Constructive Genetic Algorithm for Clustering Problems

Abstract

Genetic algorithms (GAs) have recently been accepted as powerful approaches to solving optimization problems. It is also well-accepted that building block construction (schemata formation and conservation) has a positive influence on GA behavior. Schemata are usually indirectly evaluated through a derived structure. We introduce a new approach called the Constructive Genetic Algorithm (CGA), which allows for schemata evaluation and the provision of other new features to the GA. Problems are modeled as bi-objective optimization problems that consider the evaluation of two fitness functions. This double fitness process, called fg-fitness, evaluates schemata and structures in a common basis. Evolution is conducted considering an adaptive rejection threshold that contemplates both objectives and attributes a rank to each individual in population. The population is dynamic in size and composed of schemata and structures. Recombination preserves good schemata, and mutation is applied to structures to get population diversification. The CGA is applied to two clustering problems in graphs. Representation of schemata and structures use a binary digit alphabet and are based on assignment (greedy) heuristics that provide a clearly distinguished representation for the problems. The clustering problems studied are the classical p-median and the capacitated p-median. Good results are shown for problem instances taken from the literature.

A Constructive Evolutionary Approach to School Timetabling

“…The CGA has been successfully applied to other clustering problems [14]. The weights used at the selection phase may extend the CGA to the class of multicriteria algorithms.…”

“…The Constructive Genetic Algorithm (CGA) is a recently developed approach of Lorena and Furtado [14] that provides some new features to GA, such as a population formed only by schemata, recombination among schemata, dynamic population size, mutation in complete structures, and the possibility of using heuristics in schemata and/or structure representation. Schemata do not consider all the problem data.…”

Enhanced Genetic Algorithm with K-Means for the Clustering Problem

“…The former refers to the ability to explore many different regions of the search space, whereas the latter refers to the ability to obtain high quality solutions within those regions. Examples include genetic algorithms [12]- [14], Tabu Search [15], Grasp [16].…”

Hybrid heuristics for the probabilistic maximal covering location-allocation problem

“…A dynamic population is initially formed only by schemata, but may be enlarged after the use of recombination operators, or made smaller along the generations, guided by an evolutionary parameter. The dynamic population is built, generation after generation, by directly searching for well-adapted structures (a complete solution) and also for good schemata [(Lorena and Furtado (2001)] [Oliveira and Lorena (2004)] [Oliveira and Lorena (2005)]. …”