An optimal recombination operator for two-parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this article, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this “super-sampling”: a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.

Generalized Partition Crossover (GPX) is a deterministic recombination operator developed for the Traveling Salesman Problem. Partition crossover operators return the best of 2 k reachable offspring, where k is the number of recombining components. This article introduces a new GPX2 operator, which finds more recombining components than GPX or Iterative Partial Transcription (IPT). We also show that GPX2 has O( n ) runtime complexity, while also introducing new enhancements to reduce the execution time of GPX2. Finally, we experimentally demonstrate the efficiency of GPX2 when it is used to improve solutions found by the multitrial Lin-Kernighan-Helsgaum (LKH) algorithm. Significant improvements in performance are documented on large ( n > 5000 ) and very large ( n = 100 , 000 ) instances of the Traveling Salesman Problem.

The error threshold of replication is an important notion in the quasispecies evolution model; it is a critical mutation rate (error rate) beyond which structures obtained by an evolutionary process are destroyed more frequently than selection can reproduce them. With mutation rates above this critical value, an error catastrophe occurs and the genomic information is irretrievably lost. Therefore, studying the factors that alter this magnitude has important implications in the study of evolution. Here we use a genetic algorithm, instead of the quasispecies model, as the underlying model of evolution, and explore whether the phenomenon of error thresholds is found on finite populations of bit strings evolving on complex landscapes. Our empirical results verify the occurrence of error thresholds in genetic algorithms. In this way, this notion is brought from molecular evolution to evolutionary computation. We also study the effect of modifying the most prominent evolutionary parameters on the magnitude of this critical value, and found that error thresholds depend mainly on the selection pressure and genotype length.