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This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

This research aims to create a methodology that integrates optimization techniques into preliminary cost estimates and predicts the impacts of design alternatives of steel pedestrian bridges (SPBs). The cost estimation process uses two main parameters, but the main goal is to create a cost estimation model.

This study explores a flexible model design that uses computing capabilities for decision-making. Using cost optimization techniques, the model can select an optimal pedestrian bridge system based on multiple criteria that may change independently. This research focuses on four types of SPB systems prevalent in Egypt and worldwide. The study also suggests developing a computerized cost and weight optimization model that enables decision-makers to select the optimal system for SPBs in keeping up with the criteria established for that system.

In this paper, the authors developed an optimization model for cost estimates of SPBs. The model considers two main parameters: weight and cost. The main contribution of this study based on a parametric study is to propose an approach that enables structural engineers and designers to select the optimum system for SPBs.

The implications of this research from a practical perspective are that the study outlines a feasible approach to develop a computerized model that utilizes the capabilities of computing for quick cost optimization that enables decision-makers to select the optimal system for four common SPBs based on multiple criteria that may change independently and in concert with cost optimization during the preliminary design stage.

The model can choose an optimal system for SPBs based on multiple criteria that may change independently and in concert with cost optimization. The resulting optimization model can forecast the optimum cost of the SPBs for different structural spans and road spans based on local unit costs of materials cost of steel structures, fabrication, erection and painting works.

The authors developed a computerized model that uses spreadsheet software's capabilities for cost optimization, enabling decision-makers to select the optimal system for SPBs meeting the criteria established for such a system. Based on structural characteristics and material unit costs, this study shows that using the optimization model for estimating the total direct cost of SPB systems, the project cost can be accurately predicted based on the conceptual design status, and positive prediction outcomes are achieved.

Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

In order to solve the problems faced by First Order Reliability Method (FORM) and First Order Saddlepoint Approximation (FOSA) in structural reliability optimization, this paper aims to propose a new Reliability-based Design Optimization (RBDO) strategy for offshore engineering structures based on Original Probabilistic Model (OPM) decoupling strategy. The application of this innovative technique to other maritime structures has the potential to substantially improve their design process by optimizing cost and enhancing structural reliability.

In the strategy proposed by this paper, sequential optimization and reliability assessment method and surrogate model are used to improve the efficiency for solving RBDO. The strategy is applied to the analysis of two marine engineering structure cases of ship cargo hold structure and frame ring of underwater skirt pile gripper. The effectiveness of the method is proved by comparing the original design and the optimized results.

In this paper, the proposed new RBDO strategy is used to optimize the design of the ship cargo hold structure and the frame ring of the underwater skirt pile gripper. According to the results obtained, compared with the original design, the structure of optimization design has better reliability and stability, and reduces the risk of failure. This optimization can also better balance the relationship between performance and cost. Therefore, it is recommended for related RBDO problems in the field of marine engineering.

In view of the limitations of FORM and FOSA that may produce multiple MPPs for a single performance function, the new RBDO strategy proposed in this study provides valuable insights and robust methods for the optimization design of offshore engineering structures. It emphasizes the importance of combining advanced MPP search technology and integrating SORA and surrogate models to achieve more economical and reliable design.

This study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of uncertainty analysis.

The method first introduces a dual adaptive chaotic flower pollination algorithm (DACFPA) to overcome the shortcomings of the original flower pollination algorithm (FPA), such as its susceptibility to poor accuracy and convergence efficiency when dealing with complex optimization problems. Furthermore, a DACFPA-Kriging model is developed by optimizing the relevant parameter of Kriging model via DACFPA. Finally, the dual Kriging model is constructed to improve the efficiency of uncertainty analysis, and a robust design optimization method based on DACFPA-Dual-Kriging is proposed.

The DACFPA outperforms the FPA, particle swarm optimization and gray wolf optimization algorithms in terms of solution accuracy, convergence speed and capacity to avoid local optimal solutions. Additionally, the DACFPA-Kriging model exhibits superior prediction accuracy and robustness contrasted with the original Kriging and FPA-Kriging. The proposed method for robust design optimization based on DACFPA-Dual-Kriging is applied to the motor hanger of the electric multiple units as an engineering case study, and the results confirm a significant reduction in the fluctuation of the maximum equivalent stress.

This study represents the initial attempt to enhance the prediction accuracy of the Kriging model using the improved FPA and to combine the dual Kriging model for uncertainty analysis, providing an idea for the robust optimization design of mechanical structure with black-box problem.

This paper analytically models and numerically investigates two operating levers, namely optimization of product price and optimization of product quality in the context of a manufacturer that sells the products directly in the marketplace. The study attempts to identify how optimizing product quality and product price can fulfill a manufacturer's economic aims such as maximization of the manufacturer's profit and market demand. Anchored to the extant literature, the demand is modeled as a parametric joint multiplicative function of price and quality. Further, price is modeled as a function of product quality.

First, the authors evolve the analytical expression for the manufacturer's profit. Thereafter, following the mathematical principles of unconstrained optimization, the authors arrive at the conditions for optimal product quality and product price. The authors further perform numerical experiments to understand the behavior of economic dimensions such as profit and demand with respect to sensitivities associated with cost, quality and price.

The authors find that under product quality optimization, the optimal product quality is a unique solution in that a highest possible theoretical manufacturer's profit is obtained. However, in the case of product price optimization, the optimal product price is non-unique and is a function of product quality. The authors further find that in the context of functional quality-level expectations, product quality optimization as an operating lever gives a better dividend. However, in the case of higher product quality expectations, product price optimization performs better than product quality optimization. Further, several novel findings are also obtained from numerical experimentations.

The findings of the authors' study have implications for types of industries characterized by relatively low as well as relatively high competitive intensity. Further, as opposed to several extant studies that have often carried out joint optimization of quality and price, the authors' study is one of the first to study the impact of product price and product quality on the manufacturer's economic objective in a disparate and focused manner, thus capturing individual effects.

This paper aims to present a multi-fidelity surrogate-based optimization (MFSBO) method for computationally accurate and efficient design of microfluidic concentration gradient generators (µCGGs).

Cokriging-based multi-fidelity surrogate model (MFSM) is constructed to combine data with varying fidelities and computational costs to accelerate the optimization process and improve design accuracy. An adaptive sampling approach based on parallel infill of multiple low-fidelity (LF) samples without notably adding computation burden is developed. The proposed optimization framework is compared with a surrogate-based optimization (SBO) method that relies on data from a single source, and a conventional multi-fidelity adaptive sampling and optimization method in terms of the convergence rate and design accuracy.

The results demonstrate that proposed MFSBO method allows faster convergence and better designs than SBO for all case studies with 49% more reduction in the objective function value on average. It is also found that parallel infill (MFSBO-4) with four LF samples, enables more robust, efficient and accurate designs than conventional multi-fidelity infill (MFSBO-1) that only adopts one LF sample during each iteration for more complex optimization problems.

A MFSM based on cokriging method is constructed to utilize data with varying fidelities, accuracies and computational costs for µCGG design. A parallel infill strategy based on multiple infill criteria is developed to accelerate the convergence and improve the design accuracy of optimization. The proposed methodology is proved to be a feasible method for µCGG design and its computational efficiency is verified.

The literature that is presently available on sustainable supply chain management (SSCM) combining optimization and industry 4.0 techniques falls short in its depictions of the recent developments, budding pertinent areas and the importance of SSCM in the growth of industrial economies around the world. This article's main objective is to analyze current trends, highlight the latest initiatives and perform a meta-analysis of the literature that is currently accessible in the SSCM area with a special focus on optimization and industry 4.0 techniques. The paper also proposes a conceptual framework that will assist in illuminating how the ideas of optimization and industry 4.0 may contribute to realizing sustainability in supply chains.

The proposed study systematically reviews 85 research publications published between 2010 and 2022 in referenced peer-reviewed journals in diverse fields, including engineering, business and management, services and healthcare. Numerous categories are considered throughout the examination of the literature, including year-wise publications, prominent journals, type of research design, concerned industry and research technique used.

The study demonstrates a deeper comprehension of the literature in the field and its evolution throughout numerous industry sectors, which is helpful for both practitioners and academics. The results from the content analysis highlight various future research opportunities in the domain.

This is one of the first research articles that have attempted to establish, analyze and highlight the current trends and initiatives in the SSCM domain from an optimization and industry 4.0 techniques viewpoint. The cluster-based future research propositions also enhance the novelty of the study.

The purpose of this paper is to establish a tolerance optimization method based on manufacturing difficulty computation using the genetic algorithm (GA) method. This proposal is among the authors’ perspectives of accomplished previous research work to cooperative optimal tolerance allocation approach for concurrent engineering area.

This study introduces the proposed GA modeling. The objective function of the proposed GA is to minimize total cost constrained by the equation of functional requirements tolerances considering difficulty coefficients. The manufacturing difficulty computation is based on tools for the study and analysis of reliability of the design or the process, as the failure mode, effects and criticality analysis (FMECA) and Ishikawa diagram.

The proposed approach, based on difficulty coefficient computation and GA optimization method [genetic algorithm optimization using difficulty coefficient computation (GADCC)], has been applied to mechanical assembly taken from the literature and compared to previous methods regarding tolerance values and computed total cost. The total cost is the summation of manufacturing cost and quality loss. The proposed approach is economic and efficient that leads to facilitate the manufacturing of difficult dimensions by increasing their tolerances and reducing the rate of defect parts of the assembly.

The originality of this new optimal tolerance allocation method is to make a marriage between GA and manufacturing difficulty. The computation of part dimensions difficulty is based on incorporating FMECA tool and Ishikawa diagram This comparative study highlights the benefits of the proposed GADCC optimization method. The results lead to obtain optimal tolerances that minimize the total cost and respect the functional, quality and manufacturing requirements.