Solving Assembly Line Balancing Problems by Combining IP and CP

Assembly line balancing problems consist in partitioning the work necessary to assemble a number of products among different stations of an assembly line. We present a hybrid approach for solving such problems, which combines constraint programming and integer programming.Comment: 10 pages, Sixth Annual Workshop of the ERCIM Working Group on Constraints, Prague, June 200

Ten years of feasibility pump, and counting

The Feasibility Pump (fp) is probably the best-known primal heuristic for mixed-integer programming. The original work by Fischetti et al. (Math Program 104(1):91\u2013104, 2005), which introduced the heuristic for 0\u20131 mixed-integer linear programs, has been succeeded by more than twenty follow-up publications which improve the performance of the fp and extend it to other problem classes. Year 2015 was the tenth anniversary of the first fp publication. The present paper provides an overview of the diverse Feasibility Pump literature that has been presented over the last decade

Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization

We introduce Scylla, a primal heuristic for mixed-integer optimization problems. It exploits approximate solves of the Linear Programming relaxations through the matrix-free Primal-Dual Hybrid Gradient algorithm with specialized termination criteria, and derives integer-feasible solutions via fix-and-propagate procedures and feasibility-pump-like updates to the objective function. Computational experiments show that the method is particularly suited to instances with hard linear relaxations

A Survey of Satisfiability Modulo Theory

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches. We also cover quantifiers, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201

A Comparison of CP, IP and Hybrids for Configuration Problems

We investigate different solution techniques for solving a basic part of configuration problems, namely linear arithmetic constraints over integer variables. Approaches include integer programming, constraint programming over finite domains and hybrid techniques. We also discuss important extensions of the basic problem and how these can be accommodated in the different solution approaches

An Analysis of Arithmetic Constraints on Integer Intervals

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that reduce the variable domains. We compare these approaches using a set of benchmarks. For the most promising approach we provide results that characterize the effect of constraint propagation. This is a full version of our earlier paper, cs.PL/0403016.Comment: 44 pages, to appear in 'Constraints' journa