Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441

International Journal of Current Microbiology and Applied Sciences ISSN: 2319-7706 Special Issue-6 pp. 431-441 Journal homepage: http://www.ijcmas.com

Review Article

Review on Adaptive Genetic and Methods within Optimisation

Manjusha P . Dhoke, Jyoti S. Kale And Pavan K. Dhoke

Vasantrao Naik Marathwada Krishi Vidyapeeth, Parbhani, Maharashtra, India *Corresponding author

ABSTRACT

In and , a (GA) is a

Ke yw or ds metaheuristic inspired by the process of that belongs to the larger class of evolutionary (EA). Genetic algorithms are Adaptive genetic commonly used to generate high-quality solutions to optimization and algorithm, search problems by relying on bio-inspired operators such as mutation, Stochastic crossover and selection. In a genetic algorithm, a population of candidate optimisation solutions (called individuals, creatures, or phenotypes) to an optimization

problem is evolved toward better solutions.

Introduction

In genetic algorithm each candidate solution used in the next iteration of the algorithm. has a set of properties (its chromosomes or Commonly, the algorithm terminates when genotype) which can be mutated and altered; either a maximum number of generations traditionally, solutions are represented in has been produced, or a satisfactory binary as strings of 0s and 1s, but other level has been reached for the population. encodings are also possible.[2] The usually starts from a population of randomly A typical genetic algorithm requires: generated individuals, and is an iterative process, with the population in each iteration A genetic representation of the solution called a generation. In each generation, the domain, fitness of every individual in the population is evaluated; the fitness is usually the value A to evaluate the solution of the objective function in the optimization domain. problem being solved. The more fit individuals are stochastically selected from A standard representation of each candidate [2] the current population, and each individual's solution is as an array of bits. Arrays of genome is modified (recombined and other types and structures can be used in possibly randomly mutated) to form a new essentially the same way. The main property generation. The new generation of that makes these genetic representations candidate solutions is then convenient is that their parts are easily

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 aligned due to their fixed size, which The fitness function is defined over the facilitates simple crossover operations. genetic representation and measures the Variable length representations may also be quality of the represented solution. The used, but crossover implementation is more fitness function is always problem complex in this case. -like dependent. For instance, in the knapsack representations are explored in genetic problem one wants to maximize the total programming and graph-form value of objects that can be put in a representations are explored in evolutionary knapsack of some fixed capacity. A programming; a mix of both linear representation of a solution might be an chromosomes and trees is explored in array of bits, where each bit represents a expression programming. different object, and the value of the bit (0 or 1) represents whether or not the object is in Once the genetic representation and the the knapsack. Not every such representation fitness function are defined, a GA proceeds is valid, as the size of objects may exceed to initialize a population of solutions and the capacity of the knapsack. The fitness of then to improve it through repetitive the solution is the sum of values of all application of the mutation, crossover, objects in the knapsack if the representation inversion and selection operators. is valid, or 0 otherwise.

Initialization In some problems, it is hard or even impossible to define the fitness expression; The population size depends on the nature of in these cases, a simulation may be used to the problem, but typically contains several determine the fitness function value of a hundreds or thousands of possible solutions. phenotype (e.g. computational fluid dynamics is used to determine the air Often, the initial population is generated resistance of a vehicle whose shape is randomly, allowing the entire range of encoded as the phenotype), or even possible solutions (the search space). interactive genetic algorithms are used. Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to Genetic operators be found. The next step is to generate a second Selection generation population of solutions from those selected through a combination of During each successive generation, a portion genetic operators: crossover (also called of the existing population is selected to recombination), and mutation. breed a new generation. Individual solutions are selected through a fitness-based process, For each new solution to be produced, a pair where fitter solutions (as measured by a of "parent" solutions is selected for breeding fitness function) are typically more likely to from the pool selected previously. By be selected. Certain selection methods rate producing a "child" solution using the above the fitness of each solution and methods of crossover and mutation, a new preferentially select the best solutions. Other solution is created which typically shares methods rate only a random sample of the many of the characteristics of its "parents". population, as the former process may be New parents are selected for each new child, very time-consuming. and the process continues until a new

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 population of solutions of appropriate size is generated. Although reproduction methods In addition to the main operators above, that are based on the use of two parents are other may be employed to make more "biology inspired", some research[3][4] the calculation faster or more robust. The suggests that more than two "parents" speciation penalizes crossover generate higher quality chromosomes. between candidate solutions that are too similar; this encourages population diversity These processes ultimately result in the next and helps prevent premature convergence to generation population of chromosomes that a less optimal solution.[6][7] is different from the initial generation. Generally the average fitness will have Termination increased by this procedure for the population, since only the best organisms This generational process is repeated until a from the first generation are selected for termination condition has been reached. breeding, along with a small proportion of Common terminating conditions are: less fit solutions. These less fit solutions ensure genetic diversity within the genetic A solution is found that satisfies minimum pool of the parents and therefore ensure the criteria genetic diversity of the subsequent generation of children. Fixed number of generations reached

Opinion is divided over the importance of Allocated budget (computation time/money) crossover versus mutation. There are many reached references in Fogel (2006) that support the importance of mutation-based search. The highest ranking solution's fitness is reaching or has reached a plateau such that Although crossover and mutation are known successive iterations no longer produce as the main genetic operators, it is possible better results to use other operators such as regrouping, colonization-extinction, or migration in Manual inspection genetic algorithms.[5] Combinations of the above It is worth tuning parameters such as the mutation probability, crossover probability The building block hypothesis and population size to find reasonable settings for the problem class being worked Genetic algorithms are simple to implement, on. A very small mutation rate may lead to but their behavior is difficult to understand. (which is non-ergodic in In particular it is difficult to understand why nature). these algorithms frequently succeed at generating solutions of high fitness when A recombination rate that is too high may applied to practical problems. The building lead to premature convergence of the genetic block hypothesis (BBH) consists of: algorithm. A mutation rate that is too high may lead to loss of good solutions, unless A description of a heuristic that performs elitist selection is employed. by identifying and recombining Heuristics "building blocks", i.e. low order, low

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 defining-length schemata with above there is a reasonable amount of work that average fitness. attempts to understand its limitations from the perspective of estimation of distribution A hypothesis that a genetic algorithm algorithms.[11][12][13] performs adaptation by implicitly and efficiently implementing this heuristic. Limitations

Goldberg describes the heuristic as follows: There are limitations of the use of a genetic algorithm compared to alternative "Short, low order, and highly fit schemata optimization algorithms: are sampled, recombined [crossed over], and resampled to form strings of potentially Repeated fitness function evaluation for higher fitness. In a way, by working with complex problems is often the most these particular schemata [the building prohibitive and limiting segment of artificial blocks], we have reduced the of evolutionary algorithms. Finding the optimal our problem; instead of building high- solution to complex high-dimensional, performance strings by trying every multimodal problems often requires very conceivable combination, we construct expensive fitness function evaluations. In better and better strings from the best partial real world problems such as structural solutions of past samplings. optimization problems, a single function evaluation may require several hours to "Because highly fit schemata of low several days of complete simulation. Typical defining length and low order play such an optimization methods can not deal with such important role in the action of genetic types of problem. In this case, it may be algorithms, we have already given them a necessary to forgo an exact evaluation and special name: building blocks. Just as a child use an approximated fitness that is creates magnificent fortresses through the computationally efficient. It is apparent that arrangement of simple blocks of wood, so amalgamation of approximate models may does a genetic algorithm seek near optimal be one of the most promising approaches to performance through the juxtaposition of convincingly use GA to solve complex real short, low-order, high-performance life problems. schemata, or building blocks."[8] Genetic algorithms do not scale well with Despite the lack of consensus regarding the complexity. That is, where the number of validity of the building-block hypothesis, it elements which are exposed to mutation is has been consistently evaluated and used as large there is often an exponential increase reference throughout the years. Many in search space size. This makes it extremely estimation of distribution algorithms, for difficult to use the technique on problems example, have been proposed in an attempt such as designing an engine, a house or to provide an environment in which the plane. In order to make such problems hypothesis would hold.[9][10] Although good tractable to evolutionary search, they must results have been reported for some classes be broken down into the simplest of problems, skepticism concerning the representation possible. Hence we typically generality and/or practicality of the see evolutionary algorithms encoding building-block hypothesis as an explanation designs for fan blades instead of engines, for GAs efficiency still remains. Indeed, building shapes instead of detailed

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 construction plans, and airfoils instead of programming) because crossing over a whole aircraft designs. The second problem homogeneous population does not yield new of complexity is the issue of how to protect solutions. In evolution strategies and parts that have evolved to represent good , diversity is not solutions from further destructive mutation, essential because of a greater reliance on particularly when their fitness assessment mutation. requires them to combine well with other parts. Operating on dynamic data sets is difficult, as genomes begin to converge early on The "better" solution is only in comparison towards solutions which may no longer be to other solutions. As a result, the stop valid for later data. Several methods have criterion is not clear in every problem. been proposed to remedy this by increasing genetic diversity somehow and preventing In many problems, GAs may have a early convergence, either by increasing the tendency to converge towards local optima probability of mutation when the solution or even arbitrary points rather than the quality drops (called triggered global optimum of the problem. This means hypermutation), or by occasionally that it does not "know how" to sacrifice introducing entirely new, randomly short-term fitness to gain longer-term generated elements into the gene pool fitness. The likelihood of this occurring (called random immigrants). Again, depends on the shape of the fitness evolution strategies and evolutionary landscape: certain problems may provide an programming can be implemented with a so- easy ascent towards a global optimum, called "comma strategy" in which parents others may make it easier for the function to are not maintained and new parents are find the local optima. This problem may be selected only from offspring. This can be alleviated by using a different fitness more effective on dynamic problems. function, increasing the rate of mutation, or by using selection techniques that maintain a GAs cannot effectively solve problems in diverse population of solutions,[14] although which the only fitness measure is a single the No Free Lunch theorem[15] proves that right/wrong measure (like decision there is no general solution to this problem. problems), as there is no way to converge on A common technique to maintain diversity the solution (no hill to climb). In these cases, is to impose a "niche penalty", wherein, any a random search may find a solution as group of individuals of sufficient similarity quickly as a GA. However, if the situation (niche radius) have a penalty added, which allows the success/failure trial to be repeated will reduce the representation of that group giving (possibly) different results, then the in subsequent generations, permitting other ratio of successes to failures provides a (less similar) individuals to be maintained in suitable fitness measure. the population. This trick, however, may not be effective, depending on the landscape of For specific optimization problems and the problem. Another possible technique problem instances, other optimization would be to simply replace part of the algorithms may be more efficient than population with randomly generated genetic algorithms in terms of speed of individuals, when most of the population is convergence. Alternative and too similar to each other. Diversity is complementary algorithms include evolution important in genetic algorithms (and genetic strategies, evolutionary programming,

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 , , crossovers. This has been found to help , and (e.g: prevent premature convergence at so called ant colony optimization, particle swarm Hamming walls, in which too many optimization) and methods based on integer simultaneous mutations (or crossover linear programming. The suitability of events) must occur in order to change the genetic algorithms is dependent on the chromosome to a better solution. amount of knowledge of the problem; well- known problems often have better, more Other approaches involve using arrays of specialized approaches. real-valued numbers instead of bit strings to represent chromosomes. Results from the Variants theory of schemata suggest that in general the smaller the alphabet, the better the Chromosome representation performance, but it was initially surprising to researchers that good results were The simplest algorithm represents each obtained from using real-valued chromosome as a bit string. Typically, chromosomes. This was explained as the set numeric parameters can be represented by of real values in a finite population of integers, though it is possible to use floating chromosomes as forming a virtual alphabet point representations. The floating point (when selection and recombination are representation is natural to evolution dominant) with a much lower cardinality strategies and evolutionary programming. than would be expected from a floating The notion of real-valued genetic algorithms point representation.[16] has been offered but is really a misnomer because it does not really represent the An expansion of the Genetic Algorithm building block theory that was proposed by accessible problem domain can be obtained John Henry Holland in the 1970s. This through more complex encoding of the theory is not without support though, based solution pools by concatenating several on theoretical and experimental results (see types of heterogenously encoded into below). The basic algorithm performs one chromosome. This particular approach crossover and mutation at the bit level. allows for solving optimization problems Other variants treat the chromosome as a list that require vastly disparate definition of numbers which are indexes into an domains for the problem parameters. For instruction table, nodes in a , instance, in problems of cascaded controller hashes, objects, or any other imaginable data tuning, the internal loop controller structure structure. Crossover and mutation are can belong to a conventional regulator of performed so as to respect data element three parameters, whereas the external loop boundaries. For most data types, specific could implement a linguistic controller (such variation operators can be designed. as a fuzzy system) which has an inherently Different chromosomal data types seem to different description. This particular form of work better or worse for different specific encoding requires a specialized crossover problem domains. mechanism that recombines the chromosome by section, and it is a useful When bit-string representations of integers tool for the modelling and simulation of are used, Gray coding is often employed. In complex adaptive systems, especially this way, small changes in the integer can be evolution processes. readily affected through mutations or Elitism

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441

analysis to judge the optimization states of A practical variant of the general process of the population, the adjustment of pc and pm constructing a new population is to allow the depends on these optimization states. It can best organism(s) from the current generation be quite effective to combine GA with other to carry over to the next, unaltered. This optimization methods. GA tends to be quite strategy is known as elitist selection and good at finding generally good global guarantees that the solution quality obtained solutions, but quite inefficient at finding the by the GA will not decrease from one last few mutations to find the absolute generation to the next. optimum. Other techniques (such as simple hill climbing) are quite efficient at finding Parallel implementations absolute optimum in a limited region. Alternating GA and hill climbing can Parallel implementations of genetic improve the efficiency of GA[citation needed] algorithms come in two flavours. Coarse- while overcoming the lack of robustness of grained parallel genetic algorithms assume a hill climbing. population on each of the computer nodes and migration of individuals among the This means that the rules of genetic nodes. Fine-grained parallel genetic variation may have a different meaning in algorithms assume an individual on each the natural case. For instance – provided that processor node which acts with steps are stored in consecutive order – neighbouring individuals for selection and crossing over may sum a number of steps reproduction. Other variants, like genetic from maternal DNA adding a number of algorithms for online optimization problems, steps from paternal DNA and so on. This is introduce time-dependence or noise in the like adding vectors that more probably may fitness function. follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be Adaptive GAs increased by many orders of magnitude. Moreover, the inversion operator has the Genetic algorithms with adaptive parameters opportunity to place steps in consecutive (adaptive genetic algorithms, AGAs) is order or any other suitable order in favour of another significant and promising variant of survival or efficiency. (See for instance [22] genetic algorithms. The probabilities of or example in travelling salesman problem, crossover (pc) and mutation (pm) greatly in particular the use of an edge determine the degree of solution accuracy recombination operator.) and the convergence speed that genetic algorithms can obtain. Instead of using fixed A variation, where the population as a whole values of pc and pm, AGAs utilize the is evolved rather than its individual population information in each generation members, is known as gene pool and adaptively adjust the pc and pm in order recombination. to maintain the population diversity as well as to sustain the convergence capacity. In A number of variations have been developed AGA (adaptive genetic algorithm), the to attempt to improve performance of GAs adjustment of pc and pm depends on the on problems with a high degree of fitness fitness values of the solutions. In CAGA epistasis, i.e. where the fitness of a solution (clustering-based adaptive genetic consists of interacting subsets of its algorithm), through the use of clustering variables. Such algorithms aim to learn

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441

(before exploiting) these beneficial chromosomes undergo mutation and phenotypic interactions. As such, they are recombination in a manner similar to the aligned with the Building Block Hypothesis canonical GA. But thanks to the special in adaptively reducing disruptive organization of GEP chromosomes, these recombination. Prominent examples of this genetic modifications always result in valid approach include the mGA, GEMGA and computer programs.[51] LLGA. (GP) is a related Evolutionary algorithms are a sub-field of technique popularized by John Koza in evolutionary computing. which computer programs, rather than function parameters, are optimized. Genetic Evolution strategies (ES, see Rechenberg, programming often uses tree-based internal 1994) evolve individuals by means of data structures to represent the computer mutation and intermediate or discrete programs for adaptation instead of the list recombination. ES algorithms are designed structures typical of genetic algorithms. particularly to solve problems in the real- value domain. They use self-adaptation to Grouping genetic algorithm (GGA) is an adjust control parameters of the search. De- evolution of the GA where the focus is randomization of self-adaptation has led to shifted from individual items, like in the contemporary Covariance Matrix classical GAs, to groups or subset of Adaptation (CMA-ES). items.[52] The idea behind this GA evolution proposed by Emanuel Falkenauer is that Evolutionary programming (EP) involves solving some complex problems, a.k.a. populations of solutions with primarily clustering or partitioning problems where a mutation and selection and arbitrary set of items must be split into disjoint group representations. They use self-adaptation to of items in an optimal way, would better be adjust parameters, and can include other achieved by making characteristics of the variation operations such as combining groups of items equivalent to genes. These information from multiple parents. kind of problems include bin packing, line balancing, clustering with respect to a Estimation of Distribution Algorithm (EDA) distance measure, equal piles, etc., on which substitutes traditional reproduction operators classic GAs proved to perform poorly. by model-guided operators. Such models are Making genes equivalent to groups implies learned from the population by employing chromosomes that are in general of variable techniques and represented length, and special genetic operators that as Probabilistic Graphical Models, from manipulate whole groups of items. For bin which new solutions can be sampled or packing in particular, a GGA hybridized generated from guided-crossover. with the Dominance Criterion of Martello and Toth, is arguably the best technique to Gene expression programming (GEP) also date. uses populations of computer programs. These complex computer programs are Interactive evolutionary algorithms are encoded in simpler linear chromosomes of evolutionary algorithms that use human fixed length, which are afterwards expressed evaluation. They are usually applied to as expression trees. Expression trees or domains where it is hard to design a computer programs evolve because the computational fitness function, for example,

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 evolving images, music, artistic designs and Bacteriologic algorithms (BA) inspired by forms to fit users' aesthetic preference. and, more particularly, bacteriologic adaptation. Evolutionary Swarm intelligence ecology is the study of living organisms in the context of their environment, with the Swarm intelligence is a sub-field of aim of discovering how they adapt. Its basic evolutionary computing. concept is that in a heterogeneous environment, there is not one individual that Ant colony optimization (ACO) uses many fits the whole environment. So, one needs to ants (or agents) equipped with a pheromone reason at the population level. It is also model to traverse the solution space and find believed BAs could be successfully applied locally productive areas. Although to complex positioning problems (antennas considered an Estimation of distribution for cell phones, urban planning, and so on) algorithm. or .

Particle swarm optimization (PSO) is a (CA) consists of the computational method for multi-parameter population component almost identical to optimization which also uses population- that of the genetic algorithm and, in based approach. A population (swarm) of addition, a knowledge component called the candidate solutions (particles) moves in the belief space. search space, and the movement of the particles is influenced both by their own best Differential (DS) inspired known position and swarm's global best by migration of superorganisms. known position. Like genetic algorithms, the PSO method depends on information Gaussian adaptation (normal or natural sharing among population members. In adaptation, abbreviated NA to avoid some problems the PSO is often more confusion with GA) is intended for the computationally efficient than the GAs, maximisation of manufacturing yield of especially in unconstrained problems with signal processing systems. It may also be continuous variables. used for ordinary parametric optimisation. It relies on a certain theorem valid for all Other evolutionary computing algorithms regions of acceptability and all Gaussian distributions. The efficiency of NA relies on is a sub-field of information theory and a certain theorem of the metaheuristic methods. efficiency. Its efficiency is defined as information divided by the work needed to (MA), often called get the information. Because NA maximises hybrid genetic algorithm among others, is a mean fitness rather than the fitness of the population-based method in which solutions individual, the landscape is smoothed such are also subject to local improvement that valleys between peaks may disappear. phases. The idea of memetic algorithms Therefore it has a certain "ambition" to comes from , which unlike genes, can avoid local peaks in the . adapt themselves. In some problem areas NA is also good at climbing sharp crests by they are shown to be more efficient than adaptation of the moment matrix, because traditional evolutionary algorithms. NA may maximise the disorder (average

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Int.J.Curr.Microbiol.App.Sci (2018) Special Issue-6: 431-441 information) of the Gaussian simultaneously individual solution components to be keeping the mean fitness constant. assigned a quality measure ("fitness"). The governing principle behind this algorithm is Other metaheuristic methods that of emergent improvement through selectively removing low-quality Metaheuristic methods broadly fall within components and replacing them with a stochastic optimisation methods. randomly selected component. This is decidedly at odds with a GA that selects Simulated annealing (SA) is a related global good solutions in an attempt to make better optimization technique that traverses the solutions. search space by testing random mutations on an individual solution. A mutation that Other stochastic optimisation methods increases fitness is always accepted. A mutation that lowers fitness is accepted The cross-entropy (CE) method generates probabilistically based on the difference in candidates solutions via a parameterized fitness and a decreasing temperature probability distribution. The parameters are parameter. In SA parlance, one speaks of updated via cross-entropy minimization, so seeking the lowest energy instead of the as to generate better samples in the next maximum fitness. SA can also be used iteration. within a standard GA algorithm by starting with a relatively high rate of mutation and Reactive search optimization (RSO) decreasing it over time along a given advocates the integration of sub-symbolic schedule. machine learning techniques into search heuristics for solving complex optimization (TS) is similar to simulated problems. The word reactive hints at a ready annealing in that both traverse the solution response to events during the search through space by testing mutations of an individual an internal online loop for the self- solution. While simulated annealing tuning of critical parameters. Methodologies generates only one mutated solution, tabu of interest for Reactive Search include search generates many mutated solutions machine learning and statistics, in particular and moves to the solution with the lowest , active or query energy of those generated. In order to learning, neural networks, and prevent cycling and encourage greater . movement through the solution space, a tabu list is maintained of partial or complete References solutions. It is forbidden to move to a solution that contains elements of the tabu 1. Mitchell 1996, p. 2. list, which is updated as the solution 2. Whitley 1994, p. 66. traverses the solution space. 3. Eiben, A. E. et al., (1994). "Genetic algorithms with multi-parent (EO) Unlike GAs, recombination". PPSN III: which works with a population of candidate Proceedings of the International solutions, EO evolves a single solution and Conference on Evolutionary makes local modifications to the worst Computation. The Third Conference components. This requires that a suitable on Parallel Problem Solving from representation be selected which permits Nature: 78–87.

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