Pseudo-boolean optimization

Reverse logistics problems arising in municipal waste management are both wide-ranging and varied. The usual collection system in UE countries is composed of two phases. First, citizens leave their refuse at special collection areas where different types of waste (glass, paper, plastic, organic material) are stored in special refuse bins. Subsequently, each type of waste is collected separately and moved to its final destination (a recycling plant or refuse dump). The present study focuses on the problem of locating these collection areas. We establish the relationship between the problem, the set covering problem and the MAX-SAT problem and then go on to develop a genetic algorithm and a GRASP heuristic to, respectively, solve each formulation. Finally, the quality of the algorithms is tested in a computational experience with real instances from the metropolitan area of Barcelona, as well as a reduced set of set covering instances from the literature.

Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona

https://leeds-faculty.colorado.edu/glover/fred%20pubs/338%20-%20TS%20-%20BOOP%20I-Adaptive%20Memory%20Search.pdf

Adaptive memory search for Boolean optimization problems

Local Search based meta-heuristic methods for finding good solutions to hard combinatorial optimization problems have attained a lot of success, and a plethora of methods exist, each with its own successes, and also with its own parameter settings and other method-specific details. At the same time, experience is needed to implement highly competitive code, and some of the experience applied is not easy to quantify.

ADATE is a system to automatically generate code based on a set of input-output specifications, and can work in vastly different domains. It generates code in a subset of the programming language ML and works by searching for transformations of purely functional ML programs.

Code automatically generated by the ADATE system compares with state-of-the-art handcrafted meta-heuristic optimization code. In particular, the programs generated by ADATE target the move selection part of BOOP--Boolean Optimization Problems. The baseline is a highly successful Tabu Search implementation. Comparisons are made for versions running for a limited number of iterations, being suitable for applications needing a short response time. The computational results show that the ADATE system is able to generate highly competitive code that produces more optimal solutions to hard BOOP instances within given iteration limits than the previously published Tabu Search implementation. The automatically generated code also gives new insights into the general design of meta-heuristic mechanisms, and contains novel search mechanisms.

Generating meta-heuristic optimization code using ADATE

The Boolean optimization problem (BOOP) is a highly useful formulation that embraces a variety of 0-1 integer programming problems, including weighted versions of covering, partitioning and maximum satisfiability problems Several years ago Hvattum, Lokketangen and Glover (2006) introduced an adaptive memory (tabu search) method for BOOP which proved effective compared to competing approaches However, in the intervening years, major advances have taken place in exact solvers for integer programming problems, leading to widely publicized successes by the leading commercial solvers XPRESS, CPLEX and GUROBI The implicit message is that an alternative methodology for any broad class of IP problems such as Boolean Optimization Problems would now be dominated by the newer versions of these leading solversWe test this hypothesis by performing new computational experiments comparing the tabu search method for the BOOP class against XPRESS, CPLEX and GUROBI, and documenting improvements provided by the exact codes The outcomes are somewhat surprising

/pdf/comparisons-of-commercial-mip-solvers-and-an-adaptive-memory-xcv1cqv7nc.pdf

Comparisons of Commercial MIP Solvers and an Adaptive Memory (Tabu Search) Procedure for a Class of 0-1 Integer Programming Problems

A heuristic method is proposed for the solution of a large class of binary optimization problems, which includes weighted versions of the set covering, graph stability, partitioning, maximum satisfiability, and numerous other problems. The reported substantial computational experiments amply demonstrate the efficiency of the proposed method.

Thomas Davoine

Papers

A Heuristic for Boolean Optimization Problems