A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate-based algorithms are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate-based algorithm that uses a linear combination of rectified linear units, defined in such a way that (local) optima satisfy the integer constraints. Unlike other methods, it also has a constant run-time per iteration. This method outperforms the state of the art on several synthetic benchmarks with up to 238 continuous and integer variables, and achieves competitive performance on two real-life benchmarks: XG-Boost hyperparameter tuning and Electrostatic Precipitator optimisation. CCS CONCEPTS• Mathematics of computing → Mathematical optimization; • Computing methodologies → Active learning settings; Search methodologies; • Theory of computation → Mixed discretecontinuous optimization.
The Order Acceptance and Scheduling (OAS) problem describes a class of real-world problems such as in smart manufacturing and satellite scheduling.This problem consists of simultaneously selecting a subset of orders to be processed as well as determining the associated schedule. A common generalization includes sequence-dependent setup times and time windows. A novel memetic algorithm for this problem, called Sparrow, comprises a hybridization of biased random key genetic algorithm (BRKGA) and adaptive large neighbourhood search (ALNS). Sparrow integrates the exploration ability of BRKGA and the exploitation ability of ALNS. On a set of standard benchmark instances, this algorithm obtains better-quality solutions with runtimes comparable to stateof-the-art algorithms. To further understand the strengths and weaknesses of these algorithms, their performance is also compared on a set of new benchmark instances with more realistic properties. We conclude that Sparrow is distinguished by its ability to solve difficult instances from the OAS literature, and that the hybrid steady-state genetic algorithm (HSSGA) performs well on large instances in terms of optimality gap, although taking more time than Sparrow.Adaptive large neighbourhood search, Order acceptance and scheduling, Sequence-dependent setup times 2. We compare Sparrow with state-of-the-art algorithms on a set of standard benchmark instances from the literature. The proposed algorithm obtains better-quality solutions with comparable running time.3. We study the correlation of the problem properties and the algorithm performance and find that the congestion ratio, the length of time windows, and the correlation of processing time and revenue of orders are highly related to the difficulty of the problem. 2 4. We further generate new instances that are more representative of real problem instances in satellite scheduling (more congestion), commerce (high correlation between revenue and processing time), and the travelling repairman problem (short processing times and long time windows), and compare the performance of multiple state-of-the-art algorithms on these new instances. The remainder of this article is summarized as follows: Section 2 provides 1 This algorithm combines a population-based genetic algorithm with adaptive large neighbourhood search. Each individual in a "swarm" thus has a bird's eye view of the search space -hence Sparrow. 2 These terms are defined in Section 4.3. Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max 0.10 0.10
In a parallel EA one can strictly adhere to the generational clock, and wait for all evaluations in a generation to be done. However, this idle time limits the throughput of the algorithm and wastes computational resources. Alternatively, an EA can be made asynchronous parallel. However, EAs using classic recombination and selection operators (GAs) are known to suffer from an evaluation time bias, which also influences the performance of the approach. Model-Based Evolutionary Algorithms (MBEAs) are more scalable than classic GAs by virtue of capturing the structure of a problem in a model. If this model is learned through linkage learning based on the population, the learned model may also capture biases. Thus, if an asynchronous parallel MBEA is also affected by an evaluation time bias, this could result in learned models to be less suited to solving the problem, reducing performance. Therefore, in this work, we study the impact and presence of evaluation time biases on MBEAs in an asynchronous parallelization setting, and compare this to the biases in GAs. We find that a modern MBEA, GOMEA, is unaffected by evaluation time biases, while the more classical MBEA, ECGA, is affected, much like GAs are. CCS CONCEPTS• Mathematics of computing → Evolutionary algorithms; • Theory of computation → Parallel computing models.
The industrial challenge of the GECCO 2021 conference is an expensive optimisation problem, where the parameters of a hospital simulation model need to be tuned to optimality. We show how a surrogate-based optimisation framework, with a random ReLU expansion as the surrogate model, outperforms other methods such as Bayesian optimisation, Hyperopt, and random search on this problem. CCS CONCEPTS• Mathematics of computing → Mathematical optimization;• Computing methodologies → Active learning settings.
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