BHGSO: Binary Hunger Games Search Optimization Algorithm for Feature Selection Problem

In machine learning and data mining, feature selection (FS) is a traditional and complicated optimization problem. Since the run time increases exponentially, FS is treated as an NP-hard problem. The researcher’s effort to build a new FS solution was inspired by the ongoing need for an efficient FS framework and the success rates of swarming outcomes in different optimization scenarios. This paper presents two binary variants of a Hunger Games Search Optimization (HGSO) algorithm based on V- and S-shaped transfer functions within a wrapper FS model for choosing the best features from a large dataset. The proposed technique transforms the continuous HGSO into a binary variant using V- and S-shaped transfer functions (BHGSO-V and BHGSO-S). To validate the accuracy, 16 famous UCI datasets are considered and compared with different state-of-the-art metaheuristic binary algorithms. The findings demonstrate that BHGSO-V achieves better performance in terms of the selected number of features, classification accuracy, run time, and fitness values than other state-of-the-art algorithms. The results demonstrate that the BHGSO-V algorithm can reduce dimensionality and choose the most helpful features for classification problems. The proposed BHGSO-V achieves 95% average classification accuracy for most of the datasets, and run time is less than 5 sec. for low and medium dimensional datasets and less than 10 sec for high dimensional datasets.     

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.     

Archery Algorithm: A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge. Therefore, these must be addressed utilizing proper approaches. Based on a random search space, optimization algorithms can find acceptable solutions to problems. Archery Algorithm (AA) is a new stochastic approach for addressing optimization problems that is discussed in this study. The fundamental idea of developing the suggested AA is to imitate the archer's shooting behavior toward the target panel. The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer. The AA is mathematically described, and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions. Furthermore, the proposed algorithm's performance is compared vs. eight approaches, including teaching-learning based optimization, marine predators algorithm, genetic algorithm, grey wolf optimization, particle swarm optimization, whale optimization algorithm, gravitational search algorithm, and tunicate swarm algorithm. According to the simulation findings, the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios, and it can give adequate quasi-optimal solutions to these problems. The analysis and comparison of competing algorithms’ performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.     

Comparison of genetic and binary particle swarm optimization algorithms on system maintenance scheduling using prognostics information

Recent technical advances in condition-based maintenance technology have made it possible to not only diagnose existing failures, but also forecast future failures, which is called prognostics. A common method of maintenance scheduling in condition-based maintenance is to apply thresholds to prognostics information, which is not appropriate for systems consisting of multiple serially connected machinery. Maintenance scheduling is defined as a binary optimization problem and has been solved with a genetic algorithm. In this article, various binary particle swarm optimization methods are analysed and compared with each other and a genetic algorithm on a maintenance-scheduling problem for condition-based maintenance systems using prognostics information. The trade-off between maintenance and failure is quantified as the risk to be minimized. The forecasted failure probability of serially connected machinery is utilized in the analysis of the whole system. In addition to the comparison of a genetic algorithm and binary particle swarm optimization methods, a new binary particle swarm optimization that combines the good sides of two binary particle swarm optimizations is presented.     

Optimal platform design using non-dominated sorting genetic algorithm II and technique for order of preference by similarity to ideal solution; application to automotive suspension system

Unlike conventional approaches where optimization is performed on a unique component of a specific product, optimum design of a set of components for employing in a product family can cause significant reduction in costs. Increasing commonality and performance of the product platform simultaneously is a multi-objective optimization problem (MOP). Several optimization methods are reported to solve these MOPs. However, what is less discussed is how to find the trade-off points among the obtained non-dominated optimum points. This article investigates the optimal design of a product family using non-dominated sorting genetic algorithm II (NSGA-II) and proposes the employment of technique for order of preference by similarity to ideal solution (TOPSIS) method to find the trade-off points among the obtained non-dominated results while compromising all objective functions together. A case study for a family of suspension systems is presented, considering performance and commonality. The results indicate the effectiveness of the proposed method to obtain the trade-off points with the best possible performance while maximizing the common parts.     

Preference-based Pareto optimization in certain and noisy environments

In this article a method for including a priori preferences of decision makers into multicriteria optimization problems is presented. A set of Pareto-optimal solutions is determined via desirability functions of the objectives which reveal experts’ preferences regarding different objective regions. An application to noisy objective functions is not straightforward but very relevant for practical applications. Two approaches are introduced in order to handle the respective uncertainties by means of the proposed preference-based Pareto optimization. By applying the methods to the original and uncertain Binh problem and a noisy single cut turning cost optimization problem, these approaches prove to be very effective in focusing on different parts of the Pareto front of the ori-ginal problem in both certain and noisy environments.     

基于蚁群算法的多值属性系统测试序列优化

针对系统故障诊断中的多值属性系统测试序列优化问题,该文提出一种改进的蚁群算法,将成功运用在二值属性系统中的蚁群算法扩展到多值属性系统中,根据多值属性系统特点,设计相应的状态转移规则和信息素更新机制,并采用蚁群算法和遗传算法相融合的联合优化策略,解决了多值属性系统的序列优化问题,为多值属性系统的测试优化问题提供了一条新的解决途径。     

Mode-pursuing sampling method for global optimization on expensive black-box functions

The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This article proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling method that systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitations of the method are also identified and discussed.     

Optimal reserve management for restructured power generating systems

This paper presents a technique to determine the optimal reserve structure (reserve providers and the corresponding reserve capacity) for a restructured power generating system (GS). The reserve of a GS can be provided by its own generating units and can also be purchased from other GSs through the reserve agreements. The objective of reserve management for a GS is to minimize its total reserve cost while satisfying the reliability requirement. The reserve management is a complex optimization problem, which requires a large amount of calculations. In order to simplify the evaluation, a complex generating system (CGS) consisting of different GSs and the corresponding transmitting network is represented by its multi-state reliability equivalents. The universal generating functions (UGFs) of these equivalents are developed and the special operators for these UGFs are defined to evaluate the reliability of a particular GS, which has reserve agreements with other GSs in the CGS. The genetic algorithm (GA) has been used to solve the optimization problem. An improved power system-IEEE reliability test system is used to illustrate the technique.     

Some heuristic approaches for solving extended geometric programming problems

This article introduces an extension of standard geometric programming (GP) problems, called quasi geometric programming (QGP) problems. The idea behind QGP is very simple, it means that a problem becomes a GP problem when some variables are kept constant. The consideration of this particular kind of nonlinear and possibly non-smooth optimization problem is motivated by the fact that many engineering problems can be formulated, or well approximated, as a QGP problem. However, solving a QGP problem remains a difficult task due to its intrinsic nonconvex nature. This is why this article introduces some simple approaches for easily solving this kind of nonconvex problem. The interesting thing is that the proposed methods do not require the development of a customized solver and work well with any existing solver able to solve conventional GP problems. Some considerations on the robustness issue are also presented. Various optimization problems are considered to illustrate the ability of the proposed methods for solving a QGP problem. Comparison with previously published work is also given.     

Life‐cycle cost optimization of steel structures

This article addresses the life‐cycle cost optimization of steel structures. The main factors influencing the life‐cycle cost of a structure are delineated and their effects on various cost functions are discussed. A four‐criteria optimization model is presented for the life‐cycle cost optimization of steel structures. These criteria are (i) select discrete commercially available sections with the lowest cost, (ii) select commercially available sections with the lightest weight, (iii) select the minimum number of different types of commercially available sections, and (iv) select commercially available sections with the minimum total perimeter length. The last criterion models a representative type of cost incurred over the life of the structure, that is, preventative maintenance in the form of periodic painting of an exposed steel structure to avoid corrosion. The life‐cycle cost optimization model is based on fuzzy logic with the goal of formalizing the life‐cycle design process but with some input from the design engineer through introduction of weighting coefficients reflecting the relative importance of various criteria. The model is applied to a large steel structure with over 3300 members. Copyright © 2002 John Wiley & Sons, Ltd.     

WOI-c假设下的供应链联盟转移定价研究

借鉴Nash均衡讨价还价模型和Roundy提出的序列优化算法,对实行WOI-c库存所有权模式的简单(及其扩展)二级供应链联盟中的转移定价策略进行了研究.通过将MA和OA思想相结合,运用序列优化算法和利润分享思想,为该联盟体的整体利益最大化目标提出了相适应的转移定价策略,及其为双方所接受的利润分配策略.通过一个算例对理论研究进行了证实/伪,发现根据序列优化算法得到的转移定价方法对规模较大的需求更为适用,准确性也更高.     

An improved harmony search algorithm with dynamically varying bandwidth

The present work demonstrates a new variant of the harmony search (HS) algorithm where bandwidth (BW) is one of the deciding factors for the time complexity and the performance of the algorithm. The BW needs to have both explorative and exploitative characteristics. The ideology is to use a large BW to search in the full domain and to adjust the BW dynamically closer to the optimal solution. After trying a series of approaches, a methodology inspired by the functioning of a low-pass filter showed satisfactory results. This approach was implemented in the self-adaptive improved harmony search (SIHS) algorithm and tested on several benchmark functions. Compared to the existing HS algorithm and its variants, SIHS showed better performance on most of the test functions. Thereafter, the algorithm was applied to geometric parameter optimization of a friction stir welding tool.     

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.     

Horsetail matching: a flexible approach to optimization under uncertainty*

It is important to design engineering systems to be robust with respect to uncertainties in the design process. Often, this is done by considering statistical moments, but over-reliance on statistical moments when formulating a robust optimization can produce designs that are stochastically dominated by other feasible designs. This article instead proposes a formulation for optimization under uncertainty that minimizes the difference between a design's cumulative distribution function and a target. A standard target is proposed that produces stochastically non-dominated designs, but the formulation also offers enough flexibility to recover existing approaches for robust optimization. A numerical implementation is developed that employs kernels to give a differentiable objective function. The method is applied to algebraic test problems and a robust transonic airfoil design problem where it is compared to multi-objective, weighted-sum and density matching approaches to robust optimization; several advantages over these existing methods are demonstrated.     

Recent advances in system reliability optimization driven by importance measures

System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints. Birnbaum importance is a well-known method for evaluating the effect of component reliability on system reliability. Many importance measures (IMs) are extended for binary, multistate, and continuous systems from different aspects based on the Birnbaum importance. Recently, these IMs have been applied in allocating limited resources to the component to maximize system performance. Therefore, the significance of Birnbaum importance is illustrated from the perspective of probability principle and gradient geometrical sense. Furthermore, the equations of various extended IMs are provided subsequently. The rules for simple optimization problems are summarized to enhance system reliability by using ranking or heuristic methods based on IMs. The importance-based optimization algorithms for complex or large-scale systems are generalized to obtain remarkable solutions by using IM-based local search or simplification methods. Furthermore, a general framework driven by IM is developed to solve optimization problems. Finally, some challenges in system reliability optimization that need to be solved in the future are presented.     

Global optimization for signomial discrete programming problems in engineering design

Signomial discrete programming (SDP) problems arise frequently in a variety of real applications. Although many optimization techniques have been developed to solve an SDP problem, they use too many binary variables to reformulate the problem for finding a globally optimal solution or can only derive a local or an approximate solution. This article proposes a global optimization method to solve an SDP problem by integrating an efficient linear expression of single variable discrete functions and convexification techniques. An SDP problem can be converted into a convex mixed-integer programming problem solvable to obtain a global optimum. Several illustrative examples are also presented to demonstrate the usefulness and effectiveness of the proposed method.     

Performance evaluation of ant colony optimization-based solution strategies on the mixed-model assembly line balancing problem

The aim of this article is to compare the performances of iterative ant colony optimization (ACO)-based solution strategies on a mixed-model assembly line balancing problem of type II (MMALBP-II) by addressing some particular features of real-world assembly line balancing problems such as parallel workstations and zoning constraints. To solve the problem, where the objective is to minimize the cycle time (i.e. maximize the production rate) for a predefined number of workstations in an existing assembly line, two ACO-based approaches which differ in the mission assigned to artificial ants are used. Furthermore, each ACO-based approach is conducted with two different pheromone release strategies: global and local pheromone updating rules. The four ACO-based approaches are used for solving 20 representative MMALBP-II to compare their performance in terms of computational time and solution quality. Detailed comparison results are presented.     

Nonconvex optimization of desirability functions

Desirability functions (DFs) are commonly used in optimization of design parameters with multiple quality characteristic to obtain a good compromise among predicted response models obtained from experimental designs. Besides discussing multi-objective approaches for optimization of DFs, we present a brief review of literature about most commonly used Derringer and Suich type of DFs and others as well as their capabilities and limitations. Optimization of DFs of Derringer and Suich is a challenging problem. Although they have an advantageous shape over other DFs, their nonsmooth nature is a drawback. Commercially available software products used by quality engineers usually do optimization of these functions by derivative free search methods on the design domain (such as Design-Expert), which involves the risk of not finding the global optimum in a reasonable time. Use of gradient-based methods (as in MINITAB) after smoothing nondifferentiable points is also proposed as well as different metaheuristics and interactive multi-objective approaches, which have their own drawbacks. In this study, by utilizing a reformulation on DFs, it is shown that the nonsmooth optimization problem becomes a nonconvex mixed-integer nonlinear problem. Then, a continuous relaxation of this problem can be solved with nonconvex and global optimization approaches supported by widely available software programs. We demonstrate our findings on two well-known examples from the quality engineering literature and their extensions.