}
}
private final class Residual {
final int n;
final int n2;
final int m;
final int s;
final int t;
final Edge[] edges;
final List[] adj;
final int[] d; // distance
final int[] p; // predecessor
final int[] b; // balance or demand on each vertex
final BitSet inqueue;
final IntCircularQueue queue;
int D;
public Residual() {
this.s = balances.length; // add a super source
this.t = s + 1; // add super sink
this.n = balances.length + 2; // nb of nodes
this.n2 = n - 2;
this.d = new int[n];
this.p = new int[n];
this.inqueue = new BitSet(n);
this.queue = new IntCircularQueue(n);
this.adj = new ArrayList[n];
this.b = new int[n];
for (int i = 0; i < n; i++) {
this.adj[i] = new ArrayList<>();
if (i < n - 2) {
if (balances[i] > 0) {
b[s] += balances[i];
} else if (balances[i] < 0) {
b[t] += balances[i];
}
}
}
this.m = starts.length + 2 * n2; // 2*(n-2) for extra edges to deal with demand and l(e)
this.edges = new Edge[m * 2];
for (int i = 0; i < starts.length; i++) {
int f = starts[i] - offset;
int t = ends[i] - offset;
int cost = weights[i];
edges[i] = new Edge(i, f, t, 0, cost, i + m);
this.adj[f].add(edges[i]);
edges[i + m] = new Edge(i + m, t, f, 0, -cost, i);
this.adj[t].add(edges[i + m]);
}
for (int i = 0, k = starts.length; i < n2; i++, k++) {
// from super source to i
edges[k] = new Edge(k, s, i, 0, 0, k + m);
this.adj[s].add(edges[k]);
edges[k + m] = new Edge(k + m, i, s, 0, 0, k);
this.adj[i].add(edges[k + m]);
// from super i to super sink
edges[k + n2] = new Edge(k + n2, i, t, 0, 0, k + n2 + m);
this.adj[i].add(edges[k + n2]);
edges[k + n2 + m] = new Edge(k + n2 + m, t, i, 0, 0, k + n2);
this.adj[t].add(edges[k + n2 + m]);
}
}
// https://ocw.tudelft.nl/wp-content/uploads/Algoritmiek_Extensions_to_Max_Flow_-_circulations_01.pdf
public void refresh(int a, int v) {
Arrays.fill(b, 0);
System.arraycopy(balances, 0, b, 0, balances.length);
for (int i = 0; i < starts.length; i++) {
int f = starts[i] - offset;
int t = ends[i] - offset;
int lowerCap = flows[i].getLB();
int upperCap = flows[i].getUB();
if (a == i) {
lowerCap = v;
}
b[f] -= lowerCap;
b[t] += lowerCap;
edges[i].capacity = upperCap - lowerCap;
edges[i + m].capacity = 0;
edges[i].flow = edges[i + m].flow = 0;
}
// fill super edges, if needed
int dIn = 0, dOut = 0;
for (int i = 0, k = starts.length; i < n2; i++, k++) {
edges[k].capacity = edges[k + m].capacity = edges[k + n2].capacity = edges[k + n2 + m].capacity = 0;
edges[k].flow = edges[k + m].flow = edges[k + n2].flow = edges[k + n2 + m].flow = 0;
if (b[i] > 0) {
int b_ = b[i];
b[edges[k].from] += b_;
b[edges[k].to] -= b_;
edges[k].capacity = b_;
dIn += b_;
} else if (b[i] < 0) {
int b_ = b[i];
b[edges[k + n2].from] -= b_;
b[edges[k + n2].to] += b_;
edges[k + n2].capacity = -b_;
dOut -= b_;
}
}
assert dIn == dOut;
D = dIn;
}
}
private void shortest_paths(int s) {
Arrays.fill(g.d, Integer.MAX_VALUE);
Arrays.fill(g.p, -1);
g.d[s] = 0;
g.inqueue.clear();
g.queue.clear();
g.queue.addLast(s);
while (!g.queue.isEmpty()) {
int u = g.queue.pollFirst();
g.inqueue.clear(u);
for (int i = 0; i < g.adj[u].size(); i++) {
Edge e = g.adj[u].get(i);
int v = e.to;
if (e.capacity > 0 && g.d[v] > g.d[u] + e.cost) {
g.d[v] = g.d[u] + e.cost;
g.p[v] = e.id; // not the predecessor but the arc
if (!g.inqueue.get(v)) {
g.inqueue.set(v);
g.queue.addLast(v);
}
}
}
}
}
private int minCostFlow(int a, int v) {
int fl = 0;
int cost = 0;
while (fl < g.D) {
shortest_paths(g.s);
if (g.d[g.t] == Integer.MAX_VALUE)
break;
// find max flow on that path
int f = g.D - fl;
int cur = g.p[g.t];
Edge e;
while (cur != -1) {
e = g.edges[cur];
f = Math.min(f, e.capacity);
cur = g.p[e.from];
}
// apply flow
fl += f;
cost += f * g.d[g.t];
cur = g.p[g.t];
while (cur != -1) {
e = g.edges[cur];
e.capacity -= f;
g.edges[e.rId].capacity += f;
cur = g.p[e.from];
}
}
if (fl < g.D) {
return -1;
}
for (int i = 0; i < starts.length; i++) {
if (a == i) {
cost += v * g.edges[i].cost;
} else {
cost += flows[i].getLB() * g.edges[i].cost;
}
}
return cost;
}
@Override
public ESat isEntailed() {
return ESat.TRUE;
}
}
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