The influence of mutation on population dynamics in multiobjective genetic programming

Using multiobjective genetic programming with a complexity objective to overcome tree bloat is usually very successful but can sometimes lead to undesirable collapse of the population to all single-node trees. In this paper we report a detailed examination of why and when collapse occurs. We have used different types of crossover and mutation operators (depth-fair and sub-tree), different evolutionary approaches (generational and steady-state), and different datasets (6-parity Boolean and a range of benchmark machine learning problems) to strengthen our conclusion. We conclude that mutation has a vital role in preventing population collapse by counterbalancing parsimony pressure and preserving population diversity. Also, mutation controls the size of the generated individuals which tends to dominate the time needed for fitness evaluation and therefore the whole evolutionary process. Further, the average size of the individuals in a GP population depends on the evolutionary approach employed. We also demonstrate that mutation has a wider role than merely culling single-node individuals from the population; even within a diversity-preserving algorithm such as SPEA2 mutation has a role in preserving diversity

An Empirical Study of the Effectiveness of 'Forcing Diversity' Based on a Large Population of Diverse Programs

Use of diverse software components is a viable defence against common-mode failures in redundant softwarebased systems. Various forms of "Diversity-Seeking Decisions" (“DSDs”) can be applied to the process of developing, or procuring, redundant components, to improve the chances of the resulting components not failing on the same demands. An open question is how effective these decisions, and their combinations, are for achieving large enough reliability gains. Using a large population of software programs, we studied experimentally the effectiveness of specific "DSDs" (and their combinations) mandating differences between redundant components. Some of these combinations produced much better improvements in system probability of failure per demand (PFD) than "uncontrolled" diversity did. Yet, our findings suggest that the gains from such "DSDs" vary significantly between them and between the application problems studied. The relationship between DSDs and system PFD is complex and does not allow for simple universal rules (e.g. "the more diversity the better") to apply

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Modelling and trading the Greek stock market with gene expression and genetic programing algorithms

This paper presents an application of the gene expression programming (GEP) and integrated genetic programming (GP) algorithms to the modelling of ASE 20 Greek index. GEP and GP are robust evolutionary algorithms that evolve computer programs in the form of mathematical expressions, decision trees or logical expressions. The results indicate that GEP and GP produce significant trading performance when applied to ASE 20 and outperform the well-known existing methods. The trading performance of the derived models is further enhanced by applying a leverage filter