Adaptive population models for offspring populations and parallel evolutionary algorithms

Abstract

We present two adaptive schemes for dynamically choosing the number of parallel instances in parallel evolutionary algorithms. This includes the choice of the offspring population size in a (1+λ) EA as a special case. Our schemes are parameterless and they work in a black-box setting where no knowledge on the problem is available. Both schemes double the number of instances in case a generation ends without finding an improvement. In a successful generation, the first scheme resets the system to one instance, while the second scheme halves the number of instances. Both schemes provide near-optimal speed-ups in terms of the parallel time. We give upper bounds for the asymptotic sequential time (i. e., the total number of function evaluations) that are not larger than upper bounds for a corresponding non-parallel algorithm derived by the fitness-level method.

On the effectiveness of crossover for migration in parallel evolutionary algorithms

“…Their model, in principle, also includes the use of crossover during migration, but crossover was pessimistically regarded as always being disruptive. Finally, Lässig and Sudholt presented adaptive models for dynamically choosing the number of islands [7].…”

Design and analysis of adaptive migration intervals in parallel evolutionary algorithms

“…Finally, Lässig and Sudholt [9] presented schemes for adapting the number of islands during a run of an island model (and offspring populations in a (1+λ) EA). Scheme A doubles the number of islands if no improvement was found in a generation.…”

“…Inspired by [9], we also consider a Scheme B where the migration interval is being halved once an improvement has been detected. Thus line 9 in Algorithm 1 is replaced with "Let τi := τi/2".…”

Homogeneous and Heterogeneous Island Models for the Set Cover Problem

“…In fact, all numbers of islands up to the values mentioned above yield linear speedups-for cases where the O(nm 2 )-bound for a single (global) SEMO is asymptotically tight. As remarked in [11], the bound for the complete topology with p = 1 also applies to an offspring population-version of SEMO where λ offspring are created and added to the population, before removing dominated solutions.…”

“…Also the speedup in island models has been studied rigorously: how the number of generations can be decreased by running multiple islands instead of one. Studies include pseudo-Boolean optimisation [10,11] and polynomial-time solvable problems from combinatorial optimisation [12].…”