Abstract: Trucks are the most popular transport equipment in most mega-terminals, and scheduling them to minimize makespan is a challenge that this article addresses and attempts to resolve. Specifically, the problem of scheduling a fleet of trucks to perform a set of transportation jobs with sequence-dependent processing times and different ready times is investigated, and the use of a genetic algorithm (GA) to address the scheduling problem is proposed. The scheduling problem is formulated as a mixed integer program. It is noted that the scheduling problem is NP-hard and the computational effort required to solve even small-scale test problems is prohibitively large. A crossover scheme has been developed for the proposed GA. Computational experiments are carried out to compare the performance of the proposed GA with that of GAs using six popular crossover schemes. Computational results show that the proposed GA performs best, with its solutions on average 4.05% better than the best solutions found by the other si...

Abstract: Innovative prevention, adaptation, and mitigation approaches as well as policies for sustainable flood management continue to be challenges faced by decision-makers. In this study, a mixed interval–fuzzy two-stage integer programming (IFTIP) method is developed for flood-diversion planning under uncertainty. This method improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within the optimization framework. In its modelling formulation, economic penalties as corrective measures against any infeasibilities arising because of a particular realization of the uncertainties are taken into account. The method can also be used for analysing a variety of policy scenarios that are associated with different levels of economic penalties. A management problem in terms of flood control is studied to illustrate the applicability of the proposed approach. The results...

Abstract: This article presents the application of the genetic algorithm to the optimum detailed design of reinforced concrete frames based on Indian Standard specifications. The objective function is the total cost of the frame which includes the cost of concrete, formwork and reinforcing steel for individual members of the frame. In order for the optimum design to be directly constructible without any further modifications, aspects such as available standard reinforcement bar diameters, spacing requirements of reinforcing bars, modular sizes of members, architectural requirements on member sizes and other practical requirements in addition to relevant codal provisions are incorporated into the optimum design model. The produced optimum design satisfies the strength, serviceability, ductility, durability and other constraints related to good design and detailing practice. The detailing of reinforcements in the beam members is carried out as a sub-level optimization problem. This strategy helps to reduce the size o...

Abstract: It has been over ten years since the pioneering work of particle swarm optimization (PSO) espoused by Kennedy and Eberhart. Since then, various modifications, well suited to particular application areas, have been reported widely in the literature. The evolutionary concept of PSO is clear-cut in nature, easy to implement in practice, and computationally efficient in comparison to other evolutionary algorithms. The above-mentioned merits are primarily the motivation of this article to investigate PSO when applied to continuous optimization problems. The performance of conventional PSO on the solution quality and convergence speed deteriorates when the function to be optimized is multimodal or with a large problem size. Toward that end, it is of great practical value to develop a modified particle swarm optimizer suitable for solving high-dimensional, multimodal optimization problems. In the first part of the article, the design of experiments (DOE) has been conducted comprehensively to examine the influenc...

Abstract: The optimal design problem of a water distribution system is to find the water distribution system component characteristics (e.g. pipe diameters, pump heads and maximum power, reservoir storage volumes, etc.) which minimize the system's capital and operational costs such that the system hydraulic laws are maintained (i.e. Kirchhoff's first and second laws), and constraints on quantities and pressures at the consumer nodes are fulfilled. In this study, an adaptive stochastic algorithm for water distribution systems optimal design based on the heuristic cross-entropy method for combinatorial optimization is presented. The algorithm is demonstrated using two well-known benchmark examples from the water distribution systems research literature for single loading gravitational systems, and an example of multiple loadings, pumping, and storage. The results show the cross-entropy dominance over previously published methods.

Abstract: This article presents and demonstrates a simple, straightforward genetic algorithm (GA) scheme for contamination source identification to enhance the security of water distribution systems. Related previous work on this subject has concentrated on developing analytical water quality inverse models with two major restrictions: the ability to disclose unique solutions and to handle water distribution systems of large size. These two limitations are addressed in this study by coupling a GA with EPANET. The objective function is minimization of the least-squares of the differences between simulated and measured contaminant concentrations, with the decision variables being the contaminant event characteristics of intrusion location, starting time, duration and mass rate. The developed methodology is demonstrated through base runs and sensitivity analysis of three water distribution system example applications of increasing complexity.

Abstract: Optimal storm sewer design aims at minimizing capital investment on infrastructure whilst ensuring good system performance under specified design criteria. An innovative sewer design approach based on cellular automata (CA) principles is introduced in this paper. Cellular automata have been applied as computational simulation devices in various scientific fields. However, some recent research has indicated that CA can also be a viable and efficient optimization engine. This engine is heuristic and largely relies on the key properties of CA: locality, homogeneity, and parallelism. In the proposed approach, the CA-based optimizer is combined with a sewer hydraulic simulator, the EPA Storm Water Management Model (SWMM). At each optimization step, according to a set of transition rules, the optimizer updates all decision variables simultaneously based on the hydraulic situation within each neighbourhood. Two sewer networks (one small artificial network and one large real network) have been tested in this stud...

Abstract: This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, s...

Abstract: 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 ...

Abstract: Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management where diversified customers' demands exist. In this article, three major goals are considered: (i) total utility work, (ii) total production rate variation and (iii) total setup cost. Due to the complexity of the problem, a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) is devised to obtain the locally Pareto-optimal frontier where simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed algorithm in terms of solution quality and diversity level, the algorithm is applied to various test problems and its reliability, based on different comparison metrics, is compared with three prominent multi-objective genetic algorithms, PS-NC GA, NSGA-II and SPEA-II. The computational results show that the proposed hybrid algorithm significantly outperforms existing genetic algorithm...

Abstract: This article proposes a hybrid optimization algorithm, which combines evolutionary algorithms (EA) and the gradient search technique, for optimization with continuous parameters. Inheriting the advantages of the two approaches, the new method is fast and capable of global search. The main structure of the new method is similar to that of EA except that a special individual called the gradient individual is introduced and EA individuals are located symmetrically. The gradient individual is propagated through generations by means of the quasi-Newton method. Gradient information required for the quasi-Newton method is calculated from the costs of EA individuals produced by the evolution strategies (ES). The symmetric placement of the individuals with respect to the best individual is for calculating the gradient vector by the central difference method. For the estimation of the inverse Hessian matrix, symmetric Rank-1 update shows better performance than BFGS and DFP. Numerical tests on various benchmark pro...

Abstract: The species conservation technique described here, in which the population of a genetic algorithm is divided into several groups according to their similarity, is inspired by ecology. Each group with similar characteristics is called a species and is centred on a dominating individual, called the species seed. A genetic algorithm based on this species conservation technique, called the species-conserving genetic algorithm (SCGA), was established and has been proved to be effective in finding multiple solutions of multimodal optimization problems. In this article, the SCGA is used to solve engineering design optimization problems. Different distance measures (measures of similarity) are investigated to analyse the performance of the SCGA. It is shown that the Euclidean distance is not the only possible basis for defining a species and sometimes may not make sense in engineering applications. Two structural design problems are used to demonstrate how the choice of a meaningful measure of similarity will hel...

Abstract: This study aims to determine optimal locations of dual trailing-edge flaps to achieve minimum hub vibration levels in a helicopter, while incurring low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithm to determine the flap time history for vibration minimization. The reduced hub vibration levels and required flap control power (due to flap motion) are the two objectives considered in this study and the flap locations along the blade are the design variables. It is found that second order polynomial response surfaces based on the central composite design of the theory of design of experiments describe both objectives adequately. Numerical studies for a four-bladed hingeless rotor show that both objectives are more sensitive to outboard flap location compared to the inboard flap location by an order of magnitude. Optimization results show a disjoint Pareto surface between...

Abstract: 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...

Abstract: 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.

Abstract: Design for manufacturing is often difficult for mechanical parts, since significant manufacturing knowledge is required to adjust part designs for manufacturability. The traditional trial-and-error approach usually leads to expensive iterations and compromises the quality of the final design. The authors believe the appropriate way to handle product design for manufacturing problems is not to formulate a large design problem that exhaustively incorporates design and manufacturing issues, but to separate the design and manufacturing activities and provide support for collaboration between engineering teams. In this article, the Collaborative Multidisciplinary Decision-making Methodology is used to solve a product design and manufacturing problem. First, the compromise Decision Support Problem is used as a mathematical model of each engineering teams’ design decisions and as a medium for information exchange. Second, game-theoretic principles are employed to resolve couplings or interactions between the tea...

Abstract: Variable-complexity methods are applied to aerodynamic shape design problems with the objective of reducing the total computational cost of the optimization process. Two main strategies are employed: the use of different levels of fidelity in the analysis models (variable fidelity) and the use of different sets of design variables (variable parameterization). Variable-fidelity methods with three different types of corrections are implemented and applied to a set of two-dimensional airfoil optimization problems that use computational fluid dynamics for the analysis. Variable parameterization is also used to solve the same problems. Both strategies are shown to reduce the computational cost of the optimization.

Abstract: In this study, a fuzzy multi-item economic order quantity (EOQ) problem is solved by employing four different fuzzy ranking methods. All of the parameters of the multi-item EOQ problem are defined as triangular fuzzy numbers. Fuzzy ranking methods are used to rank the fuzzy objective values and to handle the constraints in the model. The results obtained by employing different fuzzy ranking methods are also compared.

Abstract: Barrelled cylinders and domes of generalized elliptical profile are optimized for their buckling resistance when loaded by static external pressure. The optimum shells are found using either a static or adaptive tabu search method, which utilizes a repeat structural analysis tool. Results show that it is possible, through correct profiling of a meridian, to achieve failure pressures 40% and 20% higher than a benchmark cylinder and hemisphere, respectively. Numerical predictions are confirmed by pressurizing a series of laboratory-scale shells to destruction. Correlation between numerical predictions and experimental results is good.

Abstract: This article describes research relating to a user-centered evolutionary design system that evaluates both engineering and aesthetic aspects of design solutions during early-stage conceptual design. The experimental system comprises several components relating to user interaction, problem representation, evolutionary search and exploration and online learning. The main focus of the article is the evolutionary aspect of the system when using a single quantitative objective function plus subjective judgment of the user. Additionally, the manner in which the user-interaction aspect affects system output is assessed by comparing Pareto frontiers generated with and without user interaction via a multi-objective evolutionary algorithm (MOEA). A solution clustering component is also introduced and it is shown how this can improve the level of support to the designer when dealing with a complex design problem involving multiple objectives. Supporting results are from the application of the system to the design of...

Abstract: An application of evolutionary algorithms and the finite-element method to the topology optimization of 2D structures (plane stress, bending plates, and shells) and 3D structures is described. The basis of the topological evolutionary optimization is the direct control of the density material distribution (or thickness for 2D structures) by the evolutionary algorithm. The structures are optimized for stress, mass, and compliance criteria. The numerical examples demonstrate that this method is an effective technique for solving problems in computer-aided optimal design. †This is an extended and enhanced version of work presented at the mini−symposium on Evolutionary Algorithms: Recent Applications in Engineering and Science organized by Dr William Annicchiarico at the 7th World Congress on Computational Mechanics, Los Angeles, July 2006.

Abstract: Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization...

Abstract: Often in engineering systems, full-colour images have to be displayed on limited hardware, for example on mobile devices or embedded systems that can only handle a limited number of colours. Therefore an image is converted into an indexed map from where the indices point to specific colours in a fixed-size colour map generated for that image. The choice of an optimal colour map, or palette, is therefore crucial as it directly determines the quality of the resulting image. Typically, standard quantization algorithms are used to create colour maps. Whereas these algorithms employ domain specific knowledge, in this work a variant of simulated annealing (SA) was employed as a standard black-box optimization algorithm for colour map generation. The main advantage of black-box optimization algorithms is that they do not require any domain specific knowledge yet are able to provide a near optimal solution. The effectiveness of the approach is evaluated by comparing its performance with several specialized colour...

Abstract: Engineering optimization often deals with large, mixed-integer search spaces with a rigid structure due to the presence of a large number of constraints. Metaheuristics, such as evolutionary algorithms (EAs), are frequently suggested as solution algorithms in such cases. In order to exploit the full potential of these algorithms, it is important to choose an adequate representation of the search space and to integrate expert-knowledge into the stochastic search operators, without adding unnecessary bias to the search. Moreover, hybridisation with mathematical programming techniques such as mixed-integer programming (MIP) based on a problem decomposition can be considered for improving algorithmic performance. In order to design problem-specific EAs it is desirable to have a set of design guidelines that specify properties of search operators and representations. Recently, a set of guidelines has been proposed that gives rise to so-called Metric-based EAs (MBEAs). Extended by the minimal moves mutation the...

Abstract: The concept of the design space encapsulates the search for optimal design configurations of engineering systems. During this search, infeasible or unsafe regions may be encountered, representing particular combinations of parameter values which cause the system to fail. These regions need to be characterized so that they can be avoided during the search for improved designs. In addition, the proximity of a design to a feasible boundary may be related to the reliability and robustness of the design in the face of variation in manufacture and use. A chemical engineering example is used to show how feasible design regions can be modelled using integer lattices and kriging methods. An algorithm using Hilbert bases is developed and used to select points on the boundary of the feasible region with arbitrary closeness so that the properties of the kriging model are such that the model remains stable and the star-shaped necessary condition is met.

Abstract: Several evolutionary algorithms (EAs) applied to a wide class of communication network design problems modelled under the generalized Steiner problem (GSP) are evaluated. In order to provide a fault-tolerant design, a solution to this problem consists of a preset number of independent paths linking each pair of potentially communicating terminal nodes. This usually requires considering intermediate non-terminal nodes (Steiner nodes), which are used to ensure path redundancy, while trying to minimize the overall cost. The GSP is an NP-hard problem for which few algorithms have been proposed. This article presents a comparative study of pure and hybrid EAs applied to the GSP, codified over MALLBA, a general purpose library for combinatorial optimization. The algorithms were tested on several GSPs, and asset efficient numerical results are reported for both serial and distributed models of the evaluated algorithms.

Abstract: The emergence of metamodels as approximate objective function representations offers the ability to ‘design’ metamodels with favourable optimization characteristics without compromising the accurate representational capabilities of arbitrary function topologies and modalities. With non-uniform rational B-splines (NURBs) as a metamodel basis, favourable optimization properties can be obtained which allow the intelligent selection of starting points for multistart optimization algorithms and which constrain optimization searches to metamodel regions containing the global metamodel optimum. In this article NURBs-based metamodels are used to define an optimization algorithm (HyPerOp) which guarantees the discovery of the global metamodel optimum with known computational effort. Emphasis is placed on demonstrating how NURBs’ properties contribute to a favourable objective function approximation. Through a large non-linear optimization trial problem set, the claim that HyPerOp is guaranteed to find the global m...

Abstract: Accurate optimal design solutions for most engineering structures present considerable difficulties due to the complexity and multi-modality of the functional design space. The situation is made even more complex when potential manufacturing tolerances must be accounted for in the optimizing process. The present study provides an in-depth analysis of the problem, and then a technique for determining the optimal design of engineering structures, with manufacturing tolerances in the design variables accounted for, is proposed and demonstrated. The examples used to demonstrate the technique involve the design optimization of simple fibre-reinforced laminated composite structures. The technique is simple, easy to implement and, at the same time, very efficient. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus it is a worst-case scenario approach. In addition, the technique is non-probabilistic. A genetic algorithm with f...

Abstract: Systems of nonlinear equations often represent mathematical models in engineering design. This study proposes a novel method for finding all solutions of systems of nonlinear equations with free variables. The original problem is first transformed into a global optimization problem whose multiple global minima with a zero objective value correspond to all solutions of the original problem. Then, by using variable substitution on free variables and applying convexification strategies and piecewise linearization techniques on nonconvex functions, the transformed optimization problem is reformulated as a convex mixed-integer program solvable to reach an approximately global optimum. An algorithm is developed to find all solutions of the reformulated problem. Numerical examples in real applications are presented to demonstrate the usefulness of the proposed method in engineering design.