Combinatorial Search from an Energy Perspective

Most studies related to parallel and portfolio search for solving combinatorial problems, such as those found in Boolean satisfiability or constraint programming, evaluate search cost in terms of runtime. However, given the complex computing architectures available today and the focus on the environmental impact of computing, there is growing interest in also considering the energy cost associated with solving these problems. In the context of combinatorial problem-solving, a simple approximation of energy cost is the product of the number of machines multiplied by the runtime spent to solve a problem instance. However, the picture is much more complex due to the impact that the distribution of runtimes, even for solving a single specific instance, can have on search cost. In this paper we present an initial, but comprehensive, study on the impact of runtime distribution on the amount of energy required for combinatorial problem solving characterised by two common continuous runtime distributions, namely the Weibull and Pareto distributions. The primary contribution of this paper is to demonstrate that there is an interesting and non-trivial relationship between runtime, parallelisation, and energy cost in combinatorial solving that is worthy of further study.