Explicit consideration of multiple objectives in cellular manufacturing

Although many methodologies have been proposed for solving the cell-formation problem, few of them explicitly consider the existence of multiple objectives in the design process. In this article, the development of multi-objective genetic programming single-linkage cluster analysis (GP-SLCA), an evolutionary methodology for the solution of the multi-objective cell-formation problem, is described. The proposed methodology combines an existing algorithm for the solution of single-objective cell-formation problems with NSGA-II, an elitist evolutionary multi-objective optimization technique. Multi-objective GP-SLCA is able to generate automatically a set of non-dominated solutions for a given multi-objective cell-formation problem. The benefits of the proposed approach are illustrated using an example test problem taken from the literature and an industrial case study.     

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.     

TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION

This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.     

Evolutionary topology optimization using the extended finite element method and isolines

This study presents a new algorithm for structural topological optimization of two-dimensional continuum structures by combining the extended finite element method (X-FEM) with an evolutionary optimization algorithm. Taking advantage of an isoline design approach for boundary representation in a fixed grid domain, X-FEM can be implemented to improve the accuracy of finite element solutions on the boundary during the optimization process. Although this approach does not use any remeshing or moving mesh algorithms, final topologies have smooth and clearly defined boundaries which need no further interpretation. Numerical comparisons of the converged solutions with standard bi-directional evolutionary structural optimization solutions show the efficiency of the proposed method, and comparison with the converged solutions using MSC NASTRAN confirms the high accuracy of this method.     

Multi-objective optimization of space station logistics strategies using physical programming

This study extends a previously proposed single-objective optimization formulation of space station logistics strategies to multi-objective optimization. The four-objective model seeks to maximize the mean utilization capacity index, total utilization capacity index, logistics robustness index and flight independency index, aiming to improve both the utilization benefit and the operational robustness of a space station operational scenario. Physical programming is employed to convert the four-objective optimization problem into a single-objective problem. A genetic algorithm is proposed to solve the resulting physical programming-based optimization problem. Moreover, the non-dominated sorting genetic algorithm-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the physical programming-based solution. The proposed approach is demonstrated with a notional one-year scenario of China's future space station. It is shown that the designer-preferred compromise solution improving both the utilization benefit and the operational robustness is successfully obtained.     

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.     

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 multi-objective approach for multi-material topology and shape optimization

An automated multi-material approach that integrates multi-objective Topology Optimization (TO) and multi-objective shape optimization is presented. A new ant colony optimization algorithm is presented and applied to solving the TO problem, estimating a trade-off set of initial topologies or distributions of material. The solutions found usually present irregular boundaries, which are not desirable in applications. Thus, shape parameterization of the internal boundaries of the design region, and subsequent shape optimization, is performed to improve the quality of the estimated Pareto-optimal solutions. The selection of solutions for shape optimization is done by using the PROMETHEE II decision-making method. The parameterization process involves identifying the boundaries of different materials and describing these boundaries by non-uniform rational B-spline curves. The proposed approach is applied to the optimization of a C-core magnetic actuator, with two objectives: the maximization of the attractive force on the armature and the minimization of the volume of permanent magnet material.     

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.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

An extension of the directed search domain algorithm to bilevel optimization

A method is developed for generating a well-distributed Pareto set for the upper level in bilevel multiobjective optimization. The approach is based on the Directed Search Domain (DSD) algorithm, which is a classical approach for generation of a quasi-evenly distributed Pareto set in multiobjective optimization. The approach contains a double-layer optimizer designed in a specific way under the framework of the DSD method. The double-layer optimizer is based on bilevel single-objective optimization and aims to find a unique optimal Pareto solution rather than generate the whole Pareto frontier on the lower level in order to improve the optimization efficiency. The proposed bilevel DSD approach is verified on several test cases, and a relevant comparison against another classical approach is made. It is shown that the approach can generate a quasi-evenly distributed Pareto set for the upper level with relatively low time consumption.     

Optimal feeding profile in fed-batch bioreactors using a genetic algorithm

An optimal feeding profile for a fed-batch process was designed based on an evolutionary algorithm. Usually the presence of multiple objectives in a problem leads to a set of optimal solutions, commonly known as Pareto-optimal solutions. Evolutionary algorithms are well suited for deriving multi-objective optimisation since they evolve a set of non-dominated solutions distributed along the Pareto front. Several evolutionary multi-objective optimisation algorithms have been developed, among which the Non-dominated Sorting Genetic Algorithm NSGA-II is recognised to be very effective in overcoming a variety of problems. To demonstrate the applicability of this technique, an optimal control problem from the literature was solved using several methods considering the single-objective dynamic optimisation problem.     

A MODIFIED DEMPSTER-SHAFER THEORY FOR MULTICRITERIA OPTIMIZATION

Abstract

A new methodology, based on a modified Dempster-Shafer (DS) theory, is proposed for solving multicriteria design optimization problems. It is well known that considerable amount of computational information is acquired during the iterative process of optimization. Based on the computational information generated in each iteration, an evidence-based approach is presented for solving a multiobjective optimization problem. The method handles the multiple design criteria, which are often conflicting and non-commensurable, by constructing belief structures that can quantitatively evaluate the effectiveness of each design in the range 0 to 1. An overall satisfaction function is then defined for converting the original multicriteria design problem into a single-criterion problem so that standard single-objective programming techniques can be employed for the solution. The design of a mechanism in the presence of seven design criteria and eighteen design variables is considered to illustrate the computational details of the approach. This work represents the first attempt made in the literature at applying DS theory for numerical engineering optimization.     

Control parameter tuning for aircraft crosswind landing via multi-solution particle swarm optimization

Crosswind landing is one of the most complex and challenging landing manoeuvres; an aircraft can drift laterally or could even be blown off the runway under extreme crosswind conditions. This article proposes an improved multi-group swarm-based optimization method that can not only optimize the parameters of the lateral flight control system, but also find diversity solutions of the underlying optimization problem. During the optimizing process, several swarm groups are generated to search potential areas for the optimal solution. These groups exchange information with each other during the searching process and focus on their different but continuous spaces. Finally, a diverse range of solutions is presented to the engineer for the flight control system design. A nonlinear 6 degrees-of-freedom rigid model of a Boeing 747 is used as a test bed to verify the robustness and feasibility of the proposed method.     

Handling constraints using multiobjective optimization concepts

In this paper, we propose a new constraint‐handling technique for evolutionary algorithms which we call inverted‐shrinkable PAES (IS‐PAES). This approach combines the use of multiobjective optimization concepts with a mechanism that focuses the search effort onto specific areas of the feasible region by shrinking the constrained search space. IS‐PAES also uses an adaptive grid to store the solutions found, but has a more efficient memory‐management scheme than its ancestor (the Pareto archived evolution strategy for multiobjective optimization). The proposed approach is validated using several examples taken from the standard evolutionary and engineering optimization literature. Comparisons are provided with respect to the stochastic ranking method (one of the most competitive constraint‐handling approaches used with evolutionary algorithms currently available) and with respect to other four multiobjective‐based constraint‐handling techniques. Copyright© 2004 John Wiley & Sons, Ltd.     

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.     

A Hopfield Neural Network Approach to the Dual Response Problem

The application of neural networks to optimization problems has been an active research area since the early 1980s. Unconstrained optimization, constrained optimization and combinatorial optimization problems have been solved using neural networks. This study presents a new approach using Hopfield neural networks (HNNs) for solving the dual response system (DRS) problems. The major aim of the proposed method is to produce a string of solutions, rather than a ‘one‐shot’ optimum solution, to make the trade‐offs available between the mean and standard deviation responses. This gives more flexibility to the decision‐maker in exploring alternative solutions. The proposed method has been tested on two examples. The HNN results are very close to those obtained by using the NIMBUS (Nondifferentiable Interactive Multiobjective Bundle‐based Optimization System) algorithm. Choosing an appropriate solution method for a certain multi‐objective optimization problem is not easy, as has been made abundantly clear. Unlike the NIMBUS method, the HNN approach does not set any specific assumptions on the behaviour or the preference structure of the decision maker. As a result, the proposed method will still work and generate alternative solutions whether or not the decision maker has enough time and capabilities for co‐operation. Copyright © 2005 John Wiley & Sons, Ltd.     

Solving initial and boundary value problems using learning automata particle swarm optimization

In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method.     

An orthogonal design based constrained evolutionary optimization algorithm

Solving constrained optimization problems (COPs) via evolutionary algorithms (EAs) has attracted much attention. In this article, an orthogonal design based constrained optimization evolutionary algorithm (ODCOEA) to tackle COPs is proposed. In principle, ODCOEA belongs to a class of steady state evolutionary algorithms. In the evolutionary process, several individuals are chosen from the population as parents and orthogonal design is applied to pairs of parents to produce a set of representative offspring. Then, after combining the offspring generated by different pairs of parents, non-dominated individuals are chosen. Subsequently, from the parent’s perspective, it is decided whether a non-dominated individual replaces a selected parent. Finally, ODCOEA incorporates an improved BGA mutation operator to facilitate the diversity of the population. The proposed ODCOEA is effectively applied to 12 benchmark test functions. The computational experiments show that ODCOEA not only quickly converges to optimal or near-optimal solutions, but also displays a very high performance compared with another two state-of-the-art techniques.