Biomimicking Altruistic Behavior of Honey Bees in Multi-objective Genetic Algorithm Manojkumar Ramteke + and Santosh K. Gupta* Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India The altruistic behavior of honey bees provides an interesting contrast to natural selection in evolutionary biology. This is biomimicked in the framework of a multiobjective optimization algorithm, namely, genetic algorithm, GA, by exploiting the concept of elitism (preserving good parents). The effects of altruism and natural selection on the total fitness of the colony are compared. This basic algorithm is used for studying the evolution process. It is then modified to enhance the convergence rates of optimization problems and to simulate the carcinogenesis of cells using multiple queens, unlike in honeycombs, mimicking other species of hymenopterans, e.g., ants, wasps, etc. This algorithm provides a new approach for studying three problems, bee evolution, optimization, and cancer, and is used to understand conflicts in animal behavior, increase the speed of convergence of optimization problems, and for an improved understanding of the causes of cancer. 1. Introduction Biological phenomena are mimicked in various modern-day technologies. The field of optimization is no exception. Many recent optimization algorithms like simulated annealing (SA), 1 ant colony optimization, 2 etc. have been inspired by nature. A similar inspiration from evolutionary biology for solving optimization problems led to genetic algorithm (GA). 3 A further improved multiobjective version of GA is the binary-coded elitist 4 nondominated sorting genetic algorithm with the jumping gene 5 adaptation, 6 NSGA-II-aJG. In this algorithm, a population of several (N p ) parent strings (called chromosomes), each comprising several binary numbers, is generated randomly. These represent values of the decision variables. The binaries associated with each decision variable are then coded/mapped into decimal values so that they all lie within their bounds. The decoded values of each variable are used in the model equations to calculate the objective functions in a multiobjective optimiza- tion problem. The chromosomes are then classified into “ranks” or “fronts” based on the concept of nondomination. 4,7 Also, the Euclidean distance in the objective-function space between nearest neighbors, referred to as the “crowding distance”, is evaluated for all the chromosomes (in each front). Two chromosomes are picked randomly from the population of parent chromosomes, and the better of the two, based on the rank and the crowding distance, is copied into a mating pool. This is known as tournament selection. N p chromosomes are, thus, copied for subsequent operation. It may be mentioned that this procedure may lead to some inferior chromosomes also finding their way into the mating pool (this is a characteristic of GA, since it is possible that a poor chromosome may give a good daughter). These are the better “parents”. Two chromosomes are picked randomly from the N p in the mating pool to undergo crossover, 4,7 mutation, 4,7 jumping gene 6 operation, etc. to produce two (initial) daughter chromosomes. The process of crossover among any two randomly selected strings is referred to as natural selection. The N p daughters so produced are mixed with the N p better parents. These 2N p chromosomes are reranked (using nondominance), and the best N p (final) daughter chro- mosomes are selected from these. The process of picking up N p (final) daughter chromosomes from among the (2N p ) better parents and the initial daughters is called elitism since some of the better (elite) parents pass on to the next generation. Though no biological inspirations have been offered, 4,7 elitism leads to enhanced speeds of convergence. The procedure continues over several generations. The best set of solutions (in terms of the fitness of the multiple objective functions) emerges after a sufficiently large number of generations (Darwin’s law of survival of the fittest). Assigning higher fitness (selfishness or altruism) to some elite chromosomes in the population has been used in adaptations like selfish genes, Dawkins memes, (benevolent agent) prisoner dilemma in game theory, etc. by several workers 8-11 to improve the performance of the algorithm. However, these studies do not explain one important question, as to why altruism should be favored over the natural selection built-in genetic algorithm. In contrast, the haplo-diploid nature of the chromosomes in honey bee colonies favors altruism over Darwin’s natural selection since nature only recognizes the increase in the inclusiVe fitness. In this work altruism is adapted in the framework of NSGA-II-aJG quite differently by mimicking the altruistic behavior of honey bee colonies. In the first step, the algorithm developed is used to simulate bee colony as it actually is using values of the crossover and mutation probabilities that are encountered in nature (in absence of jumping genes), without worrying about its optimization efficiency. While doing this, the origin of altruism in the framework of NSGA-II-aJG is also explained. Thereafter, the optimization efficiency of the algorithm is improved using a new crossover scheme (with higher probability of mutation and also the jumping gene operator) and the multiqueen adaptation. This sequential presentation shows how biological phenomena can be mimicked in optimization algorithms. The new adaptation, Alt-NSGA-II- aJG, is then used to solve three benchmark test problems and a multiobjective optimization (MOO) problem of an industrial phthalic anhydride reactor. In the third part, the algorithm is modified for simulating carcinogenesis. Before we proceed, three benchmark problems and the procedure to analyze the convergence are described below. * To whom correspondence should be addressed. E-mail: sk.gupta@ che.iitb.ac.in. Tel.: 91-22-2576 7256. Fax: 91-22-2572 6895. On leave from IIT Kanpur 208016. + Department of Chemical Engineering, IIT Kanpur 208016. Ind. Eng. Chem. Res. 2009, 48, 9671–9685 9671 10.1021/ie9004817 CCC: $40.75  2009 American Chemical Society Published on Web 06/11/2009