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Traditionally, Computer-Aided Molecular Design (CAMD) uses heuristic search and mathematical programming to tackle the molecular design problem. But these techniques do not handle large and nonlinear search space very well. To overcome these drawbacks, graph-based evolutionary algorithms (EAs) have been proposed to evolve molecular design by mimicking chemical reactions on the exchange of chemical bonds and components between molecules. For these EAs to perform their tasks, known molecular components, which can serve as building blocks for the molecules to be designed, and known chemical rules, which govern chemical combination between different components, have to be introduced before the evolutionary process can take place. To automate molecular design without these constraints, this paper proposes an EA called Evolutionary Algorithm for Molecular Design (EvoMD). EvoMD encodes molecular designs in graphs. It uses a novel crossover operator which does not require known chemistry rules known in advanced and it uses a set of novel mutation operators. EvoMD uses atomics-based and fragment-based approaches to handle different size of molecule, and the value of the fitness function it uses is made to depend on the property descriptors of the design encoded in a molecular graph. It has been tested with different data sets and has been shown to be very promising.