A modified distance method for multicriteria optimization, using genetic algorithms

The common application areas of Genetic Algorithms (GAs) have been to single criterion difficult optimization problems. The GA selection mechanism is often dependent upon a single valued scalar objective funtion. In this paper, we present results of a modified distance method. The distance method was proposed earlier by us, for solving multiple criteria problems with GAs. The Pareto set estimation method, which is fundamental to multicriteria analysis, is used to perform the multicriteria optimization using GAs. First, the Pareto set is found out from the population of the initial generation of the GA. The fitness of a new solution, is calculated by a distance measure with reference to the Pareto set of the previous runs. We calculate the distances of a solution from all the Pareto solutions found since the previous run, but the minimum of these distances is taken under consideration while evaluating the fitness of the solution. Thus the GA tries to maximize the distance of future Pareto solutions from present Pareto solutions in the positive Pareto space of the given problem. Here we modify distance method, by using an improved algorithm to assign and make use of the latent potential of the Pareto solutions which are found during the runs. Two detailed numerical examples and computer generated results are also presented.     

Constraint handling in genetic algorithms using a gradient-based repair method

Constraint handling is one of the major concerns when applying genetic algorithms (GAs) to solve constrained optimization problems. This paper proposes to use the gradient information derived from the constraint set to systematically repair infeasible solutions. The proposed repair procedure is embedded into a simple GA as a special operator. Experiments using 11 benchmark problems are presented and compared with the best known solutions reported in the literature. Our results are competitive, if not better, compared to the results reported using the homomorphous mapping method, the stochastic ranking method, and the self-adaptive fitness formulation method.     

Genetic algorithms to solve the cover printing problem

Inspired by successful application of evolutionary algorithms to solving difficult optimization problems, we explore in this paper, the applicability of genetic algorithms (GAs) to the cover printing problem, which consists in the grouping of book covers on offset plates in order to minimize the total production cost. We combine GAs with a linear programming solver and we propose some innovative features such as the “unfixed two-point crossover operator” and the “binary stochastic sampling with replacement” for selection. Two approaches are proposed: an adapted genetic algorithm and a multiobjective genetic algorithm using the Pareto fitness genetic algorithm. The resulting solutions are compared. Some computational experiments have also been done to analyze the effects of different genetic operators on both algorithms.     

A systematic search for Pareto optimum solutions

This note presents a numerical method for determining Pareto solutions of multicriteria, two design variable optimization problems. The method, based on the set theory conditions of Pareto optimality, enables one to locate the Pareto solutions and also to identify the designs that are equally distant from these solutions. An example of the application of the method to bi-criteria optimization of a thin-walled column is given.     

Multi-objective genetic local search algorithm using Kohonen’s neural map

Genetic Algorithms (GAs) are population based global search methods that can escape from local optima traps and find the global optima regions. However, near the optimum set their intensification process is often inaccurate. This is because the search strategy of GAs is completely probabilistic. With a random search near the optimum sets, there is a small probability to improve current solution. Another drawback of the GAs is genetic drift. The GAs search process is a black box process and no one knows that which region is being searched by the algorithm and it is possible that GAs search only a small region in the feasible space. On the other hand, GAs usually do not use the existing information about the optimality regions in past iterations.In this paper, a new method called SOM-Based Multi-Objective GA (SBMOGA) is proposed to improve the genetic diversity. In SBMOGA, a grid of neurons use the concept of learning rule of Self-Organizing Map (SOM) supporting by Variable Neighborhood Search (VNS) learn from genetic algorithm improving both local and global search. SOM is a neural network which is capable of learning and can improve the efficiency of data processing algorithms. The VNS algorithm is developed to enhance the local search efficiency in the Evolutionary Algorithms (EAs). The SOM uses a multi-objective learning rule based-on Pareto dominance to train its neurons. The neurons gradually move toward better fitness areas in some trajectories in feasible space. The knowledge of optimum front in past generations is saved in form of trajectories. The final state of the neurons determines a set of new solutions that can be regarded as the probability density distribution function of the high fitness areas in the multi-objective space. The new set of solutions potentially can improve the GAs overall efficiency. In the last section of this paper, the applicability of the proposed algorithm is examined in developing optimal policies for a real world multi-objective multi-reservoir system which is a non-linear, non-convex, multi-objective optimization problem.     

Biological-based genetic algorithms for optimized disaster response resource allocation

An effective disaster response requires rapid coordination of existing resources, which can be considered a resource optimization problem. Genetic algorithms (GAs) have been proven effective for solving optimization problems in various fields. However, GAs essentially use generation succession to search for optimal solutions. Therefore, their use of reproduction, crossover, and mutation operations may exclude optimal chromosomes during generation succession and prevent full use of previous search experience. Meanwhile, premature convergence caused by inadequate diversity of chromosome populations limits the search to a local optimum. Genetic algorithms also incur high computational costs. The biological-based GAs (BGAs) proposed in this study address these problems by including mechanisms for elite reserve areas, nonlinear fitness value conversion, and migration. This study performed experimental simulations to compare BGAs with immune algorithms (IAs) and GAs in terms of effectiveness for allocating disaster refuge site staff and for planning relief supply distribution. The simulation results show that, compared to other methods, BGAs can compute optimal solutions faster. Therefore, they provide a more useful reference when performing the decision-making needed to solve disaster response resource optimization problems.     

GENETIC ALGORITHM APPLICATION TO THE STANDARD ARABIC PHONEMES CLASSIFICATION

The goal of this article is the application of genetic algorithms (GAs) to the automatic speech recognition (ASR) domain at the acoustic sequences classification level. Speech recognition has been cast as a pattern classification problem where we would like to classify an input acoustic signal into one of all possible phonemes. Also, the supervised classification has been formulated as a function optimization problem. Thus, we have attempted to recognize Standard Arabic (SA) phonemes of continuous, naturally spoken speech by using GAs, which have several advantages in resolving complicated optimization problems. In SA, there are 40 sounds. We have analyzed a corpus that contains several sentences composed of the whole SA phoneme types in the initial, medium, and final positions, recorded by several male speakers. Furthermore, the acoustic segments classification and the GAs have been explored. Among a set of classifiers such as Bayesian, likelihood, and distance classifier, we have used the distance classifier. It is based on the classification measure criterion. Therefore, we have used the decision rule Manhattan distance as the fitness functions for our GA evaluations. The corpus phonemes were extracted and classified successfully with an overall accuracy of 90.20%.     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

Genetic search: analysis using fitness moments

Genetic algorithms (GAs) are efficient and robust search methods that are being employed in a plethora of applications with extremely large search spaces. The directed search mechanism employed in GAs performs a simultaneous and balanced exploration of new regions in the search space and exploitation of already-discovered regions. This paper introduces the notion of fitness moments for analyzing the working of GAs. We show that the fitness moments in any generation may be predicted from those of the initial population. Since a knowledge of the fitness moments allows us to estimate the fitness distribution of strings, this approach provides for a method of characterizing the dynamics of GAs. In particular, the average fitness and fitness variance of the population in any generation may be predicted. We introduce the technique of fitness-based disruption of solutions for improving the performance of GAs. Using fitness moments, we demonstrate the advantages of using fitness-based disruption. We also present experimental results comparing the performance of a standard GA and two other GAs (the controlled disruption GA and the adaptive GA) that incorporate the principle of fitness-based disruption. The experimental evidence clearly demonstrates the power of fitness-based disruption     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.     

Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach

Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0/1 knapsack problem     

Multi-objective optimization of stochastic disassembly line balancing with station paralleling

One of the major activities performed in product recovery is disassembly. Disassembly line is the most suitable setting to disassemble a product. Therefore, designing and balancing efficient disassembly systems are important to optimize the product recovery process. In this study, we deal with multi-objective optimization of a stochastic disassembly line balancing problem (DLBP) with station paralleling and propose a new genetic algorithm (GA) for solving this multi-objective optimization problem. The line balance and design costs objectives are simultaneously optimized by using an AND/OR Graph (AOG) of the product. The proposed GA is designed to generate Pareto-optimal solutions considering two different fitness evaluation approaches, repair algorithms and a diversification strategy. It is tested on 96 test problems that were generated using the benchmark problem generation scheme for problems defined on AOG as developed in literature. In addition, to validate the performance of the algorithm, a goal programming approach and a heuristic approach are presented and their results are compared with those obtained by using GA. Computational results show that GA can be considered as an effective and efficient solution algorithm for solving stochastic DLBP with station paralleling in terms of the solution quality and CPU time.     

Decision making with multiple objectives using GAI networks

This paper deals with preference representation on combinatorial domains and preference-based recommendation in the context of multicriteria or multiagent decision making. The alternatives of the decision problem are seen as elements of a product set of attributes and preferences over solutions are represented by generalized additive decomposable (GAI) utility functions modeling individual preferences or criteria. Thanks to decomposability, utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees, the so-called GAI network. Using this structure, we present preference-based search algorithms for multicriteria or multiagent decision making. Although such models are often non-decomposable over attributes, we actually show that GAI networks are still useful to determine the most preferred alternatives provided preferences are compatible with Pareto dominance. We first present two algorithms for the determination of Pareto-optimal elements. Then the second of these algorithms is adapted so as to directly focus on the preferred solutions. We also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems.     

An interactive fuzzy multi-objective optimization method for engineering design

The coupling of performance functions due to common design variables and uncertainties in an engineering design process will result in difficulties in optimization design problems, such as poor collaboration among design objectives and poor resolution of design conflicts. To handle these problems, a fuzzy interactive multi-objective optimization model is developed based on Pareto solutions, where the metric function and some additional constraints are added to ensure the collaboration among design objectives. The trade-off matrix at the Pareto solutions was developed, and the method for selecting weighting coefficients of optimization objectives is also provided. The proposed method can generate a Pareto optimal set with the maximum satisfaction degree and the minimum distance from ideal solution. The favorable optimal solution can be then selected from the Pareto optimal set by analyzing the trade-off matrix and collaborative sensitivity. Two examples are presented to illustrate the proposed method.     

Genetic supervised classification of Standard Arabic fricative sounds

The purpose of this paper is the application of the Genetic Algorithms (GAs) to the supervised classification level, in order to recognize Standard Arabic (SA) fricative consonants of continuous, naturally spoken, speech. We have used GAs because of their advantages in resolving complicated optimization problems where analytic methods fail. For that, we have analyzed a corpus that contains several sentences composed of the thirteen types of fricative consonants in the initial, medium and final positions, recorded by several male Jordanian speakers. Nearly all the world’s languages contain at least one fricative sound. The SA language occupies a rather exceptional position in that nearly half of its consonants are fricatives and nearly half of fricative inventory is situated far back in the uvular, pharyngeal and glottal areas. We have used Mel-Frequency Cepstral analysis method to extract vocal tract coefficients from the speech signal. Among a set of classifiers like Bayesian, likelihood and distance classifier, we have used the distance one. It is based on the classification measure criterion. So, we formulate the supervised classification as a function optimization problem and we have used the decision rule Mahalanobis distance as the fitness function for the GA evaluation. We report promising results with a classification recognition accuracy of 82%.     

DOPGA: a new fitness assignment scheme for multi-objective evolutionary algorithms

In this article, a new fitness assignment scheme to evaluate the Pareto-optimal solutions for multi-objective evolutionary algorithms is proposed. The proposed DOmination Power of an individual Genetic Algorithm (DOPGA) method can order the individuals in a form in which each individual (the so-called solution) could have a unique rank. With this new method, a multi-objective problem can be treated as if it were a single-objective problem without drastically deviating from the Pareto definition. In DOPGA, relative position of a solution is embedded into the fitness assignment procedures. We compare the performance of the algorithm with two benchmark evolutionary algorithms (Strength Pareto Evolutionary Algorithm (SPEA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2)) on 12 unconstrained bi-objective and one tri-objective test problems. DOPGA significantly outperforms SPEA on all test problems. DOPGA performs better than SPEA2 in terms of convergence metric on all test problems. Also, Pareto-optimal solutions found by DOPGA spread better than SPEA2 on eight of 13 test problems.     

Combining genetic algorithms with BESO for topology optimization

This paper proposes a new algorithm for topology optimization by combining the features of genetic algorithms (GAs) and bi-directional evolutionary structural optimization (BESO). An efficient treatment of individuals and population for finite element models is presented which is different from traditional GAs application in structural design. GAs operators of crossover and mutation suitable for topology optimization problems are developed. The effects of various parameters used in the proposed GA on the optimization speed and performance are examined. Several 2D and 3D examples of compliance minimization problems are provided to demonstrate the efficiency of the proposed new approach and its capability of obtaining convergent solutions. Wherever possible, the numerical results of the proposed algorithm are compared with the solutions of other GA methods and the SIMP method.     

Multi-objective optimization using teaching-learning-based optimization algorithm

Two major goals in multi-objective optimization are to obtain a set of nondominated solutions as closely as possible to the true Pareto front (PF) and maintain a well-distributed solution set along the Pareto front. In this paper, we propose a teaching-learning-based optimization (TLBO) algorithm for multi-objective optimization problems (MOPs). In our algorithm, we adopt the nondominated sorting concept and the mechanism of crowding distance computation. The teacher of the learners is selected from among current nondominated solutions with the highest crowding distance values and the centroid of the nondominated solutions from current archive is selected as the Mean of the learners. The performance of proposed algorithm is investigated on a set of some benchmark problems and real life application problems and the results show that the proposed algorithm is a challenging method for multi-objective algorithms.     

基于人工免疫系统的多目标函数优化

为克服传统遗传算法退化和早熟等缺点,同时降低优化算法的复杂度,提出基于人工免疫系统（Artificial Immune System, AIS）实现无约束多目标函数的优化。使用随机权重法和自适应权重法计算种群个体的适应值,使Pareto最优解均匀分布的同时,加快算法的收敛;通过引入人工免疫系统的三个基本算子：克隆、超变异和消亡,保持种群的多样性;在进化种群外设立Pareto 解集,保存历代的近似最优解。使用了两个典型的多目标检测函数验证了该算法的有效性。优化结果表明,基于AIS的多目标优化算法可使进化种群迅速收敛到Pareto前沿,并能均匀分布,是实现多目标函数优化的有效方法。     

Facilities layout design by genetic algorithms

Genetic algorithms (GAs) are a class of adaptive search techniques which have gained popularity in optimisation. In particular they have successfully been applied to NP hard problems such as those resulted in mathematical modelling of facilities design problems. The typical steps required to implement GAs are: encoding of feasible solutions into chromosomes using a representation method, evaluation of fitness function, setting of GAs parameters, selection strategy, genetic operators, and criteria to terminate the process. This paper reports on finding of a research in design of a GA solving the quadratic assignment formulation of equal and unequal-sized facilities layout problems. Comparison is made with solutions of several test problems reported in the literature.