The unit commitment problem is an important optimization problem in the energy industry used to compute the most economical operating schedules of power plants. Typically, this problem has to be solved repeatedly with different data but with the same problem structure. Machine learning techniques have been applied in this context to find primal feasible solutions. Dantzig-Wolfe decomposition with a column generation procedure is another approach that has been shown to be successful in solving the unit commitment problem to tight tolerance. We propose the use of machine learning models not to find primal feasible solutions directly but to generate initial dual values for the column generation procedure. Our numerical experiments compare machine learning–based methods for warmstarting the column generation procedure with three baselines: column prepopulation, the linear programming relaxation, and coldstart. The experiments reveal that the machine learning approaches are able to find both tight lower bounds and accurate primal feasible solutions in a shorter time compared with the baselines. Furthermore, these approaches scale well to handle large instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete.

This paper analyses the implementation of an iterative solution method for Markov decision processes on distributed memory multiple instruction multiple data (MIMD) parallel processors. To preserve the good convergence properties of this method a parallel algorithm must be synchronous and the aim of this paper is to understand the factors which influence the efficiency of synchronous parallel algorithms for iterative methods. Models are developed for processor communication time, processor calculation time and overall run time which are also appropriate for other iterative methods. Such iterative methods are used in many other problem areas, including dynamic programming and the solution of linear and differential equations. The timing models guide the development of a phased pipeline algorithm. For 60,000 state sparse Markov decision processes using 121 processors, this algorithm gives 60-fold speed-ups relative to the best sparse serial algorithm. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

We discuss the algorithmic steps involved in common sparse matrix problems, with particular emphasis on linear programming by the revised simplex method. We then propose new architectural mechanisms which are being built into an experimental machine, the Edinburgh Sparse Processor, and which enable vector instructions to operate efficiently on sparse vectors stored in compressed form. Finally, we review the use of these new mechanisms on the linear programming problem.