A genetic algorithm for combined topology and shape optimisations

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coordinates of the keypoints of changeable boundaries constituted by curves. In both the steps the aim is that to find the variable sets producing the maximum stiffness of the structure, respecting an upper limit on the employed mass. The structural evaluations are carried out with a FEM commercial code, linked to the algorithm. Some applications have been performed and results compared with solutions reported in literature.     

A genetic algorithm for the optimisation of assembly sequences

This paper describes a Genetic Algorithm (GA) designed to optimise the Assembly Sequence Planning Problem (ASPP), an extremely diverse, large scale and highly constrained combinatorial problem. The modelling of the ASPP problem, which has to be able to encode any industrial-size product with realistic constraints, and the GA have been designed to accommodate any type of assembly plan and component. A number of specific modelling issues necessary for understanding the manner in which the algorithm works and how it relates to real-life problems, are succinctly presented, as they have to be taken into account/adapted/solved prior to Solving and Optimising (S/O) the problem. The GA has a classical structure but modified genetic operators, to avoid the combinatorial explosion. It works only with feasible assembly sequences and has the ability to search the entire solution space of full-scale, unabridged problems of industrial size. A case study illustrates the application of the proposed GA for a 25-components product.     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator

This paper presents investigations into the design of a command-shaping technique using multi-objective genetic optimisation process for vibration control of a single-link flexible manipulator. Conventional design of a command shaper requires a priori knowledge of natural frequencies and associated damping ratios of the system, which may not be available for complex flexible systems. Moreover, command shaping in principle causes delay in system's response while it reduces system vibration and in this manner the amount of vibration reduction and the rise time conflict one another. Furthermore, system performance objectives, such as, reduced overshoot, rise time, settling time, and end-point vibration are found in conflict with one another due to the construction and mode of operation of a flexible manipulator. Conventional methods can hardly provide a solution, for a designer-oriented formulation, satisfying several objectives and associated goals as demanded by a practical application due to the competing nature of those objectives. In such cases, multi-objective optimisation can provide a wide range of solutions, which trade-off these conflicting objectives so as to satisfy associated goals. A multi-modal command shaper consists of impulses of different amplitudes at different time locations, which are convolved with one another and then with the desired reference and then used as reference (for closed loop) or applied to system (for open loop) with the view to reduce vibration of the system, mainly at dominant modes. Multi-objective optimisation technique is used to determine a set of solutions for the amplitudes and corresponding time locations of impulses of a multi-modal command shaper. The effectiveness of the proposed technique is assessed both in the time domain and the frequency domain. Moreover, a comparative assessment of the performance of the technique with the system response with unshaped bang–bang input is presented.     

Optimising a complex discrete event simulation model using a genetic algorithm

A steelworks model is selected as representative of the stochastic and unpredictable behaviour of a complex discrete event simulation model. The steel-works has a number of different entity or object types. Using the number of each entity type as parameters, it is possible to find better and worse combinations of parameters for various management objectives. A simple real-coded genetic algorithm is presented that optimises the parameters, demonstrating the versatility that genetic algorithms offer in solving hard inverse problems.     

Improved genetic algorithm inspired by biological evolution

The process of mutation has been studied extensively in the field of biology and it has been shown that it is one of the major factors that aid the process of evolution. Inspired by this a novel genetic algorithm (GA) is presented here. Various mutation operators such as small mutation, gene mutation and chromosome mutation have been applied in this genetic algorithm. In order to facilitate the implementation of the above-mentioned mutation operators a modified way of representing the variables has been presented. It resembles the way genetic information is coded in living beings. Different mutation operators pose a challenge as regards the determination of the optimal rate of mutation. This problem is overcome by using adaptive mutation operators. The main purpose behind this approach was to improve the efficiency of GAs and to find widely distributed Pareto-optimal solutions. This algorithm was tested on some benchmark test functions and compared with other GAs. It was observed that the introduction of these mutations do improve the genetic algorithms in terms of convergence and the quality of the solutions.     

Runner sizing in multiple cavity injection mould by non-dominated sorting genetic algorithm

Runner system is important in the plastic injection moulding as it affects the part quality and the material costs. The layout of the runners for a multiple non-identical cavity mould is geometrically imbalance. Even for a multiple identical cavity mould, the layout can be imbalance due to various reasons. This paper presents an approach to balance the flow by adjusting the runner sizes. Runner size determination is a multiobjective optimisation problem. The non-dominated sorting genetic algorithm is adopted for determining the runner sizes. Multiple objective functions including runner balancing, part quality in terms of warpage and runner volume are incorporated into the algorithm. The moulding conditions affecting the mould cavity filling are also determined due to their sensitivity to runner sizes. This runner sizing approach is suitable for the geometric imbalance mouldings and family mouldings.     

Resource allocation by genetic algorithm with fuzzy inference

Assuming that a make-to-order manufacturing company has customer orders, the addressed capacity allocation problem is a due-date assignment problem for multiple manufacturing resources. The purpose of this study is to develop an intelligent resource allocation model using genetic algorithm and fuzzy inference for reducing lateness of orders with specific due dates. While the genetic algorithm is responsible for arranging and selecting the sequence of orders, the fuzzy inference module conveys how resources are allocated to each order. Experimental results showed that the proposed model has solved the capacity allocation problem efficiently.     

Rough milling optimisation for parts with sculptured surfaces using genetic algorithms in a Stackelberg game

In rough milling of sculptured surface parts, decisions on process parameters concern feedrate, spindle speed, cutting speed, width of cut, raster pattern angle and number of machining slices of variable thickness. In this paper three rough milling objectives are considered: minimum machining time, maximum removed material and maximum uniformity of the remaining volume at the end of roughing. Owing to the complexity of the modelled problem and the large number of parameters, typical genetic algorithms cannot achieve global optima without defining case-dependent constraints. Therefore, to achieve generality, a hierarchical game similar to a Stackelberg game is implemented in which a typical Genetic Algorithm functions as the leader and micro-Genetic Algorithms as followers. In this game, one of the leader’s parameters is responsible for creating a follower’s population and for triggering the optimisation. After properly weighing the three objectives, the follower performs single-objective optimization in steps and feeds the leader back with the objective values as they appear prior to weighing. Micro-Genetic Algorithm (follower) chromosome consists of the distribution of machining slice thickness, while the typical Genetic Algorithm (leader) consists of the milling parameters. The methodology is tested on sculptured surface parts with different properties, and a representative case is presented here.     

A memetic particle swarm optimisation algorithm for dynamic multi-modal optimisation problems

Many real-world optimisation problems are both dynamic and multi-modal, which require an optimisation algorithm not only to find as many optima under a specific environment as possible, but also to track their moving trajectory over dynamic environments. To address this requirement, this article investigates a memetic computing approach based on particle swarm optimisation for dynamic multi-modal optimisation problems (DMMOPs). Within the framework of the proposed algorithm, a new speciation method is employed to locate and track multiple peaks and an adaptive local search method is also hybridised to accelerate the exploitation of species generated by the speciation method. In addition, a memory-based re-initialisation scheme is introduced into the proposed algorithm in order to further enhance its performance in dynamic multi-modal environments. Based on the moving peaks benchmark problems, experiments are carried out to investigate the performance of the proposed algorithm in comparison with several state-of-the-art algorithms taken from the literature. The experimental results show the efficiency of the proposed algorithm for DMMOPs.     

Multi-criteria genetic optimisation of the manoeuvres of a two-stage launcher

The aim of this paper is to study the use of a genetic algorithm (GA) to optimise the ascent trajectory of a conventional two-stage launcher. The equations of motion of this system lack analytical solutions, and the number of adjustable parameters is large enough that the use of some non-traditional optimisation method becomes necessary. Two different missions are considered: first, to reach the highest possible stable, circular Low Earth Orbit (LEO); and second, to maximise the speed of a tangential escape trajectory. In this study, three variables are tuned and optimised by the GA in order to satisfy mission constraints while maximising the target function. The technical characteristics and limitations of the launcher are taken into account in the mission model, and a fixed payload weight is assumed. A variable mutation rate helps expand the search area whenever the population of solutions becomes uniform, and is shown to accelerate convergence of the GA in both cases. The obtained results are in agreement with technical specifications and solutions obtained in the past.     

A multi-population genetic algorithm for robust and fast ellipse detection

This paper discusses a novel and effective technique for extracting multiple ellipses from an image, using a genetic algorithm with multiple populations (MPGA). MPGA evolves a number of subpopulations in parallel, each of which is clustered around an actual or perceived ellipse in the target image. The technique uses both evolution and clustering to direct the search for ellipses—full or partial. MPGA is explained in detail, and compared with both the widely used randomized Hough transform (RHT) and the sharing genetic algorithm (SGA). In thorough and fair experimental tests, using both synthetic and real-world images, MPGA exhibits solid advantages over RHT and SGA in terms of accuracy of recognition—even in the presence of noise or/and multiple imperfect ellipses in an image—and speed of computation.     

CAD-based shape optimisation using adjoint sensitivities

Existing approaches to CAD-based design optimisation using adjoint sensitivities are reviewed and their shortcomings are recalled. An alternative approach is presented which uses the control points of the boundary representation (BRep) as design parameters. The sensitivity of the objective function with respect to the design variables is calculated using automatic differentiation (AD). Results for a 2-D aerofoil are presented.     

Floor shape optimization for green building design

Shape is an important consideration in green building design due to its significant impact on energy performance and construction costs. This paper presents a methodology to optimize building shapes in plan using the genetic algorithm. The building footprint is represented by a multi-sided polygon. Different geometrical representations for a polygon are considered and evaluated in terms of their potential problems such as epistasis, which occurs when one gene pair masks or modifies the expression of other gene pairs, and encoding isomorphism, which occurs when chromosomes with different binary strings map to the same solution in the design space. Two alternative representations are compared in terms of their impact on computational effectiveness and efficiency. An optimization model is established considering the shape-related variables and several other envelope-related design variables such as window ratios and overhangs. Life-cycle cost and life-cycle environmental impact are the two objective functions used to evaluate the performance of a green building design. A case study is presented where the shape of a typical floor of an office building defined by a pentagon is optimized with a multi-objective genetic algorithm.     

A genetic algorithm calibration method based on convergence due to genetic drift

The selection of Genetic Algorithm (GA) parameters is a difficult problem, and if not addressed adequately, solutions of good quality are unlikely to be found. A number of approaches have been developed to assist in the calibration of GAs, however there does not exist an accepted method to determine the parameter values. In this paper, a GA calibration methodology is proposed based on the convergence of the population due to genetic drift, to allow suitable GA parameter values to be determined without requiring a trial-and-error approach. The proposed GA calibration method is compared to another GA calibration method, as well as typical parameter values, and is found to regularly lead the GA to better solutions, on a wide range of test functions. The simplicity and general applicability of the proposed approach allows suitable GA parameter values to be estimated for a wide range of situations.     

Testing control software using a genetic algorithm

Complex software is difficult to test. When that software has been developed by a third party in response to a requirements specification and is to be used in an electronic control unit in the automotive, aerospace or marine industries, this testing process can be even more difficult, but is an essential task. However, testing all possible combinations of inputs to software can be time-consuming, tedious and may be intractable. This paper presents a genetic algorithm (GA) designed to search for significant input and output combinations to a software control system. By “significant” is meant those which produce an output (or result) which is not in line with the original specification. It is intended that such a tool should be used to support the human tester by focusing their attention on areas of concern which they can investigate further.     

A hybrid approach for multi-objective combinatorial optimisation problems in ship design and shipping

Numerous real-world problems relating to ship design and shipping are characterised by combinatorially explosive alternatives as well as multiple conflicting objectives and are denoted as multi-objective combinatorial optimisation (MOCO) problems. The main problem is that the solution space is very large and therefore the set of feasible solutions cannot be enumerated one by one. Current approaches to solve these problems are multi-objective metaheuristics techniques, which fall in two categories: population-based search and trajectory-based search. This paper gives an overall view for the MOCO problems in ship design and shipping where considerable emphasis is put on evolutionary computation and the evaluation of trade-off solutions. A two-stage hybrid approach is proposed for solving a particular MOCO problem in ship design, subdivision arrangement of a ROPAX vessel. In the first stage, a multi-objective genetic algorithm method is employed to approximate the set of pareto-optimal solutions through an evolutionary optimisation process. In the subsequent stage, a higher-level decision-making approach is adopted to rank these solutions from best to worst and to determine the best solution in a deterministic environment with a single decision maker.     

A genetic algorithm for railway scheduling with environmental considerations

A genetic algorithm is a randomized optimization technique that draws its inspiration from the biological sciences. Specifically, it uses the idea that genetics determines the evolution of any species in the natural world. Integer strings are used to encode an optimization problem and these strings are subject to combinatorial operations called reproduction, crossover and mutation, which improve these strings and cause them to ‘evolve’ to an optimal or nearly optimal solution. In this paper, the general machinations of genetic algorithms are described and a performance-enhanced algorithm is proposed for solving the important practical problem of railway scheduling. The problem under consideration involves moving a number of trains carrying mineral deposits across a long haul railway line with both single and double tracks in either direction. Collisions can only be avoided in sections of the line with double tracks. Constraints reflecting practical requirements to reduce environmental impacts from mineral transport, such as avoidance of loaded trains traversing populated areas during certain time slots, have to be satisfied. This is an NP-hard problem, which usually requires enumerative, as opposed to constructive, algorithms. For this reason, an ‘educated’ random search procedure like the genetic algorithm is an alternative and effective technique. The genetic algorithm is given difficult test problems to solve and the algorithm was able to generate feasible solutions in all cases.     

A modified genetic algorithm for distributed scheduling problems

Genetic algorithms (GAs) have been widely applied to the scheduling and sequencing problems due to its applicability to different domains and the capability in obtaining near-optimal results. Many investigated GAs are mainly concentrated on the traditional single factory or single job-shop scheduling problems. However, with the increasing popularity of distributed, or globalized production, the previously used GAs are required to be further explored in order to deal with the newly emerged distributed scheduling problems. In this paper, a modified GA is presented, which is capable of solving traditional scheduling problems as well as distributed scheduling problems. Various scheduling objectives can be achieved including minimizing makespan, cost and weighted multiple criteria. The proposed algorithm has been evaluated with satisfactory results through several classical scheduling benchmarks. Furthermore, the capability of the modified GA was also tested for handling the distributed scheduling problems.     

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.