Coevolutionary bid-based genetic programming for problem decomposition in classification

Abstract

In this work a cooperative, bid-based, model for problem decomposition is proposed with application to discrete action domains such as classification. This represents a significant departure from models where each individual constructs a direct input-outcome map, for example, from the set of exemplars to the set of class labels as is typical under the classification domain. In contrast, the proposed model focuses on learning a bidding strategy based on the exemplar feature vectors; each individual is associated with a single discrete action and the individual with the maximum bid 'wins' the right to suggest its action. Thus, the number of individuals associated with each action is a function of the intra-action bidding behaviour. Credit assignment is designed to reward correct but unique bidding strategies relative to the target actions. An advantage of the model over other teaming methods is its ability to automatically determine the number of and interaction between cooperative team members. The resulting model shares several traits with learning classifier systems and as such both approaches are benchmarked on nine large classification problems. Moreover, both of the evolutionary models are compared against the deterministic Support Vector Machine classification algorithm. Performance assessment considers the computational, classification, and complexity characteristics of the resulting solutions. The bid-based model is found to provide simple yet effective solutions that are robust to wide variations in the class representation. Support Vector Machines and classifier systems tend to perform better under balanced datasets albeit resulting in black-box solutions.

Managing team-based problem solving with symbiotic bid-based genetic programming

“…The first is the Michigan-style learning classifier system XCS [24] which is similar to the SBB approach in that it provides solutions in the form of a cooperating team of production rules evolved through a strengthbased bidding methodology. The specific XCS implementation used here, denoted XCSR, was augmented to handle real-valued inputs and has previously been evaluated on several classification problems [11]. The proposed approach was also compared against the SVM implementation LIBSVM (version 2.85) [4] on the basis that SVM models represent an established performance baseline 2 .…”

“…With the exception of the population sizes and gaps, no fine tuning of parameters was performed. Some fine tuning of the XCSR parameters was performed and the details are available in [11]. Values for the SVM cost parameter C of 1, 10, and 100 were investigated under both the radial basis function (RBF) and Sigmoid Train 93 191 3488 ----3772 Test 73 177 3178 ----3428 CEN (41) Train 187141 12382 -----199523 Test 93576 6186 -----99762 SHU (9) Train 34108 37 132 6748 2458 6 11 43500 Test 11478 13 39 2155 809 4 2 14500 kernels.…”

“…This is the same number of runs used in the XCSR evaluation [11]. The SVM results do not depend on the choice of initial conditions therefore only three runs, one for each setting of C, were performed.…”

Symbiotic coevolutionary genetic programming: a benchmarking study under large attribute spaces

“…Thus, a variable length representation is assumed, where this Individuals from the learner population assume the structure of bid-based GP ( Fig. 2) [25]. Thus, each learner is defined in terms of the tuple hc; bi; where c is a scalar class label the range of which is defined by the task domain-or for a C class problem c 2 f0; .…”

Comment on ‘Sivapragasam C, Maheswaran R, Venkatesh V. 2008. Genetic programming approach for flood routing in natural channels. Hydrological Processes 22: 623–628’

“…A popular modularization concept in LGP is the evolution of program teams (Brameier and Banzhaf, 2001). A team solution is formed by an uneven number of programs, of which every program has one vote.…”