Robin Harper

Genetic programming needs better benchmarks

Genetic programming (GP) is not a field noted for the rigor of its benchmarking. Some of its benchmark problems are popular purely through historical contingency, and they can be criticized as too easy or as providing misleading information concerning real-world performance, but they persist largely because of inertia and the lack of good alternatives. Even where the problems themselves are impeccable, comparisons between studies are made more difficult by the lack of standardization. We argue that the definition of standard benchmarks is an essential step in the maturation of the field. We make several contributions towards this goal. We motivate the development of a benchmark suite and define its goals; we survey existing practice; we enumerate many candidate benchmarks; we report progress on reference implementations; and we set out a concrete plan for gathering feedback from the GP community that would, if adopted, lead to a standard set of benchmarks.

A structure preserving crossover in grammatical evolution

Grammatical evolution is an algorithm for evolving complete programs in an arbitrary language. By utilising a Backus Naur Form grammar the advantages of typing are achieved. A separation of genotype and phenotype allows the implementation of operators that manipulate (for instance by crossover and mutation) the genotype (in grammatical evolution - a sequence of bits) irrespective of the genotype to phenotype mapping (in grammatical evolution

GE, explosive grammars and the lasting legacy of bad initialisation

an arbitrary grammar). This paper introduces a new type of crossover operator for grammatical evolution. The crossover operator uses information automatically extracted from the grammar to minimise any destructive impact from the crossover. The information, which is extracted at the same time as the genome is initially decoded, allows the swapping between entities of complete expansions of non-terminals in the grammar without disrupting useful blocks of code on either side of the two point crossover. In the domains tested, results confirm that the crossover is (i) more productive than hill-climbing; (ii) enables populations to continue to evolve over considerable numbers of generations without intron bloat; and (iii) allows populations (in the domains tested) to reach higher fitness levels, quicker.

Dynamically Defined Functions In Grammatical Evolution

This paper explores some of the initialisation schemes that can be used to create the starting population of a Grammatical Evolution (GE) run. It investigates why two typical initialisation schemes (random bit and ramped half and half) produce very different, but in each case skewed, tree types. A third methodology, Sean Lukes Probabilistic Tree-Creation version 2 (PTC2), is also examined and is shown to produce a wider variety of trees. Two experiments on different problem sets are carried out and it is shown that for each of these test cases, where the “wrong” initialisation method is utilised, the chance of achieving a successful run is decreased even if the runs are continued long enough for the populations to stagnate. This would seem to suggest that the system does not typically recover from a “bad” start.

Estimating the coherence of noise

Grammatical evolution is an extension of genetic programming, in that it is an algorithm for evolving complete programs in an arbitrary language. By utilising a Backus Naur form grammar the advantages of typing are achieved as well as a separation of genotype and phenotype. This paper introduces a meta-grammar into grammatical evolution allowing the grammar to dynamically define functions, self-adaptively at the individual level without the need for special purpose operators or constraints. The user need not determine the architecture of the dynamically defined functions. As the search proceeds through genotype/phenotype space the number and use of the functions can vary. The ability of the grammar to dynamically define such functions allows regularities in the problem space to be exploited even where such regularities were not apparent when the problem was set up.

A Self-Selecting Crossover Operator

Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than incoherent noise. We show that the coherence of a noise source can be quantified by the unitarity, which we relate to the average change in purity averaged over input pure states. We then show that the unitarity can be efficiently estimated using a protocol based on randomized benchmarking that is efficient and robust to state-preparation and measurement errors. We also show that the unitarity provides a lower bound on the optimal achievable gate infidelity under a given noisy process.

Spatial co-evolution: quicker, fitter and less bloated

This paper compares the efficacy of different crossover operators for Grammatical Evolution across a typical numeric regression problem and a typical data classification problem. Grammatical evolution is an extension of genetic programming, in that it is an algorithm for evolving complete programs in an arbitrary language. Each of the two main crossover operators struggles (for different reasons) to achieve 100% correct solutions. A mechanism is proposed, allowing the evolutionary algorithm to self-select the type of crossover utilised and this is shown to improve the rate of generating 100% successful solutions.

Evolving Robocode tanks for Evo Robocode

Operator equalisation is a methodology inspired by the cross-over bias theory that attempts to limit bloat in genetic programming (GP). This paper examines a bivariate regression problem and demonstrates that operator equalisation suffers from bloat like behaviour when attempting to solve this problem. This is in contrast to a spatial co-evolutionary mechanism (SCALP) that appears to avoid bloat, without any need for express bloat control mechanisms. A previously analysed real world problem (human oral bioavailability prediction) is examined. The behaviour of SCALP on this problem is quite different from that of standard GP and operator equalisation leading to short, general candidate solutions.

Error compensation of single-qubit gates in a surface-electrode ion trap using composite pulses

Evo Robocode is a competition where the challenge is to use evolutionary techniques to create a Java based controller for a simulated robot tank. The tank competes in a closed arena against other such tanks. The Robocode game is a programming platform that allows such tanks to compete. This article discusses the use of Grammatical Evolution (a form of genetic programming) together with spatial co-evolution. This system harnessed co-evolution to evolve relatively complex behaviours, within the program size constraints of the competition. The entry for the 2013 Evo Robocode competition was not evolved against any human coded robots and yet was able to compete effectively against many previously unseen opponents. The co-evolutionary system was then compared to a system that used a handcrafted fitness gradient consisting of pre-selected human coded robots. The top robots from the co-evolved system performed as well as those evolved using a hand crafted fitness function, scoring well against such robots in head to head battles.

Non-exponential Fidelity Decay in Randomized Benchmarking with Low-Frequency Noise

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a