Luca Manzoni

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.

Better GP benchmarks: community survey results and proposals

We present the results of a community survey regarding genetic programming benchmark practices. Analysis shows broad consensus that improvement is needed in problem selection and experimental rigor. While views expressed in the survey dissuade us from proposing a large-scale benchmark suite, we find community support for creating a “blacklist” of problems which are in common use but have important flaws, and whose use should therefore be discouraged. We propose a set of possible replacement problems.

A new implementation of geometric semantic GP and its application to problems in pharmacokinetics

Moraglio et al. have recently introduced new genetic operators for genetic programming, called geometric semantic operators. These operators induce a unimodal fitness landscape for all the problems consisting in matching input data with known target outputs (like regression and classification). This feature facilitates genetic programming evolvability, which makes these operators extremely promising. Nevertheless, Moraglio et al. leave open problems, the most important one being the fact that these operators, by construction, always produce offspring that are larger than their parents, causing an exponential growth in the size of the individuals, which actually renders them useless in practice. In this paper we overcome this limitation by presenting a new efficient implementation of the geometric semantic operators. This allows us, for the first time, to use them on complex real-life applications, like the two problems in pharmacokinetics that we address here. Our results confirm the excellent evolvability of geometric semantic operators, demonstrated by the good results obtained on training data. Furthermore, we have also achieved a surprisingly good generalization ability, a fact that can be explained considering some properties of geometric semantic operators, which makes them even more appealing than before.

Geometric Semantic Genetic Programming for Real Life Applications

In a recent contribution we have introduced a new implementation of geometric semantic operators for Genetic Programming. Thanks to this implementation, we are now able to deeply investigate their usefulness and study their properties on complex real-life applications. Our experiments confirm that these operators are more effective than traditional ones in optimizing training data, due to the fact that they induce a unimodal fitness landscape. Furthermore, they automatically limit overfitting, something we had already noticed in our recent contribution, and that is further discussed here. Finally, we investigate the influence of some parameters on the effectiveness of these operators, and we show that tuning their values and setting them “a priori” may be wasted effort. Instead, if we randomly modify the values of those parameters several times during the evolution, we obtain a performance that is comparable with the one obtained with the best setting, both on training and test data for all the studied problems.

Unconventional Computation and Natural Computation

We consider the measurement of physical quantities that are thresholds. We use hybrid computing systems modelled by Turing machines having as an oracle physical equipment that measures thresholds. The Turing machines compute with the help of qualitative information provided by the oracle. The queries are governed by timing protocols and provide the equipment with numerical data with (a) infinite precision, (b) unbounded precision, or (c) finite precision. We classify the computational power in polynomial time of a canonical example of a threshold oracle using non-uniform complexity classes.

m-Asynchronous cellular automata: from fairness to quasi-fairness

A new model for the study of asynchronous cellular automata dynamical behavior is introduced with the main purpose of unifying several existing paradigms. The main idea is to measure the set of updating sequences to quantify the dependency of the properties under investigation from them. We propose to use the class of quasi-fair measures, namely measures that satisfy some fairness conditions on the updating sequences. Basic set properties like injectivity and surjectivity are adapted to the new setting and studied. In particular, we prove that they are dimensions sensitive properties (i.e., they are decidable in dimension 1 and undecidable in higher dimensions). A first exploration of dynamical properties is also started, some results about equicontinuity and expansivity behaviors are provided.

Asynchronous cellular automata and dynamical properties

In this article the dynamical behaviour of asynchronous cellular automata (CA) is formally studied. Classical CA properties as surjectivity, injectivity, sensitivity, expansivity, transitivity, dense periodic orbits and equicontinuity have been adapted to the asynchronous case. We also deal with stability of properties with respect to perturbations on some update sequences which produce a significant dynamical behaviour.

Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions

Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP), rooted in a geometric theory of representations, that searches directly the semantic space of functions/programs, rather than the space of their syntactic representations (e.g., trees) as in traditional GP. Remarkably, the fitness landscape seen by GSGP is always -- for any domain and for any problem -- unimodal with a linear slope by construction. This has two important consequences: (i) it makes the search for the optimum much easier than for traditional GP; (ii) it opens the way to analyse theoretically in a easy manner the optimisation time of GSGP in a general setting. The runtime analysis of GP has been very hard to tackle, and only simplified forms of GP on specific, unrealistic problems have been studied so far. We present a runtime analysis of GSGP with various types of mutations on the class of all Boolean functions.

Computing Issues of Asynchronous CA

This work studies some aspects of the computational power of fully asynchronous cellular automata ACA. We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences specifying which are “universal”, i.e., allowing a specific family of ACA to simulate any Turing machine on any input. We also consider the computational cost of such simulations. Finally, we deal with ACA equipped with peculiar updating sequences, namely those generated by random walks.

Membrane Division, Oracles, and the Counting Hierarchy

Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary leaf membrane division rules are allowed, the computing power decreases to PPP = P#P, the class of problems solvable in polynomial time by deterministic Turing machines equipped with oracles for counting or majority problems. In this paper we investigate a variant of intermediate power, limiting membrane nesting hence membrane division to constant depth, and we prove that the resulting P systems can solve all problems in the counting hierarchy CH, which is located between PPP and PSPACE. In particular, for each integer k ≥ 0 we provide a lower bound to the computing power of P systems of depth k.