Quadratic Assignment Formulation for the Multifactor Facilities Layout Problem

This paper proposes a new heuristic approach for solving facility layout problem (FLP) which is traditionally formulated as quadratic assignment problem (QAP). In this paper, FLP is formulated as linear assignment problem (LAP) consisting of facility pair and location pair. Being linear in nature LAP can be solved efficiently. Solution of LAP provides lower bound on corresponding QAP formulation of FLP. Heuristic procedure is applied to solve FLP from sets of LAP solution. Proposed heuristic is tested on benchmark instances taken from literature and compared with other heuristics available in literature. Computational results show that proposed heuristic provides a good quality approximate solution. This solution can be taken as initial solution for any improvement heuristic to get optimal/near optimal solution for FLP.

Signed graphs are graphs with an assignment of a positive or a negative sign to each edge. These graphs are helpful to represent different types of networks. For instance, they have been used in social networks, where a positive sign in an edge represents friendship between the two endpoints of that edge, while a negative sign represents enmity. Given a signed graph, an important question is how to embed such a graph in a metric space so that in the embedding every vertex is closer to its positive neighbors than to its negative ones. This problem is known as Sitting Arrangement (SA) problem and it was introduced by Kermarrec et al. (Proceedings of the 36th International Symposium on Mathematical Foundations of Computer Science (MFCS), pp. 388---399, 2011). Cygan et al. (Proceedings of the 37th International Symposium on Mathematical Foundations of Computer Science (MFCS), 2012) proved that the decision version of SA problem is NP-Complete when the signed graph has to be embedded into the Euclidean line. In this work, we study the minimization version of SA (MinSA) problem in the Euclidean line. We relate MinSA problem to the well known quadratic assignment (QA) problem. We establish such a relation by proving that local minimums in MinSA problem are equivalent to local minimums in a particular case of QA problem. In this document, we design two heuristics based on the combinatorial structure of MinSA problem. We experimentally compare their performances against heuristics designed for QA problem. This comparison favors the proposed heuristics.

In this paper, an approximate algorithm is proposed to solve facility layout problem (FLP) which is formulated as quadratic assignment problem (QAP). In the proposed approach, linear assignment problem (LAP) is formulated which is solvable in polynomial time. The proposed heuristic is applied to solve FLP from the set of LAP solution. To evaluate the performance of the heuristic a comparison between optimal and heuristic solution is also provided. The approach is tested on numerous benchmark problems available in literature. An encouraging comparative performance of this procedure is thus reported.

The multi-criteria facilities layout problem can be formulated as a quadratic assignment model that can handle multiple qualitative and quantitative factors in the objective function. Some studies have shown that the techniques and tools of facilities layout problems can equally be applied for the layout design of user interface components in human-computer interface. This paper presents an alternate approach, which handles multiple qualitative and quantitative factors in a different manner separately in the objective function to obtain the initial layouts. The proposed approach also consists of a layout procedure, in which the pair of facilities with the least composite criterion value has been selected to be placed far apart in the layout to generate an initial layout in the construction procedure. The results of the proposed approach are compared with that of an existing approach which handles a number of qualitative and quantitative factors in the same manner as in the objective function to obtain the initial layouts for the example task of the user interface components layout problem under consideration.

This article uses neural networks in forecasting stock market prices. With their ability to discover patterns in nonlinear and chaotic systems, neural networks offer the ability to predict market directions more accurately than current techniques such as technical analysis, fundamental analysis, and regression compared with neural network performance. Proposed intelligent stock market prediction system is based on the quantitative and qualitative factors. Three feedforward neural models can be used to analyze these factors. Input data to the neural network proposed are quantitative factors. Input data to the neural network proposed for qualitative factors can be factors related to the political effect considered. Third neural network consists of decision integration in which input data will be the outputs of above-mentioned neural networks. This facilitates to make right decision whether stock market is influenced by quantitative or qualitative factors

New complexity measures for the facility layout problem: an empirical study using traditional and neural network analysis

-Quadratic assignment problems (QAPs) are NP-hard combinatorial optimization problems often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator whose instances can be used as benchmark for meta-heuristics. Our generator aggregates various QAP instances into a larger size QAP instance in order to obtain an large size, additively decomposable QAP. We assume that a QAP instance that is difficult for local search has many local optima from which local search needs to escape from. We call the resulting QAPs the composite QAP instances (cQAPs). We use numerical and empirical techniques for the landscape analysis of generated composite QAPs. The comparison between our QAP instances with the other QAPs from the literature classify cQAPs as difficult. We show that heuristic algorithms that exploit the particularities of the cQAP search space, like iterated local search, can outperform other heuristics that do not consider the structure of this search space, like the multi-restart local search.

The facility layout design problem is an extensively studied research problem and belongs to nonpolynomial hard (NP-hard) combinatorial optimization problem. Quadratic assignment problem (QAP) is one of the formulations that is investigated for facility layout design because of its wide applicability. Ant colony optimization (ACO), a biologically inspired heuristic has centered on solving the QAP by achieving approximation as good as possible. This paper presents a population-based hybrid ant system (PHAS), which is an extension of the hybrid ant system (HAS) in which the size of the ant colony has been fixed. The performance of the proposed ant algorithm for QAP is compared with the existing metaheuristic implementations such as tabu search, reactive tabu search, simulated annealing, genetic hybrid method, HAS, and max–min ant system. The experimental results show that the proposed PHAS perform significantly better than the other existing algorithms of QAP.

Quadratic assignment problems (QAPs) is a NP-hard combinatorial optimization problem. QAPs are often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator that can be used for benchmarking for heuristic algorithms. Our QAP generator combines small size QAPs with known optimum solution into a larger size QAP instance. We call these instances composite QAPs (cQAPs), and we show that the cost function of cQAPs is additively decomposable. We give mild conditions for which a cQAP instance has known optimum solution. We generate cQAP instances using uniform distributions with different bounds for the component QAPs and for the rest of the cQAP elements. Numerical and analytical techniques that measure the difficulty of the cQAP instances in comparison with other QAPs from the literature are introduced. These methods point out that some cQAP instances are difficult for local search with many local optimum of various values, low epistasis and non-trivial asymptotic behaviour.

This paper presents a qualitative and quantitative research to explore and understand the agents that determine the level of productiveness and the importance of qualitative factors. A questionnaire was conducted to estimate the outcome of the qualitative agents or factors in improving the productivity of microtunneling projects. Information was collected from 26 competent professionals in microtunneling projects for almost 20years through an expert's opinion, using a semi-structured questionnaire. The Analytical Hierarchy Process and the clustering analysis technique have been used to account for the twenty qualitative agents or factors concerned in developing a proposed assessment model. The present research has developed an assessment model that stems from the result of qualitative factors on microtunneling to investigate the effect induced by the qualitative agents on productiveness. The assessment model is thereafter confirmed, showing an analytical outcome of 79.85% moderately justified percent. This study proved that the qualitative factors affecting the productivity of microtunneling projects can be assessed through the productivity index concept. This paper helps the industry parties to understand the factors influencing the success of microtunneling projects as well as, development of an assessment model to calculate productivity. Most of the past research on productivity models are based on quantitative factors only. This paper presents qualitative research to explore and understand the factors that affect productivity and the importance of qualitative factors. The developed assessment model presented is the first in connecting theory, analytical methods, and experts' opinions to help practitioners to understand and assess the productivity of microtunneling projects.

The quadratic assignment problem (QAP) has attracted a surpassing algorithmic research interest since its introduction in 1957 by Koopmans and Beckmann. A wide variety of algorithms and heuristics have been developed to solve the QAP exactly or approximately. Moreover, since all the problems described in Chapter 2 are closely related to the QAP, one could modify the available exact and approximate techniques for the QAP and utilize them to “solve” every one of these problems. While this is conceptually correct, we do not recommend to solve e.g. traveling salesman problems this way, because the largest size QAP solved to optimality, so far, has n = 30; see Clausen [1994], Mans et al. [1992], Pardalos et al. [1994], and Resende et al. [1994]. More to the point, this means that existing algorithms for QAPs are nowhere close to solving practical problems arising from real-life applications to optimality. This state of affairs is unsatisfactory, but not surprising since very little is known about the mathematical properties of QAPs. A straight-forward application of the appropriately modified QAP algorithms to solve its variants can thus not be expected to solve large-scale instances of these problems. While many authors propose (different) mixed zero-one formulations of QAPs, they are hardly exploited in the numerical computations and the facial structure of the associated integer polyhedra has not been studied in any detail.KeywordsAssignment ProblemTravel Salesman ProblemMaster ProblemTask GraphQuadratic Assignment ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Characterizing linearizable QAPs by the level-1 reformulation-linearization technique

The purpose of the study is to form an economic and mathematical instrument for assessing the role of quantitative and qualitative factors in changing the output of dairy products. Objectives: to determine the main theoretical provisions for calculating the indicator of dairy production depending on the resources used; to present a formalized expression for calculating quantitative factors of dairy output growth; to substantiate methodological tools for calculating qualitative, intensive factors of dairy output growth. The object of research is the scientific and technological development of the dairy subcomplex. The economic-mathematical and economic-statistical research methods were used. It has been established that the scientific and technological development of the dairy subcomplex is expressed, first of all, in an increase in the values of qualitative factors, the formal expression of which may be the values of labor productivity, capital productivity, yield or productivity; In periods with a constant level of technical development, quantitative factors receive priority - the number of workers, the cost of basic funds, the acreage, and the number of cows. A toolkit has been developed to assess the cumulative impact of both quantitative and qualitative factors on the resulting indicator of milk production, which will make it possible to reasonably assess the scientific and technological development of the dairy subcomplex. The qualitative factors include the productivity of the workers of the dairy subcomplex, the return on capital and the productivity of cows. Possible combinations of the influence of factors on the resulting indicator of milk production are determined. The key features of changes in influencing variables during periods with a constant level of technical development and in the context of the emergence of new, innovative technological solutions are characterized. Possible directions for further research to assess the scientific and technological de-velopment of the dairy-food subcomplex are outlined.

Exact [formula omitted]-optimal designs for a second-order response surface model on a circle with qualitative factors

: This thesis analyzes the effect of quantitative and qualitative factors used in the admissions process at the U.S. Naval Academy in determining the performance of candidates admitted. In determining student performance, graduation, Order of Merit (OOM), cumulative academic Quality Point Ratio (QPR), cumulative military QPR, and striper selection are used as performance outcome measures. The data is from Naval Academy graduation year groups 1995 through 2001. The analysis separates the Naval Academy's Whole Person Multiple into quantitative and qualitative inputs. The Candidate Multiple (CM) is the quantitative input to the admissions process derived from a statistics-based scoring model anchored in proven high school performance measures such as the SAT and high school GPA. The Recommendations of the Admissions Board (RAB) are the qualitative input, which awards points for subjective traits not captured in the CM or that are from various other subjective measures, such as student interviews and essays. This research highlights the properties of the two admissions factors and their estimated impact on student performance. The results show that student performance increased as CM and RAB increased, revealing the importance of a combined quantitative and qualitative admissions process, and emphasizing qualitative input as the value added factor that provides an increased predictability of student success. (26 tables, 22 figures, 26 refs.)