Proceedings of the World Congress on Engineering and Computer Science 2014 Vol II WCECS 2014, 22-24 October, 2014, San Francisco, USA Simulated Metamorphosis - A Novel Optimizer Michael Mutingi, Charles Mbohwa Abstract—This paper presents a novel metaheuristic schedules, the decision maker has to incorporate the algorithm, simulated metamorphosis (SM), inspired by the imprecision in preferences and management goals and biological concepts of metamorphosis evolution. The algorithm choices. Moreover, it is important to balance workload is motivated by the need for interactive, multi-objective, and fast optimization approaches to solving problems with fuzzy assignment, if shift fairness and equity are to be achieved. conflicting goals and constraints. The algorithm mimics the Preferences of patients or clients have to be considered as metamorphosis process, going through three phases: well. Though imprecise and conflicting, these factors have to initialization, growth, and maturation. Initialization involves be considered when constructing work schedules [4] [5]. random but guided generation of a candidate solution. After Similar situations are commonplace in hard combinatorial initialization, the algorithm successively goes through two problems. loops, that is, growth and maturation. Computational tests performed on benchmark problems in the literature show that, In view of the above highlighted needs for interactive when compared to competing metaheuristic algorithms, SM is fuzzy multi-objective optimization approaches, the purpose more efficient and effective, producing better solutions within of this research is to introduce a novel simulated reasonable computation times. metamorphosis algorithm, a fuzzy metaheuristic algorithm that is derived from the biological metamorphosis evolution Index Terms—Metamorphosis, evolution, optimization, process. Our objectives are as follows: algorithm, metaheuristics 1) To present the basic concepts of the metamorphosis evolution process; 2) To derive, from the metamorphosis concepts, an I. INTRODUCTION interactive fuzzy evolutionary algorithm; and, IMULATED Metamorphosis (SM) is a novel evolutionary 3) To apply the algorithm to typical nurse scheduling S approach to metaheuristic optimization inspired by the problems, demonstrating its effectiveness. natural biological process of metamorphosis common in The rest of the paper is structured as follows. The next many insect species [1] [2]. The metaheuristic approach is section presents the basic concepts of metamorphosis motivated by several problem situations in the operations evolution. Section III proposes the simulated metamorphosis research and operations management community, such as algorithm. Section IV presents the nurse scheduling nurse scheduling [3] [4] [5], vehicle routing problems [6], problem. Section V presents a simulated metamorphosis for and task assignment [7]. In particular, the metaheuristic is the nurse scheduling problem. Computational illustrations motivated by hard optimization problems that are associated are provided in Section VI. Section VII concludes the paper. with multiple conflicting objectives, imprecise fuzzy goals and constraints, and the need for interactive optimization II. METAMORPHOSIS: BASIC CONCEPTS approaches that can incorporate the choices, intuitions and Metamorphosis is an evolutionary process common in expert judgments of the decision maker [4] [8]. insects such as butterflies [2]. The process begins with an In a fuzzy environment, addressing hard optimization egg that hatches into an instar larva (instar). Subsequently, problems with conflicting goals requires interactive tools the first instar transforms into several instar larvae, then into that are fast, flexible, and easily adaptable to specific a pupa, and finally into the adult insect [1] [2]. The process problem situations. Decision makers often desire to use is uniquely characterized with radical evolution and judicious approaches that can find a cautious tradeoff hormone controlled growth and maturation. between the many goals, which is a common scenario in real world problems [2]. Addressing ambiguity, imprecision, and uncertainties of management goals is highly desirable in practice [4] [8]. For instance, in a hospital setting, where nurses are often allowed to express their preferences on shift Adult Egg Pupa Manuscript received June 13, 2014; revised August 30, 2014. M. Mutingi is a doctoral student with the Faculty of Engineering and the Built Environment, University of Johannesburg, Bunting Road Instar 1 Instar 3 Campus, P. O. Box 524, Auckland Park 2006, Johannesburg, South Africa (phone: +27789578693; e-mail: [email protected]). Instar 2 C. Mbohwa is a professor with the Department of Quality and Operations Management, Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg, Bunting Road Fig. 1 Metamorphosis evolution Campus, P. O. Box 524, Auckland Park 2006, Johannesburg, South Africa (e-mail: [email protected]). ISBN: 978-988-19253-7-4 WCECS 2014 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) Proceedings of the World Congress on Engineering and Computer Science 2014 Vol II WCECS 2014, 22-24 October, 2014, San Francisco, USA A. Metamorphosis Evolution Initialize When an insect grows and develops, it must periodically nitialize shed its rigid exoskeleton in a process called molting. The I insect grows a new loose exoskeleton that provides the Evaluation insect with room for more growth [2]. The insect transforms in body structure as it molts from a juvenile to an adult form, Transformation a process called metamorphosis. Growth The concept of metamorphosis refers to the change of Regeneration physical form, structure, or substance; a marked and more or less abrupt developmental change in the form or structure of no Metamorphose? an animal (such as a butterfly or a frog) occurring yes subsequent to hatching or birth [1]. A species changes body shape and structure at a particular point in its life cycle, such Maturation as when a tadpole turns into a frog. Sometimes, in locusts for example, the juvenile form is quite similar to the adult one. no Terminate? Maturation In others, they are radically different, and unrecognizable as yes the same species. The different forms may even entail a completely new lifestyle or habitat, such as when a ground- Solution bound, leaf-eating caterpillar turns into a long distance flying, nectar-eating butterfly. Fig. 2 Simulated metamorphosis algorithm A. Hormonal Control The evaluation function Ft, at iteration t, should be a Insect molting and development is controlled by several normalized function obtained from its constituent hormones [1]. The hormones trigger the insect to shed its normalized functions denoted by µh (h = 1,…,n), where n is exoskeleton and, at the same time, grow from smaller the number of constituent objective functions. juvenile forms (e.g., a young caterpillar) to larger adult In this approach, we use fuzzy multi-factor evaluation forms (e.g., a winged moth) [2]. The hormone that causes an method, that is, insect to molt is called ecdysone. The hormone, in combination with another, called juvenile hormone, also Ft()() s t w h h s t (1) determines whether the insect will undergo metamorphosis. h III. SIMULATED METAMORPHOSIS where, st is the current solution at iteration t; and wh denotes There are three basic phases: initialization, growth, and the weight of the function µh. The use of the max-min maturation. Each of these phases has specific operators. operator is avoided so as to prevent possible loss of vital information. A. Initialization Phase 2) Transformation In the initialization stage, an initial solution is created as a The growth mechanism is achieved through selection and seed for the evolutionary algorithm. In our approach, we use transformation operators. Selection determines whether a a problem specific heuristic that is guided by hard constituent element ei of the candidate solution st should be constraints of the problem. This ensures generation of a retained for the next iteration, or selected for transformation feasible initial solution. Alternatively, a decision maker can operation. The goodness or fitness ηi of element ei (i = enter a user-generated solution as a seed. The initial 1,…,I) is compared with probability pt∊[0,1], generated at candidate solution st (t = 1,…,T) consists of constituent each iteration t. That is, if ηi ≤ pt, then ei is transformed, elements ei (i = 1,…,I) where I is the constituent number of otherwise, it will survive into the next iteration. Deriving elements in the candidate solution. from the biological metamorphosis, the magnitude of pt Following the creation phase, the algorithm goes into a should decrease over time to guarantee convergence. From loop for a maximum of T iterations (generations). our preliminary empirical computations, pt should follow a decay function of the form, B. Growth Phase The growth phase comprises the evaluation, p p eat T (2) transformation, and the regeneration operators. t 0 1) Evaluation The choice of the evaluation function is very crucial to the where, p0∊[0,1] is a randomly generated number; T is the success of evaluation operator and the overall algorithm. maximum number of iterations; a is an adjustment factor. First, the evaluation function should ensure that it measures It follows that the higher the goodness, the higher the the relevant quality of the candidate solution. Second, the likelihood of survival in the current solution. Therefore,