A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.     

A modified power spectral density test applied to?weighing matrices with small weight

The power spectral density test has been used for at least a decade in the search for many kinds of combinatorial matrices, such as weighing matrices for instance. In this paper we establish a modified power spectral density test that we apply to the search for weighing matrices of small weights constructed from two circulants. The main novelty of our approach is to define the Discrete Fourier Transform on the support of the first rows of the two circulants, thus exploiting the inherent sparsity of the problem. This new formalism turns out to be very efficient for small weights 9,18,36 and we find 10 new weighing matrices W(2⋅p,18) for prime p∈{37,47,53,59,61,67,73,79,83,97}. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.     

Polynomially solvable special cases of the quadratic bottleneck assignment problem

Quadratic bottleneck assignment problems (QBAP) are obtained by replacing the addition of cost terms in the objective function of a quadratic (sum) assignment problem by taking their maximum. Since the QBAP is an NP\mathcal{NP}-hard problem, polynimially solvable special cases of the QBAP are of interest. In this paper we specify conditions on the cost matrices of QBAP leading to special cases which can be solved to optimality in polynomial time. In particular, the following three cases are discussed: (i) any permutation is optimal (constant QBAP), (ii) a certain specified permutation is optimal (constant permutation QBAP) and (iii) the solution can be found algorithmically by a polynomial algorithm. Moreover, the max-cone of bottleneck Monge matrices is investigated, its generating matrices are identified and it is used as a tool in proving polynomiality results.     

Floating ideas—An experiment in enhancing hypergames with maps

Within the OR community, an increasing emphasis is being placed on developing approaches to tackle complex, ‘messy’ decision problems. The work described in this paper arose out of the premise that it would be desirable to integrate ideas from a number of different approaches of this type. Specifically, the paper describes one experimental attempt to link methods for modelling conflict situations (the analysis of options and hypergames) with the cognitive mapping approach to eliciting subjective data. Taking a personally-owned decision problem, mapping was used to enrich the game-based approaches by providing a way of documenting the argumentation underlying the models used. Though difficult to generalise from, the experiment not only suggested that such an extension is likely to be an improvement, but also highlighted some deficiencies in the existing versions of the game-based approaches themselves.     

Deterministic construction of compressed sensing matrices based on semilattices

A central problem in compressed sensing is the construction of sensing matrices. In this paper, we show how to construct sensing matrices by using semilattices, and give many examples of sensing matrices constructed from specific semilattices. Moreover, we show that the new construction for some examples with small parameters gives better sensing matrices compared with previously known constructions.     

A special combinatorial problem: pitch arrangement for pneumatic tires

In this paper, we introduce a combinatorial problem faced in the tire industry and then define it and optimize it by tabu search from the perspective of operational research. Such a problem is termed the pitch arrangement problem and involves both selecting and sequencing problems along with noninteger design variables. Pitch arrangement is an essential procedure for tires before their manufacture. Using this procedure, engineers have to choose an optimal groove distribution on tire treads for the purpose of manufacturing low-noise tires. Most research works on pitch arrangement are supported by tire companies, and their results are patented instead of being published. In this study, we define the abovementioned problem clearly and optimize it by tabu search. Two actual manufactured tires are chosen for the case studies. In addition, two patents and two types of pitch sequences optimized by genetic algorithms are also applied to these two tires for comparison. The pitch arrangement is optimized successfully and the performance of tabu search is found to be outstanding.     

Best routes selection in multimodal networks using multi-objective genetic algorithm

In this study, we propose a bi-level multi-objective Taguchi genetic algorithm for a multimodal routing problem with time windows. The mathematic model is constructed, which is featured by two optimal objectives, multiple available transportation manners and different demanded delivery times. After thoroughly analyzing the characteristics of the formulated model, a corresponding bi-level multi-objective Taguchi genetic algorithm is designed to find the Pareto-optimal front. At the upper level, a genetic multi-objective algorithm simultaneously searches the Pareto-optimal front and provides the most feasible routing path choices for the lower level. After generalizing the matrices of costs and time in a multimodal transportation network, the \(k\) -shortest path algorithm is applied to providing some potential feasible paths. A multi-objective genetic algorithm is proposed at the lower level to determine the local optimal combination of transportation manners for these potential feasible paths. To make the genetic algorithm more robust, sounder and faster, the Taguchi (orthogonal) experimental design method is adopted in generating the initial population and the crossover operator. The case study shows that the proposed algorithm can effectively find the Pareto-optimal front solutions and offer series of transportation routes with best combinations of transportation manners. The shipper can easily select the required shipping schemes with specified demands.     

An Integrated Risk Assessment Model of Township‐Scaled Land Subsidence Based on an Evidential Reasoning Algorithm and Fuzzy Set Theory

Land subsidence risk assessment (LSRA) is a multi‐attribute decision analysis (MADA) problem and is often characterized by both quantitative and qualitative attributes with various types of uncertainty. Therefore, the problem needs to be modeled and analyzed using methods that can handle uncertainty. In this article, we propose an integrated assessment model based on the evidential reasoning (ER) algorithm and fuzzy set theory. The assessment model is structured as a hierarchical framework that regards land subsidence risk as a composite of two key factors: hazard and vulnerability. These factors can be described by a set of basic indicators defined by assessment grades with attributes for transforming both numerical data and subjective judgments into a belief structure. The factor‐level attributes of hazard and vulnerability are combined using the ER algorithm, which is based on the information from a belief structure calculated by the Dempster‐Shafer (D‐S) theory, and a distributed fuzzy belief structure calculated by fuzzy set theory. The results from the combined algorithms yield distributed assessment grade matrices. The application of the model to the Xixi‐Chengnan area, China, illustrates its usefulness and validity for LSRA. The model utilizes a combination of all types of evidence, including all assessment information—quantitative or qualitative, complete or incomplete, and precise or imprecise—to provide assessment grades that define risk assessment on the basis of hazard and vulnerability. The results will enable risk managers to apply different risk prevention measures and mitigation planning based on the calculated risk states.     

An upper bound on the minimal total cost of the transportation problem with varying demands and supplies

In general cases, to find the exact upper bound on the minimal total cost of the transportation problem with varying demands and supplies is an NP-hard problem. In literature, there are only two approaches with several shortcomings to solve the problem. In this paper, the problem is formulated as a bi-level programming model, and proven to be solvable in a polynomial time if the sum of the lower bounds for all the supplies is no less than the sum of the upper bounds for all the demands; and a heuristic algorithm named TPVDS-A based on genetic algorithm is developed as an efficient and robust solution method of the model. Computational experiments on benchmark and new randomly generated instances show that the TPVDS-A algorithm outperforms the two existing approaches.     

Robotic-Cell Scheduling: Special Polynomially Solvable Cases of the Traveling Salesman Problem on Permuted Monge Matrices

In this paper, we introduce the 1 − K robotic-cell scheduling problem, whose solution can be reduced to solving a TSP on specially structured permuted Monge matrices, we call b-decomposable matrices. We also review a number of other scheduling problems which all reduce to solving TSP-s on permuted Monge matrices. We present the important insight that the TSP on b-decomposable matrices can be solved in polynomial time by a special adaptation of the well-known subtour-patching technique. We discuss efficient implementations of this algorithm on newly defined subclasses of permuted Monge matrices.     

The maximum dispersion problem

In the maximum dispersion problem, a given set of objects has to be partitioned into a number of groups. Each object has a non-negative weight and each group has a target weight, which may be different for each group. In addition to meeting the target weight of each group, all objects assigned to the same group should be as dispersed as possible with respect to some distance measure between pairs of objects. Potential applications for this problem come from such diverse fields as the problem of creating study groups or the design of waste collection systems. We develop and compare two different (mixed-) integer linear programming formulations for the problem. We also study a specific relaxation that enables us to derive tight bounds that improve the effectiveness of the formulations. Thereby, we obtain an upper bound by finding in an auxiliary graph subsets of given size with minimal diameter. A lower bound is derived based on the relation of the optimal solution of the relaxation to the chromatic number of a series of auxiliary graphs. Finally, we propose an exact solution scheme for the maximum dispersion problem and present extensive computational experiments to assess its efficiency.     

Newly deterministic construction of compressed sensing matrices via singular linear spaces over finite fields

A valuable opportunity is provided by compressed sensing (CS) to accomplish the tasks of high speed sampling, the transmission of large volumes of data, and storage in signal processing. To some extent, CS has brought tremendous changes in the information technologies that we use in our daily lives. However, the construction of compressed sensing matrices still can pose substantial problems. In this paper, we provide a kind of deterministic construction of sensing matrices based on singular linear spaces over finite fields. In particular, by choosing appropriate parameters, we constructed binary sensing matrices that are superior to existing matrices, and they outperform DeVore’s matrices. In addition, we used an embedding manipulation to merge our binary matrices with matrices that had low coherence, thereby improving such matrices. Compared with the quintessential binary matrices, the improved matrices possess better ability to compress and recover signals. The favorable performance of our binary and improved matrices was demonstrated by numerical simulations.     

基于随机权重多目标遗传算法的多目标动态单元构建方法

考虑多变的市场需求环境下单元生产系统在多个计划期具有多个目标的动态构建决策问题。通过对单元生产构建过程中的总费用、设备负载与能力之间最大偏差以及零部件跨单元移动的总次数3个目标进行权衡,建立了非线性多目标动态单元构建的数学模型。采用自适应小生境技术、惩罚技术、双轮盘赌法和精华选择策略,提出了基于精华保留策略的随机权重多目标遗传算法求解该组合优化问题。结合实例对模型和算法进行了仿真分析,结果显示了算法对解决多目标动态单元构建问题的有效性。     

Do colored cells in risk matrices affect decision-making and risk perception? Insights from randomized controlled studies

Risk matrices communicate the likelihood and potential impact of risks and are often used to inform decision-making around risk mitigations. The merits and demerits of risk matrices in general have been discussed extensively, yet little attention has been paid to the potential influence of color in risk matrices on their users. We draw from fuzzy-trace theory and hypothesize that when color is present, individuals are likely to place greater value on reducing risks that cross color boundaries (i.e., the boundary-crossing effect), leading to sub-optimal decision making. In two randomized controlled studies, employing forced-choice and willingness-to-pay measures to investigate the boundary-crossing effect in two different color formats for risk matrices, we find preliminary evidence to support our hypotheses that color can influence decision making. The evidence also suggests that the boundary-crossing effect is only present in, or is stronger for, higher numeracy individuals. We therefore recommend that designers should consider avoiding color in risk matrices, particularly in situations where these are likely to be used by highly numerate individuals, if the communication goal is to inform in an unbiased way.     

一种差异工件单机批调度问题的蚁群优化算法

由于在利用蚁群算法构建差异工件(即工件有尺寸差异)单机批调度问题的解时,批的加工时间是不确定的.从而不能类似于经典调度问题的蚁群算法把批加工时间的倒数作为蚁群算法中的启发式信息,引入批的利用率和批的负载均衡率作为蚁群算法中的启发式信息,提出了JACO(ant colony optimization based a job sequence)和BACO(ant colony optimization based a batch sequence)两种蚁群优化算法.在算法JACO中,解的编码为工件序列,它对应着用BF(best fit)分批规则生成的调度方案,信息素代表工件间的排列顺序;在算法BACO中,解的编码为批序列,信息素代表工件间的批相关性,由此信息素通过中间信息素量来构造相应的解,并引入特定的局部优化策略,提高了算法的搜索效率.实验表明,与以往文献中的SA(simula-ted annealing)、GA(genetic algorithm)算法以及FFLPT(first-fit longest processing time)、BFLPT (best-fit longest processing time)启发式规则相比,算法JACO和BACO明显优于它们,且BACO算法比JACO算法效果更好.     

Testing of the ‘reduction of compound alternatives’ principle

This paper reports an empirical investigation of the effects of three pictorial forms of problem representation on conformance with the Reduction of Compound Alternatives Principle of expected utility theory. The most common form of representation, written problem statements, was compared with three pictorial representations: tubes containing one hundred labeled balls, decision matrices with each column proportional in size to the probability of the corresponding event, and bar graphs. The tubes representation led to fewer violations of the Principle. In addition, when subjects were trained to construct proportional matrices from written problem statements, they exhibited fewer violations than those who received the same problems already formatted in proportional matrices. The results reported here should contribute to the development of a theory of the way people frame decision problems.     

A multi-objective particle swarm for a flow shop scheduling problem

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in strong sense, an effective multi-objective particle swarm (MOPS), exploiting a new concept of the Ideal Point and a new approach to specify the superior particle's position vector in the swarm, is designed and used for finding locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm, i.e. SPEA-II. The computational results show that the proposed MOPS performs better than the genetic algorithm, especially for the large-sized problems.     

GM模型的病态性问题

本文指出GM模型的方程组存在着严重的方程病态性问题,探讨了GM模型产生病态的原因:(1)矩阵由累加数构成,累加数之间有较大的数量级差别;(2)GM模型中的蜕化使矩阵中元素数量级差别过大;(3)GM模型的矩阵生成方式使得我们难以降低方程组的病态性。并对一个被广泛引用的算例进行了分析。最后,我们认为必须小心使用GM模型。     

A hybrid approach to constrained evolutionary computing: Case of product synthesis

Evolutionary computing (EC) is comprised of techniques involving evolutionary programming, evolution strategies, genetic algorithms (GA), and genetic programming. It has been widely used to solve optimization problems for large scale and complex systems. However, when insufficient knowledge is incorporated, EC is less efficient in terms of searching for an optimal solution. In addition, the GA employed in previous literature is modeled to solve one problem exactly. The GA needs to be redesigned, at a cost, for it to be applied to another problem. Due to these two reasons, this paper develops a generic GA incorporating knowledge extracted from the rough set theory. The advantages of the proposed solution approach include: (i) solving problems that can be decomposed into functional requirements, and (ii) improving the performance of the GA by reducing the domain range of initial population and constraining crossover using the rough set theory. The solution approach is exemplified by solving the problem of product synthesis, where there is a conflict between performance and cost. Manufacturing or assembling a product of high performance and quality at a low cost is critical for a company to maximize its advantages. Based on our experimental results, this approach has shown great promise and has reduced costs when the GA is in processing.     

A genetic algorithm for thepart family formation problem

Recently, there has been a lot of interest in group technology (GT) from researchers as well as from practitioners. This interest is explained by the fact that GT supports new manufacturing philosophies. One of the main issues in GT is the part family formation problem which is concerned with grouping similar products into same families. Many researchers have tackled this problem and many algorithms have been proposed for it. In this paper, we present a genetic technique-based heuristic for the quadratic integer programming model of the part family formation problem which was formulated by Kusiak et al. (1986). The heuristic is tested on several problems from the literature, and preliminary results are very promising.