Applying tabu search and simulated annealing to the optimal design of sewer networks

Optimizations of sewer network designs create complicated and highly nonlinear problems wherein conventional optimization techniques often get easily bogged down in local optima and cannot successfully address such problems. In the past decades, heuristic algorithms possessing robust and efficient global search capabilities have helped to solve continuous and discrete optimization problems and have demonstrated considerable promise. This study applied tabu search (TS) and simulated annealing (SA) to the optimization of sewer network designs. For a case study, this article used the sewer network design of a central Taiwan township, which contains significantly varied elevations, and the optimal designs from TS and SA were compared with the original official design. The results show that, in contrast with the original design's failure to satisfy the minimum flow-velocity requirements, both TS and SA achieved least-cost solutions that also fulfilled all the constraints of the design criteria. According to the average performance of 200 trials, SA outperformed TS in both robustness and efficiency for solving sewer network optimization problems.     

HYBRID MULTIMODAL OPTIMIZATION WITH CLUSTERING GENETIC STRATEGIES

Abstract

Two-stage hybrid multimodal optimization approaches that combine cluster identification techniques in genetic algorithms with sharing and gradient-based local search methods are proposed. The multimodal optimization comprises the use of a sharing function implementation in genetic searches to pursue multiple local optima and subsequent executions of local searches to locate each local optimum when an extreme-containing region is identified. A new cluster identification technique is proposed for automatic and adaptive identification of the locations and sizes of design clusters in genetic algorithms with sharing. The first stage of the hybrid multimodal optimization is to use sharing-enhanced genetic algorithms for the identification of the near-optimum designs inside extreme-containing regions. The second stage simply involves consecutive employment of efficient gradient-based local searches by using the near-optimum designs as initial designs. Two strategies defining the coupling of the genetic search and local searches are proposed. The proposed hybrid optimization strategies are tested in a number of illustrative multimodal optimization problems.     

Creating targeted initial populations for genetic product searches in heterogeneous markets

Genetic searches often use randomly generated initial populations to maximize diversity and enable a thorough sampling of the design space. While many of these initial configurations perform poorly, the trade-off between population diversity and solution quality is typically acceptable for small-scale problems. Navigating complex design spaces, however, often requires computationally intelligent approaches that improve solution quality. This article draws on research advances in market-based product design and heuristic optimization to strategically construct ‘targeted’ initial populations. Targeted initial designs are created using respondent-level part-worths estimated from discrete choice models. These designs are then integrated into a traditional genetic search. Two case study problems of differing complexity are presented to illustrate the benefits of this approach. In both problems, targeted populations lead to computational savings and product configurations with improved market share of preferences. Future research efforts to tailor this approach and extend it towards multiple objectives are also discussed.     

Scatter search heuristic for least-cost design of water distribution networks

The optimization problems of water distribution networks are complex, multi-modal and discrete-variable problems that cannot be easily solved with conventional optimization algorithms. Heuristic algorithms such as genetic algorithms, simulated annealing, tabu search and ant colony optimization have been extensively employed over the last decade. This article proposed an optimization procedure based on the scatter search (SS) framework, which is also a heuristic algorithm, to obtain the least-cost designs of three well-known looped water distribution networks (two-loop, Hanoi and New York networks). The computational results obtained with the three benchmark instances indicate that SS is able to find solutions comparable to those provided by some of the most competitive algorithms published in the literature.     

An optimization technique using the characteristics of genetic algorithm

Optimization problems could happen often in discrete or discontinuous search space. Therefore, the traditional gradient‐based methods are not able to apply to this kind of problems. The discrete design variables are considered reasonably and the heuristic techniques are generally adopted to solve this problem, and the genetic algorithm based on stochastic search technique is one of these. The genetic algorithm method with discrete variables can be applied to structural optimization problems, such as composite laminated structures or trusses. However, the discrete optimization adopted in genetic algorithm gives rise to a troublesome task that is a mapping between each strings and discrete variables. And also, its solution quality could be restricted in some cases. In this study, a technique using the genetic algorithm characteristics is developed to utilize continuous design variables instead of discrete design variables in discontinuous solution spaces. Additionally, the proposed algorithm, which is manipulating a fitness function artificially, is applied to example problems and its results are compared with the general discrete genetic algorithm. The example problems are to optimize support positions of an unstable structure with discontinuous solution spaces.     

Fuzzy computer-aided design of process manufacturing facilities

Preliminary design of process manufacturing facilities involves, among other things, the synthesis of detailed layout designs. In current practice, this spatial design process is very labor-intensive and expensive. This paper describes a prototype CAD system which models design decision-making, providing a computable framework for automation. The CAD system performs auto-elicitation of an expert's judgment in the form of fuzzy sets using interactive computer graphics. These fuzzy sets are then used in a heuristic search process employing multi-objective, non-linear optimization. Designs synthesized by this fuzzy CAD system are comparable to those generated by hand, and in some cases exceed a practitioner's design in quality. The CAD system, as presently constructed, provides multiple solutions. Conclusions and recommendations regarding processing speed and unrepresented heuristic content are made.     

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.     

Bayesian design of experiments for generalized linear models and dimensional analysis with industrial and scientific application

ABSTRACT

The design of an experiment can always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables and measured responses. Bayesian methods allow uncertainty in these decisions to be incorporated into design selection through prior distributions that encapsulate information available from scientific knowledge or previous experimentation. Further, a design may be explicitly tailored to the aim of the experiment through a decision-theoretic approach using an appropriate loss function. We review the area of decision-theoretic Bayesian design, with particular emphasis on recent advances in computational methods. For many problems arising in industry and science, experiments result in a discrete response that is well described by a member of the class of generalized linear models. Bayesian design for such nonlinear models is often seen as impractical as the expected loss is analytically intractable and numerical approximations are usually computationally expensive. We describe how Gaussian process emulation, commonly used in computer experiments, can play an important role in facilitating Bayesian design for realistic problems. A main focus is the combination of Gaussian process regression to approximate the expected loss with cyclic descent (coordinate exchange) optimization algorithms to allow optimal designs to be found for previously infeasible problems. We also present the first optimal design results for statistical models formed from dimensional analysis, a methodology widely employed in the engineering and physical sciences to produce parsimonious and interpretable models. Using the famous paper helicopter experiment, we show the potential for the combination of Bayesian design, generalized linear models, and dimensional analysis to produce small but informative experiments.     

Optimal design of multi-response experiments using semi-definite programming

Optimal design of multi-response experiments for estimating the parameters of multi-response linear models is a challenging problem. The main drawback of the existing algorithms is that they require the solution of many optimization problems in the process of generating an optimal design that involve cumbersome manual operations. Furthermore, all the existing methods generate approximate design and no method for multi-response n-exact design has been cited in the literature. This paper presents a unified formulation for multi-response optimal design problem using Semi-Definite Programming (SDP) that can generate D-, A- and E-optimal designs. The proposed method alleviates the difficulties associated with the existing methods. It solves a one-shot optimization model whose solution selects the optimal design points among all possible points in the design space. We generate both approximate and n-exact designs for multi-response models by solving SDP models with integer variables. Another advantage of the proposed method lies in the amount of computation time taken to generate an optimal design for multi-response models. Several test problems have been solved using an existing interior-point based SDP solver. Numerical results show the potentials and efficiency of the proposed formulation as compared with those of other existing methods. The robustness of the generated designs with respect to the variance-covariance matrix is also investigated.     

Response surface optimization for a nonlinearly constrained irregular experimental design space

Finding optimum conditions for process factors in an engineering optimization problem with response surface functions requires structured data collection using experimental design. When the experimental design space is constrained owing to external factors, its design space may form an asymmetrical and irregular shape and thus standard experimental design methods become ineffective. Computer-generated optimal designs, such as D-optimal designs, provide alternatives. While several iterative exchange algorithms for D-optimal designs are available for a linearly constrained irregular design space, it has not been clearly understood how D-optimal design points need to be generated when the design space is nonlinearly constrained and how response surface models are optimized. This article proposes an algorithm for generating the D-optimal design points that satisfy both feasibility and optimality conditions by using piecewise linear functions on the design space. The D-optimality-based response surface design models are proposed and optimization procedures are then analysed.     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

Space-filling designs for computer experiments: A review

ABSTRACT

Improving the quality of a product/process using a computer simulator is a much less expensive option than the real physical testing. However, simulation using computationally intensive computer models can be time consuming and, therefore, directly doing the optimization on the computer simulator can be infeasible. Experimental design and statistical modeling techniques can be used to overcome this problem. This article reviews experimental designs known as space-filling designs that are suitable for computer simulations. In the article, a special emphasis is given for a recently developed space-filling design called maximum projection design. Its advantages are illustrated using a simulation conducted for optimizing a milling process.     

MISO: mixed-integer surrogate optimization framework

We introduce MISO, the mixed-integer surrogate optimization framework. MISO aims at solving computationally expensive black-box optimization problems with mixed-integer variables. This type of optimization problem is encountered in many applications for which time consuming simulation codes must be run in order to obtain an objective function value. Examples include optimal reliability design and structural optimization. A single objective function evaluation may take from several minutes to hours or even days. Thus, only very few objective function evaluations are allowable during the optimization. The development of algorithms for this type of optimization problems has, however, rarely been addressed in the literature. Because the objective function is black-box, derivatives are not available and numerically approximating the derivatives requires a prohibitively large number of function evaluations. Therefore, we use computationally cheap surrogate models to approximate the expensive objective function and to decide at which points in the variable domain the expensive objective function should be evaluated. We develop a general surrogate model framework and show how sampling strategies of well-known surrogate model algorithms for continuous optimization can be modified for mixed-integer variables. We introduce two new algorithms that combine different sampling strategies and local search to obtain high-accuracy solutions. We compare MISO in numerical experiments to a genetic algorithm, NOMAD version 3.6.2, and SO-MI. The results show that MISO is in general more efficient than NOMAD and the genetic algorithm with respect to finding improved solutions within a limited budget of allowable evaluations. The performance of MISO depends on the chosen sampling strategy. The MISO algorithm that combines a coordinate perturbation search with a target value strategy and a local search performs best among all algorithms.     

Coupling ant colony optimization and the extended great deluge algorithm for the discrete facility layout problem

This article uses a hybrid optimization approach to solve the discrete facility layout problem (FLP), modelled as a quadratic assignment problem (QAP). The idea of this approach design is inspired by the ant colony meta-heuristic optimization method, combined with the extended great deluge (EGD) local search technique. Comparative computational experiments are carried out on benchmarks taken from the QAP-library and from real life problems. The performance of the proposed algorithm is compared to construction and improvement heuristics such as H63, HC63-66, CRAFT and Bubble Search, as well as other existing meta-heuristics developed in the literature based on simulated annealing (SA), tabu search and genetic algorithms (GAs). This algorithm is compared also to other ant colony implementations for QAP. The experimental results show that the proposed ant colony optimization/extended great deluge (ACO/EGD) performs significantly better than the existing construction and improvement algorithms. The experimental results indicate also that the ACO/EGD heuristic methodology offers advantages over other algorithms based on meta-heuristics in terms of solution quality.     

Batch sequential design to achieve predictive maturity with calibrated computer models

Sequential experiment design strategies have been proposed for efficiently augmenting initial designs to solve many problems of interest to computer experimenters, including optimization, contour and threshold estimation, and global prediction. We focus on batch sequential design strategies for achieving maturity in global prediction of discrepancy inferred from computer model calibration. Predictive maturity focuses on adding field experiments to efficiently improve discrepancy inference. Several design criteria are extended to allow batch augmentation, including integrated and maximum mean square error, maximum entropy, and two expected improvement criteria. In addition, batch versions of maximin distance and weighted distance criteria are developed. Two batch optimization algorithms are considered: modified Fedorov exchange and a binning methodology motivated by optimizing augmented fractional factorial skeleton designs.     

An interdisciplinary course in engineering synthesis

The interdisciplinary courseSynthesis of Engineering Systems has been offered by the Engineering Design Research Center over the last 3 years. Students are exposed to two major paradigms for design synthesis: mathematical programming and knowledge-based expert systems. The former emphasizes the mathematical formulation of optimization problems that involve discrete and continuous variables for the selection of topologies and parameters in engineering systems. The latter emphasizes representations and search techniques for processing qualitative knowledge for synthesis of designs by heuristic classification and hierarchical decomposition.An integral part of the course is a term project in which the students apply both synthesis approaches to a design problem in their domain. The projects deal with different engineering problems, reflecting the disciplinary background of the students. The projects explore a number of different schemes for combining mathematical optimization and knowledge-based approaches. Some use knowledge-based techniques for preliminary screening or as critics of mathematical optimization, while others show a direct comparison between the two approaches. This paper summarizes the experience gained in the course, illustrates representative student projects, discusses major results and conclusions, and provides a perspective for future research needs and educational approaches in this area.     

Soft computing approach for reliability optimization: State-of-the-art survey

In the broadest sense, reliability is a measure of performance of systems. As systems have grown more complex, the consequences of their unreliable behavior have become severe in terms of cost, effort, lives, etc., and the interest in assessing system reliability and the need for improving the reliability of products and systems have become very important. Most solution methods for reliability optimization assume that systems have redundancy components in series and/or parallel systems and alternative designs are available. Reliability optimization problems concentrate on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirement. In the past two decades, numerous reliability optimization techniques have been proposed. Generally, these techniques can be classified as linear programming, dynamic programming, integer programming, geometric programming, heuristic method, Lagrangean multiplier method and so on. A Genetic Algorithm (GA), as a soft computing approach, is a powerful tool for solving various reliability optimization problems. In this paper, we briefly survey GA-based approach for various reliability optimization problems, such as reliability optimization of redundant system, reliability optimization with alternative design, reliability optimization with time-dependent reliability, reliability optimization with interval coefficients, bicriteria reliability optimization, and reliability optimization with fuzzy goals. We also introduce the hybrid approaches for combining GA with fuzzy logic, neural network and other conventional search techniques. Finally, we have some experiments with an example of various reliability optimization problems using hybrid GA approach.     

New Tabu search heuristics for the dynamic facility layout problem

A manufacturing facility is a dynamic system that constantly evolves due to changes such as changes in product demands, product designs, or replacement of production equipment. As a result, the dynamic facility layout problem (DFLP) considers these changes and is defined as the problem of assigning departments to locations during a multi-period planning horizon such that the sum of the material handling and re-arrangement costs is minimised. In this paper, three tabu search (TS) heuristics are presented for this problem. The first heuristic is a simple TS heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic TS heuristic. To test the performances of the heuristics, two sets of test problems from the literature are used in the analysis. The results show that the second heuristic out-performs the other proposed heuristics and the heuristics available in the literature.     

Combining iterative heuristic optimization and uncertainty analysis methods for robust parameter design

A number of investigators have pointed out that products and processes lack quality because of performance inconsistency, which is often due to uncontrollable parameters in the manufacturing process or product usage. Robust design methods are aimed at finding product/process designs that are less sensitive to parameter variation. Robust design of computer simulations requires a large number of runs, which are very time consuming. A novel methodology for robust design is presented in this article. It integrates an iterative heuristic optimization method with uncertainty analysis to achieve effective variability reductions, exploring a large parameter domain with an accessible number of simulations. To demonstrate the effectiveness of this methodology, the robust design of a 0.15 μm CMOS device is shown.