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The pb library contains algorithms for solving pseudo boolean optimization problems.
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/*******************************************************************************
 * SAT4J: a SATisfiability library for Java Copyright (C) 2004-2008 Daniel Le Berre
 *
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU Lesser General Public License Version 2.1 or later (the
 * "LGPL"), in which case the provisions of the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of the LGPL, and not to allow others to use your version of
 * this file under the terms of the EPL, indicate your decision by deleting
 * the provisions above and replace them with the notice and other provisions
 * required by the LGPL. If you do not delete the provisions above, a recipient
 * may use your version of this file under the terms of the EPL or the LGPL.
 * 
 * Based on the pseudo boolean algorithms described in:
 * A fast pseudo-Boolean constraint solver Chai, D.; Kuehlmann, A.
 * Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on
 * Volume 24, Issue 3, March 2005 Page(s): 305 - 317
 * 
 * and 
 * Heidi E. Dixon, 2004. Automating Pseudo-Boolean Inference within a DPLL 
 * Framework. Ph.D. Dissertation, University of Oregon.
 *******************************************************************************/
/*=============================================================================
 * parser for CSP instances represented in XML format
 * 
 * Copyright (c) 2006 Olivier ROUSSEL (olivier.roussel  cril.univ-artois.fr)
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 * 
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 *=============================================================================
 */
package org.sat4j.pb.reader;

import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;

import org.sat4j.core.Vec;
import org.sat4j.core.VecInt;
import org.sat4j.pb.IPBSolver;
import org.sat4j.reader.ParseFormatException;
import org.sat4j.specs.ContradictionException;
import org.sat4j.specs.IVec;
import org.sat4j.specs.IVecInt;

/**
 * Reader complying with the PB07 input format.
 * 
 * Non-linear to linear translation adapted from the PB07 readers provided by
 * Olivier Roussel and Vasco Manquinho (was available in C++, not in Java)
 * 
 * http://www.cril.univ-artois.fr/PB07/parser/SimpleParser.java
 * http://www.cril.univ-artois.fr/PB07/parser/SimpleParser.cc
 * 
 * @author parrain
 * @author daniel
 * 
 */
public class OPBReader2007 extends OPBReader2006 {

	/**
     * 
     */
	private static final long serialVersionUID = 1L;

	/**
	 * @param solver
	 */
	public OPBReader2007(IPBSolver solver) {
		super(solver);
	}

	@Override
	protected boolean isGoodFirstCharacter(char c) {
		return Character.isLetter(c) || c == '_' || c == '~';
	}

	@Override
	protected void checkId(StringBuffer s) throws ParseFormatException {
		// Small check on the coefficient ID to make sure everything is ok
		int cpt = 1;
		if (s.charAt(0) == '~')
			cpt = 2;
		int varID = Integer.parseInt(s.substring(cpt));
		if (varID > nbVars) {
			throw new ParseFormatException(
					"Variable identifier larger than #variables in metadata.");
		}
	}

	/**
	 * contains the number of new symbols generated to linearize products
	 */
	protected int nbNewSymbols;

	@Override
	protected void readTerm(StringBuffer coeff, StringBuffer var)
			throws IOException, ParseFormatException {
		readInteger(coeff);

		skipSpaces();

		var.setLength(0);
		IVec tmpLit = new Vec();
		StringBuffer tmpVar = new StringBuffer();
		while (readIdentifier(tmpVar)) {
			tmpLit = tmpLit.push(tmpVar.toString());
			skipSpaces();
		}
		if (tmpLit.size() == 0)
			throw new ParseFormatException("identifier expected");
		if (tmpLit.size() == 1) {
			// it is a "normal" term
			var.append(tmpLit.last());
			tmpLit.pop();
		} else {
			// it is a product term
			try {
				var.append(linearizeProduct(tmpLit));
			} catch (ContradictionException e) {
				throw new ParseFormatException(e);
			}
		}
	}

	/**
	 * callback called when we read a term of a constraint
	 * 
	 * @param var
	 *            the identifier of the variable
	 * @param lits
	 *            a set of literals in DIMACS format in which var once
	 *            translated will be added.
	 * @throws ParseFormatException
	 */
	protected void literalInAProduct(String var, IVecInt lits)
			throws ParseFormatException {
		int beginning = ((var.charAt(0) == '~') ? 2 : 1);
		int id = Integer.parseInt(var.substring(beginning));
		int lid = ((var.charAt(0) == '~') ? -1 : 1) * id;
		if (lid == 0 || Math.abs(lid) >= nbNewSymbols) {
			throw new ParseFormatException("Wrong variable id");
		}
		lits.push(lid);
	}

	/**
	 * callback called when we read a term of a constraint
	 * 
	 * @param var
	 *            the identifier of the variable
	 * @param lits
	 *            a set of literals in DIMACS format in which var once
	 *            translated will be added.
	 */
	protected void negateLiteralInAProduct(String var, IVecInt lits) {
		int beginning = ((var.charAt(0) == '~') ? 2 : 1);
		int id = Integer.parseInt(var.substring(beginning));
		int lid = ((var.charAt(0) == '~') ? 1 : -1) * id;
		lits.push(lid);
	}

	/**
	 * read the first comment line to get the number of variables and the number
	 * of constraints in the file calls metaData with the data that was read
	 * 
	 * @throws IOException
	 * @throws ParseException
	 */
	@Override
	protected void readMetaData() throws IOException, ParseFormatException {
		char c;
		String s;

		// get the number of variables and constraints
		c = get();
		if (c != '*')
			throw new ParseFormatException(
					"First line of input file should be a comment");
		s = readWord();
		if (eof() || !"#variable=".equals(s))
			throw new ParseFormatException(
					"First line should contain #variable= as first keyword");

		nbVars = Integer.parseInt(readWord());
		nbNewSymbols = nbVars + 1;

		s = readWord();
		if (eof() || !"#constraint=".equals(s))
			throw new ParseFormatException(
					"First line should contain #constraint= as second keyword");

		nbConstr = Integer.parseInt(readWord());
		charAvailable = false;
		if (!eol()) {
			String rest = in.readLine();

			if (rest != null && rest.indexOf("#product=") != -1) {
				String[] splitted = rest.trim().split(" ");
				if (splitted[0].equals("#product=")) {
					Integer.parseInt(splitted[1]);
				}

				// if (splitted[2].equals("sizeproduct="))
				// readWord();

			}
		}
		// callback to transmit the data
		metaData(nbVars, nbConstr);
	}

	@Override
	protected int translateVarToId(String var) throws ParseFormatException {
		int beginning = ((var.charAt(0) == '~') ? 2 : 1);
		int id = Integer.parseInt(var.substring(beginning));
		if (id == 0 || id >= nbNewSymbols) {
			throw new ParseFormatException("Wrong variable id format: " + var);
		}
		return ((var.charAt(0) == '~') ? -1 : 1) * id;
	}

	private String linearizeProduct(IVec tmpLit)
			throws ContradictionException, ParseFormatException {
		tmpLit.sort(String.CASE_INSENSITIVE_ORDER);
		String newVar = getProductVariable(tmpLit);
		if (newVar == null) {
			// generate a new symbol
			newVar = "X" + nbNewSymbols++;
			// linearization proposed by O. Roussel (PB07)
			// generate the clause
			// product => newSymbol (this is a clause)
			// not x1 or not x2 ... or not xn or newSymbol
			if (tmpLit.size() == 2) {
				Map map1 = binaryProductToVar
						.get(tmpLit.get(0));
				if (map1 == null) {
					map1 = new HashMap();
					binaryProductToVar.put(tmpLit.get(0), map1);
				}
				map1.put(tmpLit.get(1), newVar);
			}
			varToProduct.put(newVar, tmpLit);
			IVecInt newLits = new VecInt();
			for (Iterator iterator = tmpLit.iterator(); iterator
					.hasNext();)
				negateLiteralInAProduct(iterator.next(), newLits);
			literalInAProduct(newVar, newLits);
			solver.addClause(newLits);
			// generate the PB-constraint
			// newSymbol => product translated as
			// x1+x2+x3...+xn-n*newSymbol>=0
			newLits.clear();
			IVec newCoefs = new Vec();
			for (Iterator iterator = tmpLit.iterator(); iterator
					.hasNext();) {
				literalInAProduct(iterator.next(), newLits);
				newCoefs.push(BigInteger.ONE);
			}
			literalInAProduct(newVar, newLits);
			newCoefs.push(new BigInteger(String.valueOf(-tmpLit.size())));
			solver.addPseudoBoolean(newLits, newCoefs, true, BigInteger.ZERO);
			// nbConstraintsRead += 2;
		}
		return newVar;
	}

	private final Map> varToProduct = new HashMap>();

	private final Map> binaryProductToVar = new HashMap>();

	private String getProductVariable(IVec lits) {
		if (lits.size() == 2) {
			Map map = binaryProductToVar.get(lits.get(0));
			if (map == null)
				return null;
			return map.get(lits.get(1));
		}
		for (Map.Entry> c : varToProduct.entrySet())
			if (c.getValue().equals(lits))
				return c.getKey();
		return null;
	}

	@Override
	public String decode(int[] model) {
		StringBuffer stb = new StringBuffer();
		int p;
		for (int i = 0; i < model.length; i++) {
			p = model[i];
			if (Math.abs(p) <= nbVars) {
				if (p < 0) {
					stb.append("-x");
					stb.append(-p);
				} else {
					stb.append("x");
					stb.append(p);
				}
				stb.append(" ");
			}
		}
		return stb.toString();
	}

	@Override
	public void decode(int[] model, PrintWriter out) {
		int p;
		for (int i = 0; i < model.length; i++) {
			p = model[i];
			if (Math.abs(p) <= nbVars) {
				if (model[i] < 0) {
					out.print("-x");
					out.print(-p);
				} else {
					out.print("x");
					out.print(p);
				}
				out.print(" ");
			}
		}
	}

}