Chapter 13 - Gene expression models

Chapter 17 - Appraisal of multigene genetic programming for estimating optimal properties of lined open channels with circular shapes incorporating constant and variable roughness scenarios

Linear genetic programming (LGP) is a genetic programming paradigm based on a linear sequence of instructions being executed. An LGP individual can be decoded into a directed acyclic graph. The graph intuitively reflects the primitives and their connection. However, existing studies on LGP miss an important aspect when seeing LGP individuals as graphs, that is, the reverse transformation from graph to LGP genotype. Such reverse transformation is an essential step if one wants to use other graph-based techniques and applications with LGP. Transforming graphs into LGP genotypes is nontrivial since graph information normally does not convey register information, a crucial element in LGP individuals. Here we investigate the effectiveness of four possible transformation methods based on different graph information including frequency of graph primitives, adjacency matrices, adjacency lists, and LGP instructions for sub-graphs. For each transformation method, we design a corresponding graph-based genetic operator to explicitly transform LGP parent’s instructions to graph information, then to the instructions of offspring resulting from breeding on graphs. We hypothesize that the effectiveness of the graph-based operators in evolution reflects the effectiveness of different graph-to-LGP genotype transformations. We conduct the investigation by a case study that applies LGP to design heuristics for dynamic scheduling problems. The results show that highlighting graph information improves LGP average performance for solving dynamic scheduling problems. This shows that reversely transforming graphs into LGP instructions based on adjacency lists is an effective way to maintain both primitive frequency and topological structures of graphs.

We propose the Quantum-Inspired Multi-Gene Lin-ear Genetic Programming (QIMuLGP), which is a generalization of Quantum-Inspired Linear Genetic Programming (QILGP) model for symbolic regression. QIMuLGP allows us to explore a different genotypic representation (i.e. linear), and to use more than one genotype per individual, combining their outputs using least squares method (multi-gene approach). We used 11 benchmark problems to experimentally compare QIMuLGP with: canonical tree Genetic Programming, Multi-Gene tree-based GP (MGGP), and QILGP. QIMuLGP obtained better results than QILGP in almost all experiments performed. When compared to MGGP, QIMuLGP achieved equivalent errors for some experiments with its runtime always shorter (up to 20 times and 8 times on average), which is an important advantage in high dimensional-scalable problems.

A machine code-based genetic programming for suspended sediment concentration estimation

In this paper, a variation of traditional Genetic Programming(GP) is used to model the MagnetoencephaloGram(MEG) of Epileptic Patients. This variation is Linear Genetic Programming(LGP). LGP is a particular subset of GP wherein computer programs in population are represented as a sequence of instructions from imperative programming language or machine language. The derived models from this method were simplified using genetic algorithms. The proposed method was used to model the MEG signal of epileptic patients using 6 different datasets. Each dataset uses different number of previous values of MEG to predict the next value. The models were tested in datasets different from the ones which were used to produce them and the results were very promising.

This paper describes a novel evolutionary method for automatic induction of target recognition procedures from examples. The learning process starts with training data containing SAR images with labeled targets and consists in coevolving the population of feature extraction agents that cooperate to build an appropriate representation of the input image. Features extracted by a team of cooperating agents are used to induce a machine learning classifier that is responsible for making the final decision of recognizing a target in a SAR image. Each agent (individual) contains feature extraction procedure encoded according to the principles of linear genetic programming (LGP). Like 'plain' genetic programming, in LGP an agent's genome encodes a program that is executed and tested on the set of training images during the fitness calculation. The program is a sequence of calls to the library of parameterized operations, including, but not limited to, global and local image processing operations, elementary feature extraction, and logic and arithmetic operations. Particular calls operate on working variables that enable the program to store intermediate results, and therefore design complex features. This paper contains detailed description of the learning and recognition methodology outlined here. In experimental part, we report and analyze the results obtained when testing the proposed approach for SAR target recognition using MSTAR database.

Low-frequency oscillation damping in the electric network through the optimal design of UPFC coordinated PSS employing MGGP

Wire and arc additive manufacturing (WAAM) is a novel rapid prototyping process that employs gas tungsten arc welding, controlled by a robot, to build complex 3D parts by successive layer deposition technique. Experimental studies on WAAM are useful for understanding the physics of the process however the quantification and optimization of process parameters is difficult due to complex mechanisms involved in WAAM process. In this present work, the measurement of two bead dimensions (bead height and bead width) based on the three inputs (peak current, wire feed speed, and travel speed) is done using the gas tungsten arc welding machine. Experimental study is followed by proposition of two variants of advanced evolutionary algorithms (gene expression programming and multi-gene genetic programming) in formulation of the functional expressions for the two bead dimensions based on the three inputs. The performance analysis of the two proposed models is conducted based on the four statistical error metrics, hypothesis tests and cross-validation. The relationships extracted between the bead dimensions and the three inputs reveals that the peak current influences both the bead height and bead width simultaneously. The findings reported will have a positive implication on the industry in predictive monitoring of the bead dimensions during the WAAM process.

Graph representations promise several desirable properties for genetic programming (GP); multiple-output programs, natural representations of code reuse and, in many cases, an innate mechanism for neutral drift. Each graph GP technique provides a program representation, genetic operators and overarching evolutionary algorithm. This makes it difficult to identify the individual causes of empirical differences, both between these methods and in comparison to traditional GP. In this work, we empirically study the behaviour of Cartesian genetic programming (CGP), linear genetic programming (LGP), evolving graphs by graph programming and traditional GP. By fixing some aspects of the configurations, we study the performance of each graph GP method and GP in combination with three different EAs: generational, steady-state and (1+lambda ). In general, we find that the best choice of representation, genetic operator and evolutionary algorithm depends on the problem domain. Further, we find that graph GP methods can increase search performance on complex real-world regression problems and, particularly in combination with the (1 + lambda) EA, are significantly better on digital circuit synthesis tasks. We further show that the reuse of intermediate results by tuning LGP’s number of registers and CGP’s levels back parameter is of utmost importance and contributes significantly to better convergence of an optimization algorithm when solving complex problems that benefit from code reuse.

This paper proposes a novel approach for the formulation of elastic modulus of both normal-strength concrete (NSC) and high-strength concrete (HSC) using a variant of genetic programming (GP), namely linear genetic programming (LGP). LGP-based models relate the modulus of elasticity of NSC and HSC to the compressive strength, as similarly presented in several codes of practice. The models are developed based on experimental results collected from the literature. A subsequent parametric analysis is further carried out to evaluate the sensitivity of the elastic modulus to the compressive strength variations. The results demonstrate that the proposed formulas can predict the elastic modulus with an acceptable degree of accuracy. The LGP results are found to be more accurate than those obtained using the buildings codes and various solutions reported in the literature. The LGP-based formulas are quite simple and straightforward and can be used reliably for routine design practice.

This paper proposes a new approach for the formulation of compressive strength of carbon fiber reinforced plastic (CFRP) confined concrete cylinders using a promising variant of genetic programming (GP) namely, linear genetic programming (LGP). The LGP-based models are constructed using two different sets of input data. The first set of inputs comprises diameter of concrete cylinder, unconfined concrete strength, tensile strength of CFRP laminate and total thickness of utilized CFRP layers. The second set includes unconfined concrete strength and ultimate confinement pressure which are the most widely used parameters in the CFRP confinement existing models. The models are developed based on experimental results collected from the available literature. The results demonstrate that the LGP-based formulas are able to predict the ultimate compressive strength of concrete cylinders with an acceptable level of accuracy. The LGP results are also compared with several CFRP confinement models presented in the literature and found to be more accurate in nearly all of the cases. Moreover, the formulas evolved by LGP are quite short and simple and seem to be practical for use. A subsequent parametric study is also carried out and the trends of the results have been confirmed via some previous laboratory studies.

In this chapter it is shown how Automatically Defined Functions are encoded in the genotype/phenotype system of Gene Expression Programming. As an introduction, the fundamental differences between Gene Expression Programming and its predecessors, Genetic Algorithms and Genetic Programming, are briefly summarized so that the evolutionary advantages of Gene Expression Programming are better understood. The introduction proceeds with a detailed description of the architecture of the main players of Gene Expression Programming (chromosomes and expression trees), focusing mainly on the interactions between them and how the simple, yet revolutionary, structure of the chromosomes allows the efficient, unconstrained exploration of the search space. The work proceeds with an introduction to Automatically Defined Functions and how they are implemented in Gene Expression Programming. Furthermore, the importance of Automatically Defined Functions in Evolutionary Computation is thoroughly analyzed by comparing the performance of sophisticated learning systems with Automatically Defined Functions with much simpler ones on the sextic polynomial problem. 1. Genetic Algorithms: Historical Background The way nature solves problems and creates complexity has inspired scientists to create artificial systems that learn how to solve a particular problem without human intervention. The first attempts were done in the 1950s by Friedberg (Friedberg 1958; Friedberg et al. 1959), but ever since highly sophisticated systems have been developed that apply Darwin’s ideas of natural evolution to the artificial world of computers and modeling. Of particular interest to this work are the Genetic Algorithms (GAs) and the Genetic Programming (GP) technique as they are the predecessors of Gene Expression Programming (GEP), an extremely versatile genotype/phenotype system. The way Automatically Defined Functions (ADFs) are implemented in GEP is another example of the great versatility of this algorithm and the versatility of GEP ADFs opens up new grounds for the creation of even more sophisticated artificial learning systems. So let’s start by introducing briefly these three techniques in order to appreciate the versatility of the genotype/phenotype system of Gene Expression Programming with and without ADFs.

AISI steel 304 is used in nuclear reactors for the cladding of fuel rods. In the literature, various mathematical modelling methods such as support vector regression (SVR), artificial neural network (ANN) and multi-gene genetic programming (MGGP) have been applied to study the properties of this steel. Among these methods, MGGP possesses the ability to evolve the model structure and its coefficients. The model participating in the evolutionary stage of the MGGP algorithm is a weighted linear sum of several genes, with the weights determined by selecting the genes randomly and combining them using the least squares method to form a MGGP model. As a result, there is a possibility that a gene of lower performance can degrade the performance of the model. To counter this, a modified MGGP (M-MGGP) method is proposed and which introduces a new technique of stepwise regression for the selective combination of genes of only higher performance. The M-MGGP method is applied to the true stress value data obtained from tensile tests conducted on austenitic stainless steel 304 subjected to different strain rates and temperatures. The results show that the M-MGGP model is able to extrapolate the values of true stress more satisfactorily than those of the standardized MGGP, ANN and SVR models. The M-MGGP models are also smaller in size than those from MGGP. The results suggest that the M-MGGP method provides compact and accurate models that can be deployed by experts for efficiently studying the properties of the steel at elevated temperatures.

A developmental co-evolutionary genetic programming approach (PAM DGP) is compared to a standard linear genetic programming (LGP) implementation for trading of stocks across market sectors. Both implementations were found to be impressively robust to market fluctuations while reacting efficiently to opportunities for profit, where PAM DGP proved slightly more reactive to market changes than LGP. PAM DGP outperformed, or was competitive with, LGP for all stocks tested. Both implementations had very impressive accuracy in choosing both profitable buy trades and sells that prevented losses, where this occurred in the context of moderately active trading for all stocks. The algorithms also appropriately maintained maximal investment in order to profit from sustained market upswings.

Dispatching rules are most commonly used to solve scheduling problems under dynamic conditions. Since designing new dispatching rules is a time-consuming process, it can be automated by using various machine learning and evolutionary computation methods. In previous research, genetic programming has been the most commonly used method for automatically designing new dispatching rules. However, there are many other evolutionary methods that use representations other than genetic programming that can be used to create dispatching rules. Some, such as gene expression programming, have already been used successfully, while others, such as Cartesian genetic programming or grammatical evolution, have not yet been used to generate dispatching rules. In this paper, six different methods (genetic programming, gene expression programming, Cartesian genetic programming, grammatical evolution, stack representation, and analytic programming) for generating dispatching rules for the unrelated machines environment are tested and the results for various scheduling criteria are analysed. It is also analysed how different individual sizes in the tested methods affect the performance and average size of the generated dispatching rules. The results show that, with the exception of grammatical evolution and analytic programming, all tested methods perform quite similarly, with results depending on the selected scheduling criterion. The results also show that Cartesian genetic programming is the most resistant to the occurrence of bloat and evolves dispatching rules with the smallest average size.