Evolving knowledge for the solution of clustering problems in cellular manufacturing

Hierarchical clustering has been widely used for the solution of problems in the area of cellular manufacturing. Hierarchical clustering procedures utilize coefficients that quantify the level of similarity between pairs of machines or parts in the plant. An evolutionary methodology is proposed for the construction of new similarity coefficients that can be used by standard hierarchical clustering methodologies for the solution of cell-formation problems. A typical application is presented for the simplest case of the cell-formation problem. However, alternative similarity coefficients can be evolved for advanced formulations of the problem by suitably modifying the set of fitness cases that constitute the environment of the evolutionary process.     

Customized evolutionary optimization procedure for generating minimum weight compliant mechanisms

In this article, a customized evolutionary optimization procedure is developed for generating minimum weight compliant mechanisms. A previously-suggested concept of multi-objectivization in which a helper objective is introduced in addition to the primary objective of the original single-objective optimization problem (SOOP) is used here. The helper objective is chosen in a way such that it is in conflict with the primary objective, thereby causing an evolutionary multi-objective optimization algorithm to maintain diversity in its population from one generation to another. The elitist non-dominated sorting genetic algorithm (NSGA-II) is customized with a domain-specific initialization strategy, a domain-specific crossover operator, and a domain-specific solution repairing strategy. To make the search process computationally tractable, the proposed methodology is made suitable for parallel computing. A local search methodology is applied on the evolved non-dominated solutions found by the above-mentioned modified NSGA-II to refine the solutions further. Two case studies for tracing curvilinear and straight-line paths are performed. Results demonstrate that solutions having smaller weight than the reference design solution obtained by SOOP are found by the proposed procedure. Interesting facts and observations brought out by the study are also narrated and conclusions of the study are made.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

Sequential interactive evolution for finding high-quality topologies

Finding a diverse set of high-quality (HQ) topologies for a single-objective optimization problem using an evolutionary computation algorithm can be difficult without a reliable measure that adequately describes the dissimilarity between competing topologies. In this article, a new approach for enhancing diversity among HQ topologies for engineering design applications is proposed. The technique initially selects one HQ solution and then searches for alternative HQ solutions by performing an optimization of the original objective and its dissimilarity with respect to the previously found solution. The proposed multi-objective optimization approach interactively amalgamates user articulated preferences with an evolutionary search so as sequentially to produce a set of diverse HQ solutions to a single-objective problem. For enhancing diversity, a new measure is suggested and an approach to reducing its computational time is studied and implemented. To illustrate the technique, a series of studies involving different topologies represented as bitmaps is presented.     

An entropy-based three-stage approach for multi-objective system reliability optimization considering uncertainty

This article presents a three-stage approach for solving multi-objective system reliability optimization problems considering uncertainty. The reliability of each component is considered in the formulation as a component reliability estimate in the form of an interval value and discrete values. Component reliability may vary owing to variations in the usage scenarios. Uncertainty is described by defining a set of usage scenarios. To address this problem, an entropy-based approach to the redundancy allocation problem is proposed in this study to identify the deterministic reliability of each component. In the second stage, a multi-objective evolutionary algorithm (MOEA) is applied to produce a Pareto-optimal solution set. A hybrid algorithm based on k-means and silhouettes is performed to select representative solutions in the third stage. Finally, a numerical example is presented to illustrate the performance of the proposed approach.     

Design of cellular manufacturing system with quasi-dynamic dual resource using multi-objective GA

A new concept is presented in this paper of quasi-dynamic cell formation for the design of a cellular manufacturing system, based on analysing the fact that static and dynamic cell formation could not reflect the real situation of a modern cellular manufacturing system. Further, workforce resources are integrated into quasi-dynamic cell formation and thus a quasi-dynamic dual-resource cell-formation problem is proposed. For solving this problem, this paper first establishes a non-linear mixed integer programming model, where inter-cell and intra-cell material cost, machine relocation cost, worker operation time, loss in batch quality and worker salary are to be minimised. Then, a multi-objective GA is developed to solve this model. Finally, a real life case study is conducted to validate the proposed model and algorithm. The actual operation results show that the case enterprise significantly decreases its material handling cost and workforce number and obviously increases its product quality after carrying out the obtained scheme.     

Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.     

A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front.     

A similarity coefficient measure and machine-parts grouping in cellular manufacturing systems

For more than three decades, similarity coefficient measures one of the important tools for solving group technology problems have gained the attention of the research community in cellular manufacturing systems. A new similarity coefficient measure that uses a set of important characteristic properties for grouping is developed here for use as an intermediate tool to form cohesive cells. A mathematical model that uses this similarity coefficient for optimally solving the cell-formation problems in cellular manufacturing is developed. A heuristic procedure that improves the optimal methodology in term of solution capability of the large instances is devised for an efficient solution. Both the optimal methodology and the heuristic are applied to some well-known problems from literature to compare the grouping efficiencies. The similarity coefficient and the solution methodologies developed are able to solve the cell formation problems efficiently.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Pareto layer: Its formulation and search by way of evolutionary multi-objective optimization

This article examines multi-objective problems where a solution (product) is related to a cluster of performance vectors within a multi-objective space. Here the origin of such a cluster is not uncertainty, as is typical, but rather the range of performances attainable by the product. It is shown that, in such cases, comparison of a solution to other solutions should be based on its best performance vectors, which are extracted from the cluster. The result of solving the introduced problem is a set of Pareto optimal solutions and their representation in the objective space, which is referred to here as the Pareto layer. The authors claim that the introduced Pareto layer is a previously unattended novel representation. In order to search for these optimal solutions, an evolutionary multi-objective algorithm is suggested. The article also treats the selection of a solution from the obtained optimal set.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

A methodology for the strategic design of reverse logistics networks and its application in the Turkish white goods industry

In this study, a multi-objective model for the reverse logistics network design (RLND) problem and a novel methodology are proposed. The proposed methodology is comprised of two stages: the centralised return centre (CRC) evaluation stage and the reverse logistics network design (RLND) stage. In the first stage an integrated ANP and fuzzy-TOPSIS methodology is utilised. In the second stage, using the CRC weights obtained in the first stage, the RLND model is solved via genetic algorithms (GAs). The proposed methodology is applied to a case from the Turkish white goods industry. The results are discussed and analysed.     

A cross-disciplinary technology transfer for search-based evolutionary computing: from engineering design to software engineering design

Although object-oriented conceptual software design is difficult to learn and perform, computational tool support for the conceptual software designer is limited. In conceptual engineering design, however, computational tools exploiting interactive evolutionary computation (EC) have shown significant utility. This article investigates the cross-disciplinary technology transfer of search-based EC from engineering design to software engineering design in an attempt to provide support for the conceptual software designer. Firstly, genetic operators inspired by genetic algorithms (GAs) and evolutionary programming are evaluated for their effectiveness against a conceptual software design representation using structural cohesion as an objective fitness function. Building on this evaluation, a multi-objective GA inspired by a non-dominated Pareto sorting approach is investigated for an industrial-scale conceptual design problem. Results obtained reveal a mass of interesting and useful conceptual software design solution variants of equivalent optimality—a typical characteristic of successful multi-objective evolutionary search techniques employed in conceptual engineering design. The mass of software design solution variants produced suggests that transferring search-based technology across disciplines has significant potential to provide computationally intelligent tool support for the conceptual software designer.     

A surrogate assisted parallel multiobjective evolutionary algorithm for robust engineering design

A number of multi-objective evolutionary algorithms have been proposed in recent years and many of them have been used to solve engineering design optimization problems. However, designs need to be robust for real-life implementation, i.e. performance should not degrade substantially under expected variations in the variable values or operating conditions. Solutions of constrained robust design optimization problems should not be too close to the constraint boundaries so that they remain feasible under expected variations. A robust design optimization problem is far more computationally expensive than a design optimization problem as neighbourhood assessments of every solution are required to compute the performance variance and to ensure neighbourhood feasibility. A framework for robust design optimization using a surrogate model for neighbourhood assessments is introduced in this article. The robust design optimization problem is modelled as a multi-objective optimization problem with the aim of simultaneously maximizing performance and minimizing performance variance. A modified constraint-handling scheme is implemented to deal with neighbourhood feasibility. A radial basis function (RBF) network is used as a surrogate model and the accuracy of this model is maintained via periodic retraining. In addition to using surrogates to reduce computational time, the algorithm has been implemented on multiple processors using a master–slave topology. The preliminary results of two constrained robust design optimization problems indicate that substantial savings in the actual number of function evaluations are possible while maintaining an acceptable level of solution quality.     

Bi-objective partial flexible job shop scheduling problem: NSGA-II,NRGA, MOGA and PAES approaches

This paper deals with a problem of partial flexible job shop with the objective of minimising makespan and minimising total operation costs. This problem is a kind of flexible job shop problem that is known to be NP-hard. Hence four multi-objective, Pareto-based, meta-heuristic optimisation methods, namely non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) and Pareto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal Pareto front. A new solution representation is introduced with the aim of solving the addressed problem. For the purpose of performance evaluation of our proposed algorithms, we generate some instances and use some benchmarks which have been applied in the literature. Also a comprehensive computational and statistical analysis is conducted in order to analyse the performance of the applied algorithms in five metrics including non-dominated solution, diversification, mean ideal distance, quality metric and data envelopment analysis are presented. Data envelopment analysis is a well-known method for efficiently evaluating the effectiveness of multi-criteria decision making. In this study we proposed this method of assessment of the non-dominated solutions. The results indicate that in general NRGA and PAES have had a better performance in comparison with the other two algorithms.     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.     

MONSS: A multi-objective nonlinear simplex search approach

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.