Initial Solve

Calling the initial solve method solves a given MILP from scratch, as described above. The first action taken is to create an instance of the tree manager module that will control execution of the algorithm. If the algorithm is to be executed in parallel on a distributed architecture, the master module spawns a separate tree manager process that will autonomously control the solution process. The tree manager in turn creates the modules for processing the nodes of the search tree, generating cuts, and maintaining cut pools. These modules work in concert to execute the solution process. When it makes sense, sets of two or more modules, such as a node processing module and a cut generation module may be combined to yield a single process in which the combined modules work in concert and communicate with each other through shared memory instead of across the network. When running as separate process, the modules communicate with each other using a standard communications protocol. Currently, the only option supported is PVM, but it would be relatively easy to add an MPI implementation.

The overall flow of the algorithm is similar to other branch and bound implementations and is detailed below. A priority queue of candidate subproblems available for processing is maintained at all times and the candidates are processed in an order determined by the search strategy. The algorithm terminates when the queue is empty or when another specified condition is satisfied. A new feature in SYMPHONY 5.3.4 is the ability to stop the computation based on exceeding a given time limit, exceeding a given limit on the number of processed nodes, achieving a target percentage gap between the upper and lower bounds, or finding the first feasible solution. After halting prematurely, the computation can be restarted after modifying parameters or problem data. This enables the implementation of a wide range of dynamic and on-line solution algorithms, as we describe next.

Ted Ralphs