Combining multiple heuristics on discrete resources

Abstract

Abstract-In this work we study the portfolio problem which is to find a good combination of multiple heuristics to solve given instances on parallel resources in minimum time. The resources are assumed to be discrete, it is not possible to allocate a resource to more than one heuristic. Our goal is to minimize the average completion time of the set of instances, given a set of heuristics on homogeneous discrete resources. This problem has been studied in the continuous case in [18]. We first show that the problem is hard and that there is no constant ratio polynomial approximation in the general case. Then, we design several approximation schemes for a restricted version of the problem where each heuristic must be used at least once. These results are obtained by using oracle with several guesses, leading to various tradeoff between the size of required information and the approximation ratio. Some additional results based on experiments are finally reported using a benchmark of instances on SAT solvers.

A Periodic Portfolio Scheduler for Scientific Computing in the Data Center

“…Streeter et al [35] consider the duration of heuristics when selected one of them, in the context of dynamic allocation of CPU time. Bougeret [36] and Goldman et al [37] study the concurrent execution of different heuristics on parallel resources. Besides scheduling of constituent heuristics, Streeter et al [38] simultaneously address predicting the runtime of heuristics.…”

Combining SAT solvers on discrete resources

“…This problem can be informally recalled as follows: given a set of opportunities, an amount of possible investments on the set of opportunities and the payoff obtained when investing an amount on each opportunity, what is the best amount of investment to make on each opportunity in order to maximize the sum of the payoffs? This scheme can be adapted to algorithms using the algorithm portfolio approach [2,1,7,4]. A portfolio of algorithms is a collection of different algorithms (or the same algorithm with different parameters) running in an interleaved scheme.…”

“…Morever the interest to allocate for every instance to solve the adequate resources on more than one algorithm is that we may not know which is the best suited SAT solver for each instance before actually solving it. Our proposed approaches aim at improving those introduced in [7,4] from the observation that they do not focus on the necessity to provide an answer for all the considered instances.…”

“…In [8], the authors study how to interleave the execution of different heuristics in order to reduce the execution time of a set of instances and applied to solve SAT. In [7,3,4] the authors study how resources can be shared for SAT solvers such as to efficiently solve instances closed to those of a predefined benchmark. In [10], the authors propose a dynamic algorithm portfolio model in which the allocation of resources to SAT solvers can be changed during the execution of an instance.…”

“…We propose two new approaches based on the usage of a representative benchmark of SAT instances. In the first approach, we improve a problem introduced in [7,4] such as to reduce the number of unsolved SAT instances. The second approach extends a naive solution for combining SAT solvers in a parallel context in introducing the selection of a convenient set of SAT solvers.…”