DCABB: A framework for the development of distributed branch and bound algorithms

Gautham K Kudva, Purdue University

Abstract

The solution of large combinatorial optimization problems is becoming increasingly important in diverse areas of chemical engineering such as batch process design and scheduling, molecular simulations, and process control. Branch and bound is a well established framework that is at the core of existing methods for rigorously solving hard combinatorial problems. Though parallel and distributed computers offer great promise in reducing the execution times of branch-and-bound computations, the time and effort needed to parallelize algorithms has prevented their routine use for solving combinatorial problems. A framework that can reduce the burden associated with implementing parallel branch-and-bound algorithms can contribute significantly in enabling the solution of large problem instances encountered in practice. This thesis is concerned with the development of such a framework. The design goal of DCABB (Distributed Control Architecture for Branch and Bound) is to automate implementation aspects of distributed algorithms without imposing rigid protocol formats that restrict their flexibility. Algorithm customizability is a critical consideration in the design of DCABB since it can have a dramatic impact on the size of practical problems that can be solved. Support is provided for the implementation of a novel parallelization paradigm known as Competing Search Trees. Viability of the framework is demonstrated by implementing two distributed branch-and-bound algorithms using DCABB--an algorithm for a multiple resource constrained sequencing problem that can solve instances with up to 75 jobs and three resource constraints and a Mixed Integer Linear Programming (MILP) solver that has been used to solve problems derived from practical applications including problems from the MIPLIB test suite. A generic branch-and-bound search process has been developed to characterize the performance of distributed algorithms on various network architectures. Experiments using an Ethernet network and a high bandwidth DEC giga-switch network demonstrate the effect of network bandwidth on distributed branch-and-bound computations. Results are presented using up to 32 workstations on a geographically distributed network. To our knowledge this is the largest number of machines used for branch-and-bound in a heterogeneous environment. A heuristic algorithm for scheduling multiproduct plants with deadlines and intermediate feeds and product draw-offs is described in the context of an industrial case study.

Degree

Ph.D.

Advisors

Pekny, Purdue University.

Subject Area

Chemical engineering|Operations research|Computer science

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