Genetic algorithms in mesh optimization for visualization and finite element models

This paper investigates the use of a genetic algorithm (GA) to perform the large-scale triangular mesh optimization process. This optimization process consists of a combination of mesh reduction and mesh smoothing that will not only improve the speed for the computation of a 3D graphical or finite element model, but also improve the quality of its mesh. The GA is developed and implemented to replace the original mesh with a re-triangulation process. The GA features optimized initial population, constrained crossover operator, constrained mutation operator and multi-objective fitness evaluation function. While retaining features is important to both visualization models and finite element models, this algorithm also optimizes the shape of the triangular elements, improves the smoothness of the mesh and performs mesh reduction based on the needs of the user.     

A comparative analysis of genetic algorithms and directed grid search for parametric optimization

In this paper, a comparative analysis of the performance of the Genetic Algorithm (GA) and Directed Grid Search (DGS) methods for optimal parametric design is presented. A genetic algorithm is a guided random search mechanism based on the principle of natural selection and population genetics. The Directed Grid Search method uses a selective directed search of grid points in the direction of descent to find the minimum of a real function, when the initial estimate of the location of the minimum and the bounds of the design variables are specified. An experimental comparison and a discussion on the performance of these two methods in solving a set of eight test functions is presented.     

A Pareto-optimal genetic algorithm for warehouse multi-objective optimization

The automated warehouse management requires to fulfill objectives that are usually conflicting with each other. The decisions taken must ensure optimized usage of resources, cost reduction and better customer service. The warehouse replenishment task is a typical example of multi-objective optimization. In this paper, a genetic algorithm with a new crossover operator is developed to solve the replenishment problem. This algorithm is applied to real warehouse data and produces Pareto-optimal permutations of the stored products. A fuzzy rule-base is proposed to increase the diversity of the optimal solutions.     

Simple models of coevolutionary genetic algorithms

The use of evolutionary computing techniques in coevolutionary/multiagent systems is becoming increasingly popular. This paper presents some simple models of the genetic algorithm in such systems, with the aim of examining the effects of different types of interdependence between individuals. Using the models, it is shown that for a fixed amount of interdependence between homogeneous coevolving individuals, the existence of partner gene variance, gene symmetry, and the level at which fitness is applied can have significant effects. Similarly, for heterogeneous coevolving systems with fixed interdependence, partner gene variance and fitness application are also found to have a significant effect, as is the partnering strategy used.     

A note on the variance of rank-based selection strategies for genetic algorithms and genetic programming

This paper evaluates different forms of rank-based selection that are used with genetic algorithms and genetic programming. Many types of rank based selection have exactly the same expected value in terms of the sampling rate allocated to each member of the population. However, the variance associated with that sampling rate can vary depending on how selection is implemented. We examine two forms of tournament selection and compare these to linear rank-based selection using an explicit formula. Because selective pressure has a direct impact on population diversity, we also examine the interaction between selective pressure and different mutation strategies.     

An application of genetic algorithm methods for teacher assignment problems

The arrangement of courses at universities is an optimal problem to be discussed under multiple constraints. It can be divided into two parts: teacher assignments and class scheduling. This paper focused primarily on teacher assignments. Consideration was given to teacher's professional knowledge, teacher preferences, fairness of teaching overtime, school resources, and the uniqueness of the school's management. Traditional linear programming methods do not obtain satisfactory results with this complex problem.In this paper, genetic algorithm methods were used to deal with the issue of multiple constraints. As a global optimal searching method, the results of this study indicated that genetic algorithms can save significant time spent on teacher assignments and are more acceptable by the teachers.     

Emergent nature inspired algorithms for multi-objective optimization

Many real-world decision-making situations possess both a discrete and combinatorial structure and involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of large size and contains several objectives to be “optimized”. Although Multiple Objective Optimization is a well-established field of research, one branch, namely nature inspired metaheuristics is currently experienced a tremendous growth. Over the last few years, developments of new methodologies, methods, and techniques to deal with multi-objective large size problems in particular those with a combinatorial structure and the strong improvement on computing technologies (during and after the 80s) made possible to solve very hard problems with the help of inspired nature based metaheuristics.     

Evolving rule induction algorithms with multi-objective grammar-based genetic programming

Multi-objective optimization has played a major role in solving problems where two or more conflicting objectives need to be simultaneously optimized. This paper presents a Multi-Objective grammar-based genetic programming (MOGGP) system that automatically evolves complete rule induction algorithms, which in turn produce both accurate and compact rule models. The system was compared with a single objective GGP and three other rule induction algorithms. In total, 20 UCI data sets were used to generate and test generic rule induction algorithms, which can be now applied to any classification data set. Experiments showed that, in general, the proposed MOGGP finds rule induction algorithms with competitive predictive accuracies and more compact models than the algorithms it was compared with.

Proposal and validation of an optimization method using Monte Carlo method for multi-objective functions

Solving optimization problems is essential for many engineering applications and research tools. In a previous report, we proposed a new optimization method, MOST (Monte Carlo Stochastic Optimization), using the Monte Carlo method, and applied it to benchmark problems for optimization methods, and optimization of neural network machine learning. While the proposed method MOST was a single objective, this study is an extension of MOST so that it can be applied to multi-objective functions for the purpose of improving generality. As the verification, it was applied to the optimization problem with the restriction condition first, and it was also applied to the benchmark problem for the multi-objective optimization technique verification, and the validity was confirmed. For comparison, the calculation by genetic algorithm was also carried out, and it was confirmed that MOST was excellent in calculation accuracy and calculation time.     

Multiobjective topology optimization of structures using genetic algorithms with chromosome repairing

In this work, a genetic algorithm (GA) for multiobjective topology optimization of linear elastic structures is developed. Its purpose is to evolve an evenly distributed group of solutions to determine the optimum Pareto set for a given problem. The GA determines a set of solutions to be sorted by its domination properties and a filter is defined to retain the Pareto solutions. As an equality constraint on volume has to be enforced, all chromosomes used in the genetic GA must generate individuals with the same volume value; in the coding adopted, this means that they must preserve the same number of “ones” and, implicitly, the same number of “zeros” along the evolutionary process. It is thus necessary: (1) to define chromosomes satisfying this propriety and (2) to create corresponding crossover and mutation operators which preserve volume. Optimal solutions of each of the single-objective problems are introduced in the initial population to reduce computational effort and a repairing mechanism is developed to increase the number of admissible structures in the populations. Also, as the work of the external loads can be calculated independently for each individual, parallel processing was used in its evaluation. Numerical applications involving two and three objective functions in 2D and two objective functions in 3D are employed as tests for the computational model developed. Moreover, results obtained with and without chromosome repairing are compared.     

Implementation of polynomial multi-objective optimization in Mathematica

We describe implementation of main methods for solving polynomial multi-objective optimization problems by means of symbolic processing available in the programming language MATHEMATICA. Symbolic transformations of unevaluated expressions, representing objective functions and constraints, into the corresponding representation of the single-objective constrained problem are especially emphasized. We also describe a function for the verification of Pareto optimality conditions and a function for graphical illustration of Pareto optimal points and given constraint set.     

Obtaining transparent models of chaotic systems with multi-objective simulated annealing algorithms

Transparent models search for a balance between interpretability and accuracy. This paper is about the estimation of transparent models of chaotic systems from data, which are accurate and simple enough for their expression to be understandable by a human expert. The models we propose are discrete, built upon common blocks in control engineering (gain, delay, sum, etc.) and optimized both in their complexity and accuracy.The accuracy of a discrete model can be measured by means of the average error between its prediction for the next sampling period and the true output at that time, or ‘one-step error’. A perfect model has zero one-step error, but a small error is not always associated with an approximate model, especially in chaotic systems. In chaos, an arbitrarily low difference between two initial states will produce uncorrelated trajectories, thus a model with a low one-step error may be very different from the desired one. Even though a recursive evaluation (multi-step prediction) improves the fitting, in this work we will show that a learning algorithm may not converge to an appropriate model, unless we include some terms that depend on estimates of certain properties of the model (so called ‘invariants’ of the chaotic series). We will show this graphically, by means of the reconstructed attractors of the original system and the model. Therefore, we also propose to follow a multi-objective approach to model chaotic processes and to apply a simulated annealing-based optimization to obtain transparent models.     

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.     

Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

A single front genetic algorithm for parallel multi-objective optimization in dynamic environments

This paper proposes a new parallel evolutionary procedure to solve multi-objective dynamic optimization problems along with some measures to evaluate multi-objective optimization in dynamic environments. These dynamic optimization problems appear in quite different real-world applications with actual socio-economic relevance. In these applications, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online whilst the size of the changes is unknown. Although parallel processing could be very useful in these problems to meet the solution quality requirements and constraints, to date, not many parallel approaches have been reported in the literature. Taking this into account, we introduce a multi-objective optimization procedure for dynamic problems that are based on PSFGA, a parallel evolutionary algorithm previously proposed by us for multi-objective optimization. It uses an island model where a process divides the population among the remaining processes and allows the communication and coordination among the subpopulations in the different islands. The proposed algorithm makes an exclusive use of non-dominating individuals for the selection and variation operator and applies a crowding mechanism to maintain the diversity and the distribution of the solutions in the Pareto front. We also propose a model to understand the benefits of parallel processing in multi-objective problems and the speedup figures obtained in our experiments.     

Efficient solutions for Mastermind using genetic algorithms

We present a new genetic algorithm for playing the game of Mastermind. The algorithm requires low run-times and results in a low expected number of guesses. Its performance is comparable to that of other meta-heuristics for the standard setting with four positions and six colors, while it outperforms the existing algorithms when more colors and positions are examined. The central idea underlying the algorithm is the creation of a large set of eligible guesses collected throughout the different generations of the genetic algorithm, the quality of each of which is subsequently determined based on a comparison with a selection of elements of the set.     

An optimal layout methodology for cold forming rectangular parts using genetic algorithms

Cold forming is widely used in manufacturing processing, and the layout of rectangular parts in the strip is manually accomplished, which is a time-consuming task and may be a major bottleneck in effectively improving the utilization ratio of material and the productivity. The mathematical model for optimal layout of cold forming is first developed, and then the constrained optimal layout problem is transformed to an unconstrained optimal one with penalty function strategy. A simple genetic algorithms for this optimal layout is proposed, and an example is examined to show the validity of this proposed genetic methodology. Although the simple genetic algorithms is employed, a higher material utilization ratio and productivity is achieved.     

Methodology for shape optimization of ultrasonic amplifier using genetic algorithms and simplex method

Designing devices for ultrasonic vibration applications is mostly done by intuitively adjusting the geometry to obtain the desired mode of vibration at a specific operating frequency. Recent studies have shown that with optimization methods, new devices with improved performance can be easily found. In this investigation, a new methodology for designing an ultrasonic amplifier through shape optimization using genetic algorithms and simplex method with specific fitness functions is presented. Displacements at specific functional areas, main functionality, and mode frequency are considered to determine the properties of an individual shape to meet the stated criteria. Length, diameter, position of mountings, and further specific geometric parameters are set up for the algorithm search for an optimized shape. Beginning with genetic algorithms, the basic shape fitting the stated requirements is found. After that the simplex method further improves the found shape to most appropriately minimize the fitness function. At the end, the fittest individual is selected as the final solution. Finally, resulting shapes are experimentally tested to show the effectiveness of the methodology.     

Economic and environmental assessment of irrigation water policies: A bioeconomic simulation study

We present a bioeconomic modeling approach that links the biophysical crop growth model CropSyst to an economic decision model at field scale. The developed model is used in conjunction with a genetic algorithm to optimize management decisions in potato production in the Broye catchment (Switzerland) in the context of different irrigation policy scenarios. More specifically, we consider the effects of water bans, water quotas, and water prices on water consumption, profitability, and the financial risks of potato production. The use of a genetic algorithm enables the direct integration of the considered decision variables as management input factors in CropSyst. We employ the farmer's certainty equivalent, measured as the expected profit margin minus a risk premium, as the objective function. Using this methodological framework allows us to consider the potential impacts of policy measures on farmers' crop management decisions due to their effects on both expected income levels and income variability.Our results show that the region's current water policy, which frequently prevents irrigation during hot and dry periods by banning water withdrawal, causes high levels of income risk for the farmer and increases the average water demand in potato production. In contrast, the implementation of an appropriate water quota could significantly decrease water consumption in potato production while allowing the farmer's certainty equivalent to remain at the same level as it is under the current irrigation water policy.     

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided.