Brian W. Goldman

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.

Parameter-less population pyramid

Real world applications of evolutionary techniques are often hindered by the need to determine problem specific parameter settings. While some previous methods have reduced or removed the need for parameter tuning, many do so by trading efficiency for general applicability. The Parameter-less Population Pyramid (P3) is an evolutionary technique that requires no parameters and is still broadly effective. P3 strikes a balance between continuous integration of diversity and exploitative elitist operators, allowing it to solve easy problems quickly and hard problems eventually. When compared with three optimally tuned, state of the art optimization techniques, P3 always finds the optimum at least a constant factor faster across four benchmarks (Deceptive Trap, Deceptive Step Trap, HIFF, Rastrigin). More importantly, on three randomized benchmarks (NK Landscapes, Ising Spin Glasses, MAX-SAT), P3 has a lower order of computational complexity as measured by evaluations. We also provide outlines for expected runtime analysis of P3, setting the stage for future theory based conclusions. Based on over 1 trillion evaluations, our results suggest P3 has wide applicability to a broad class of problems.

Analysis of Cartesian Genetic Programming’s Evolutionary Mechanisms

Understanding how search operators interact with solution representation is a critical step to improving search. In Cartesian genetic programming (CGP), and genetic programming (GP) in general, the complex genotype to phenotype map makes achieving this understanding a challenge. By examining aspects such as tuned parameter values, the search quality of CGP variants at different problem difficulties, node behavior, and offspring replacement properties we seek to better understand the characteristics of CGP search. Our focus is two-fold: creating methods to prevent wasted CGP evaluations (skip, accumulate, and single) and creating methods to overcome CGPs search limitations imposed by genome ordering (reorder and DAG). Our results on Boolean problems show that CGP evolves genomes that are highly inactive, very redundant, and full of seemingly useless constants. On some tested problems we found that less than 1% of the genome was actually required to encode the evolved solution. Furthermore, traditional CGP ordering results in large portions of the genome that are never used by any ancestor of the evolved solution. Reorder and DAG allow evolution to utilize the entire genome. More generally, our results suggest that skip-reorder and single-reorder are most likely to solve hard problems using the least number of evaluations and the least amount of time while better avoiding degenerate behavior.

Fast and efficient black box optimization using the parameter-less population pyramid

The parameter-less population pyramid (P3) is a recently introduced method for performing evolutionary optimization without requiring any user-specified parameters. P3’s primary innovation is to replace the generational model with a pyramid of multiple populations that are iteratively created and expanded. In combination with local search and advanced crossover, P3 scales to problem difficulty, exploiting previously learned information before adding more diversity. Across seven problems, each tested using on average 18 problem sizes, P3 outperformed all five advanced comparison algorithms. This improvement includes requiring fewer evaluations to find the global optimum and better fitness when using the same number of evaluations. Using both algorithm analysis and comparison, we find P3’s effectiveness is due to its ability to properly maintain, add, and exploit diversity. Unlike the best comparison algorithms, P3 was able to achieve this quality without any problem-specific tuning. Thus, unlike previous parameter-less methods, P3 does not sacrifice quality for applicability. Therefore we conclude that P3 is an efficient, general, parameter-less approach to black box optimization which is more effective than existing state-of-the-art techniques.

Self-configuring crossover

Crossover is a core genetic operator in many evolutionary algorithms (EAs). The performance of such EAs on a given problem is dependent on properly configuring crossover. A small set of common crossover operators is used in the vast majority of EAs, typically fixed for the entire evolutionary run. Selecting which crossover operator to use and tuning its associated parameters to obtain acceptable performance on a specific problem often is a time consuming manual process. Even then a custom crossover operator may be required to achieve optimal performance. Finally, the best crossover configuration may be dependent on the state of the evolutionary run. This paper introduces the Self-Configuring Crossover operator encoded with linear genetic programming which addresses these shortcomings while relieving the user from the burden of crossover configuration. To demonstrate its general applicability, the novel crossover operator was applied without any problem specific tuning. Results are presented showing it to outperform the traditional crossover operators arithmetic crossover, uniform crossover, and n-point crossover on the Rosenbrock, Rastrigin, Offset Rastrigin, DTrap, and NK Landscapes benchmark problems.

Linkage tree genetic algorithms: variants and analysis

Discovering and exploiting the linkage between genes during evolutionary search allows the Linkage Tree Genetic Algorithm (LTGA) to maximize crossover effectiveness, greatly reducing both population size and total number of evaluations required to reach success on decomposable problems. This paper presents a comparative analysis of the most prominent LTGA variants and a newly introduced variant. While the deceptive trap problem (Trap-k) is one of the canonical benchmarks for testing LTGA, when LTGA is combined with applying steepest ascent hill climbing to the initial population, as is done in all significant LTGA variations, trap-k is trivially solved. This paper introduces the deceptive step trap problem (StepTrap-k,s), which shows the novel combination of smallest first subtree ordering with global mixing (LTS-GOMEA) is effective for black box optimization, while least linked first subtree ordering (LT-GOMEA) is effective on problems where partial reevaluation is possible. Finally, nearest neighbor NK landscapes show that global mixing is not effective on problems with complex overlapping linkage structure that cannot be modeled correctly by a linkage tree, emphasizing the need to extend how LTGA stores linkage to allow the power of global mixing to be applied to these types of problems.

From Cues to Signals: Evolution of Interspecific Communication via Aposematism and Mimicry in a Predator-Prey System

Current theory suggests that many signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often evolves to mimic the toxic species, exploiting the signaling system for its own protection. We investigated the evolutionary dynamics of predator cue utilization and prey signaling in a digital predator-prey system in which prey could evolve to alter their appearance to mimic poison-free or poisonous prey. In predators, we observed rapid evolution of cue recognition (i.e. active behavioral responses) when presented with sufficiently poisonous prey. In addition, active signaling (i.e. mimicry) evolved in prey under all conditions that led to cue utilization. Thus we show that despite imperfect and dishonest signaling, given a high cost of consuming poisonous prey, complex systems of interspecific communication can evolve via predator cue recognition and prey signal manipulation. This provides evidence supporting hypotheses that cues may serve as stepping-stones in the evolution of more advanced communication and signaling systems that incorporate information about the environment.

Reducing wasted evaluations in cartesian genetic programming

Cartesian Genetic Programming (CGP) is a form of Genetic Programming (GP) where a large proportion of the genome is identifiably unused by the phenotype. This can lead mutation to create offspring that are genotypically different but phenotypically identical, and therefore do not need to be evaluated. We investigate theoretically and empirically the effects of avoiding these otherwise wasted evaluations, and provide evidence that doing so reduces the median number of evaluations to solve four benchmark problems, as well as reducing CGPs sensitivity to the mutation rate. The similarity of results across the problem set in combination with the theoretical conclusions supports the general need for avoiding these unnecessary evaluations.

Length bias and search limitations in cartesian genetic programming

In this paper we examine how Cartesian Genetic Programmings (CGPs) method for encoding directed acyclic graphs (DAGs) and its mutation operator bias the effective length of individuals as well as the distribution of inactive nodes in the genome. We investigate these biases experimentally using two CGP variants as comparisons: Reorder, a method for shuffling node ordering without effecting individual evaluation, and DAG, a method for removing the concept of node position. Experiments were performed on four problems tailored to highlight potential search limitations, with further testing on the 3-bit multiplier problem. Unlike previous work, our experiments show that CGP has an innate parsimony pressure that makes it very difficult to evolve individuals with a high percentage of active nodes. This bias is particularly prevalent as the length of an individual increases. Furthermore, these problems are compounded by CGPs positional biases which can make some problems effectively unsolvable. Both Reorder and DAG appear to avoid these problems and outperform Normal CGP on preliminary benchmark testing. Finally, these new techniques require more reasonable genome sizes than those suggested in current CGP, with some evidence that solutions are also more terse.

Gray-Box Optimization using the Parameter-less Population Pyramid

Unlike black-box optimization problems, gray-box optimization problems have known, limited, non-linear relationships between variables. Though more restrictive, gray-box problems include many real-world applications in network security, computational biology, VLSI design, and statistical physics. Leveraging these restrictions, the Hamming-Ball Hill Climber (HBHC) can efficiently find high quality local optima. We show how 1) a simple memetic algorithm in conjunction with HBHC can find global optima for some gray-box problems and 2) a gray-box version of the Parameter-less Population Pyramid (P3), utilizing both the HBHC and the known information about variable relationships, outperforms all of the examined algorithms. While HBHCs inclusion into P3 adds a parameter, we show experimentally it can be fixed to 1 without adversely effecting search. We provide experimental evidence on NKq-Landscapes and Ising Spin Glasses that Gray-Box P3 is effective at finding the global optima even for problems with thousands of variables. This capability is complemented by its efficiency, with running time and memory usage decreased by up to a linear factor from Black-Box P3. On NKq this results in a 375x speedup for problems with at least 1,000 variables.