Optimization (Mathematics)

Abstract: This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.

Weld quality mainly depends on the weld bead geometry and mechanical-metallurgical characteristics of the welded joint which has a direct relationship with the type of welding process being used and its input process parameters i.e. welding current, arc voltage, travel speed etc. In the present study, determination of tungsten inert gas (TIG) welding input parameters for achieving maximum tensile strength of 316L austenitic stainless steel is investigated. Box-Behnken design of response surface methodology has been employed to formulate the experimental plan to identify the effect of process parameters on tensile strength. Square butt joint configuration has been made using three factors - three levels of welding input parameters. Joint strength has been evaluated by notch tensile strength (NTS) and Unnotch tensile strength (UTS) method and correlated with microstructure and micro hardness of the weld. The results indicate that gas flow rate has greater influence on both NTS and UTS...

We study the problem of linear programming in the setting of a vector space over a linearly ordered (commutative or skew) field. The dimension of the space may be infinite. The objective function is a linear mapping into another linearly ordered vector space over the same field. In that algebraic setting, we recall known results: Farkas' Lemma, Gale's Theorem of the alternative, and the Duality Theorem for linear programming with a finite number of linear constraints. Given that "semi-infinite" case, i.e. results for finite systems of linear inequalities in an infinite-dimensional space, we are motivated to consider the infinite case: infinite systems of linear inequalities in an infinite-dimensional space. Given such a system, we assume that only a finite number of the left-hand sides is non-zero at a point. We shall also assume a certain constraint qualification (CQ), presenting counterexamples violating the (CQ). Then, in the described setting, we formulate an infinite variant of Farkas' Lemma along with an infinite variant of Gale's Theorem of the alternative; we also formulate the problem of an infinite linear programming, its dual problem, and the Duality Theorem for the problems. Finally, we show an application to the problems of semi-infinite linear programming and put a question for further research.

In this research, a new algorithm of conjugation algorithms was developed to solve nonlinear optimization problems. This algorithm depend on a new search direction(í µí²… í µí²Š = −í µí±¯ í µí²Š −í µí¿ í µí²ˆ í µí²Š + í µí²‘í µí²ˆ í µí²Š). Numerical results proved the efficiency of the proposed algorithm compared to other algorithms

Multicasting is emerging as an enabling technology for multimedia transmissions over wireless networks to support several groups of users with flexible quality of service (QoS) requirements. Although multicast has huge potential to push the limits of next generation communication systems; it is however one of the most challenging issues currently being addressed. In this survey, we explain multicast group formation and various forms of group rate determination approaches. We also provide a systematic review of recent channel-aware multicast scheduling and resource allocation (MSRA) techniques proposed for downlink multicast services in OFDMA based systems. We study these enabling algorithms, evaluate their core characteristics, limitations and classify them using multidimensional matrix. We cohesively review the algorithms in terms of their throughput maximization, fairness considerations, performance complexities, multi-antenna support, optimality and simplifying assumptions. We discuss existing standards employing multicasting and further highlight some potential research opportunities in multicast systems.

The specification of the factor used by the ancient Egyptians to locate their royal pyramids has been an age-old great interest of many archaeologists, some of them concluded that the reason behind the locating of the ancient royal pyramids over such a large territory may never been deduced. This article proposes a new theorem entitled "Royal Pyramids Linearity" (RPL) to introduce a common factor between the majorities of the ancient royal pyramids' locations in Egypt. The theorem is developed based on an assumption of the existence of linear connections between the ancient locations of some pyramids in Giza, Abusir, Saqqara and Dahshur. The theorem is proved mathematically through the construction of an optimization model that combined hypothesis testing and regression analysis. The model examined 43 royal pyramids. The results emphasized the existence of mathematical linear relationships of 34 that represent all the known royal pyramids constructed starting from the ...

A chromatography-based model of retention time and peak width is rigorously derived. The model predicts peak capacity and density of peak capacity for complex samples. Direct application to separation of urine samples for global metabolic profiling. Successful model application to multi-factorial optimization of UHPLC-MS methods. The model is satisfactory to predict the MS-detected feature density of metabolites.

This study aims to develop a simulation/optimization model for the
solution to the problem of determining on-street parking places in urban road networks. The problem is dealt within the Discrete Network Design (DND) context due to the binary decision variables and the bi-level programming technique is used for the solution of the problem. The upper level represents the determination of on-street parking places while the reaction of drivers’ to the design is handled in user equilibrium manner in the lower level. The upper level problem is formulized
as a non-linear mixed integer programming problem and the meta-heuristic Harmony Search (HS) optimization technique is employed for the solution. In the proposed model, VISUM traffic analysis software is utilized as the simulation tool for solving the lower level problem. The performance of the proposed model is tested on Sioux-Falls road network which has widely been used on DND studies in the previous works. Results show that determining optimal or near-optimal
on-street parking places may be achieved by using the proposed model.

Applying method of Lagrange multipliers, an attempt has been made to derive mathematical formulation to workout optimal purchasing policy in order to maximize utility of an individual consumer subject to multiple constraints; in this particular illustration, two constraints: 1) budget constraint, and 2) coupon constraint. An explicit example is given in order to examine the behaviour of an individual consumer and to support the analytical arguments, using comparative static analysis.

This paper presents a new modification of Harmony Search (HS) algorithm to improve its accuracy and convergence speed and eliminates setting parameters that have to be defined before optimization process and it is difficult to predict fixed values for all kinds of problems. The proposed algorithm is named Global Dynamic Harmony Search (GDHS). In this modification, all the key parameters are changed to dynamic mode and there is no need to predefine any parameters; also the domain is changed to dynamic mode to help a faster convergence. Two experiments, with large sets of benchmark functions, are executed to compare the proposed algorithms with other ones. In the first experiment, 15 benchmark problems are used to compare the proposed algorithm with other similar algorithms based on the Harmony Search method and in the second experiment, 47 benchmark problems are used to compare the performance of the GDHS with other algorithms from different families, including: GA, PSO, DE and ABC algorithms. Results showed that the proposed algorithm outperforms the other algorithms, considering the point that the GDHS does not require any predefined parameter.

In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR , PRP with
two new Beta .These two new Beta possess global convergence properties using the exact line search. Preliminary numerical
results show that, the two new Beta  is very promising and efficient when compared to CG coefficients FR  , PRP

Satellite scheduling, like all scheduling, is the problem of mapping tasks (observation, communication, downlink, control maneuvers, etc.) to resources (sensor satellites, relay satellites, ground stations, etc.). Through our work on satellite scheduling problems, we have encountered many different constraints that are particular to the satellite-scheduling domain. In this paper, we will introduce the satellite mission-operation scheduling problem, describing the problem constraints that are particular to satellite scheduling, and then present the constraint-based techniques that we have used to address these problems.

Competition in the current marketplace requires businesses to provide consumers with the utmost convenience in purchas-ing services and goods. Buyers expect that, as an aftersales service and risk reliever, they can “return ” goods if they are not satisfied with them. Such product returns significantly influence retailers ’ profits not only because of a reduction in net sales but also because of increased costs. Despite its substantial impact, research focused on retailer–consumer return policies has been limited. To fill this gap, we study a retailer that has to set the product return policy parameters—specifically, the price and the return period. The impact of these parameters on consumers ’ valuation function is also taken into account. We study the model analytically and provide insights through various numerical examples. We find that even with fraudulent consumers ’ negative effect on sales, a retailer could expect both its profits and prices to increase with an optimally det...

We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) MATLAB code, students can optimally solve instances with up to 70 cities in a few minutes by adding cuts from the stronger formulation to the weaker, but simpler one. AMS subject classifications. 90C10, 90C11, 90C27, 90C57, 90-01, 97D40 PII. S0036144502368551 1. Introduction.

Mathematical modeling is an important step for developing many advanced technologies in various domains such as network security, data mining and etc…  This lecture introduces a process  that the speaker summarizes from his past practice of mathematical modeling and  algorithmic solutions in IT industry, as  an applied mathematician, algorithm specialist or software engineer , and even as an  entrepreneur.  A practical problem from DLP  system will be used as an example for creating math models and providing algorithmic solutions.

Employees are regarded as the organization's backbone. The personnel who work for it determine the success or failure of a company. When trained, competent, and experienced personnel depart for greater opportunities, businesses must deal with the resulting challenges. The purpose of the research was to determine the level of employee unhappiness and the reasons why they would choose to change jobs. Once the dissatisfaction factor(s) of employees has/have been discovered, businesses can take appropriate action, which may aid in lowering the turnover rate. In this research, we attempt to develop a system that can forecast employee attrition using data from the Kaggle website's Employee dataset. To visualise the relationships between the attributes, we created a heatmap. We employed four different machine learning methods for prediction, including KNN (K-Nearest Neighbor), SVM (Support Vector Machine), Decision Tree, and Random Forest. The reasons for employee attrition in any ...

With the increasing variability of the demand and the growing intensity of the competition, it became indispensable for companies to make sure to meet their customers' needs. In this context, the coordination of operations plays an important role to satisfy not only the customers but also all partners of a supply chain. The coordination can be considered as one of the main elements of supply chain management. In order to achieve the objective of coordination, it is possible for a company to collaborate with their partners, or even competitors. This paper first reviews the existing methods to achieve coordination in decentralized systems, with the stochastic information, to satisfy variable demand, and then classifies these solutions into a framework. 

Preface Linear Optimization 1 (LO) is one of the most widely taught and applied mathematical techniques. Due to revolutionary developments both in computer technology and algorithms for linear optimization, 'the last ten years have seen an estimated six orders of magnitude speed improvement'. 2 This means that problems that could not be solved 10 years ago, due to a required computational time of one year, say, can now be solved within some minutes. For example, linear models of airline crew scheduling problems with as many as 13 million variables have recently been solved within three minutes on a four-processor Silicon Graphics Power Challenge workstation. The achieved acceleration is due partly to advances in computer technology and for a significant part also to the developments in the field of so-called interior-point methods for linear optimization. Until very recently, the method of choice for solving linear optimization problems was the Simplex Method of Dantzig [59]. Since the initial formulation in 1947, this method has been constantly improved. It is generally recognized to be very robust and efficient and it is routinely used to solve problems in Operations Research, Business, Economics and Engineering. In an effort to explain the remarkable efficiency of the Simplex Method, people strived to prove, using the theory of complexity, that the computational effort to solve a linear optimization problem via the Simplex Method is polynomially bounded with the size of the problem instance. This question is still unsettled today, but it stimulated two important proposals of new algorithms for LO. The first one is due to Khachiyan in 1979 [167]: it is based on the ellipsoid technique for nonlinear optimization of Shor [255]. With this technique, Khachiyan proved that LO belongs to the class of polynomially solvable problems. Although this result has had a great theoretical impact, the new algorithm failed to deliver its promises in actual computational efficiency. The second proposal was made in 1984 by Karmarkar [165]. Karmarkar's algorithm is also polynomial, with a better complexity bound 1 The field of Linear Optimization has been given the name Linear Programming in the past. The origin of this name goes back to the Dutch Nobel prize winner Koopmans. See Dantzig [60]. Nowadays the word 'programming' usually refers to the activity of writing computer programs, and as a consequence its use instead of the more natural word 'optimization' gives rise to confusion. Following others, like Padberg [230], we prefer to use the name Linear Optimization in the book. It may be noted that in the nonlinear branches of the field of Mathematical Programming (like Combinatorial Optimization, Discrete Optimization, Semidefinite Optimization, etc.) this terminology has already become generally accepted. 2 This claim is due to R.E. Bixby, professor of Computational and Applied Mathematics at Rice University, and director of CPLEX Optimization, Inc., a company that markets algorithms for linear and mixed-integer optimization. See the news bulletin of the Center For Research on Parallel Computation, Volume 4, Issue 1, Winter 1996. Bixby adds that parallelization may lead to 'at least eight orders of magnitude improvement-the difference between a year and a fraction of a second!' 4 For Convex Optimization the reader may consult den Hertog [140], Nesterov and Nemirovski [226] and Jarre [161]. For Semidefinite Optimization we refer to Nesterov and Nemirovski [226], Vandenberghe and Boyd [48] and Ramana and Pardalos [236]. We also mention Shanno and Breitfeld and Simantiraki [252] for the related topic of barrier methods for nonlinear programming. 5 A recent survey on affine scaling methods was given by Tsuchiya [272]. 6 We refer the reader to, e.g., Potra [235], Bonnans and Potra [45], Wright [295, 297], Wright and Ralph [296] and the recent book of Wright [298].

This paper introduces an interactive approach to support multi-criteria decision analysis of project portfolios. In high-scale strategic decision domains, scientific studies suggest that the Decision Maker (DM) can find help by using many-objective optimisation methods, which are supposed to provide values in the decision variables that generate highquality solutions. Even so, DMs usually wish to explore the possibility of reaching some levels of benefits in some objectives. Consequently, they should repeatedly run the optimisation method. However, this approach cannot perform well-in an interactive way-for large instances under the presence of many objective functions. We present a mathematical model that is based on compromise programming and fuzzy outranking to aid DMs in analysing multi-criteria project portfolios on the fly. This approach allows relaxing the problem of rapidly optimising portfolios while preserving the beneficial properties of the DM's preferences expressed by outranking relations. Our model supports the decision analysis on two instance benchmarks: for the first one, a better compromise solution was generated 84% of the runs; for the second one, this ranged from 93% to 97%. Our model was also applied to a real-world problem involving social projects, obtaining satisfactory results.

Our aim is to estimate the perspective-effected geometric distortion of a scene from a video feed. In contrast to most related previous work, in this task we are constrained to using low-level, spatio-temporally local motion features only. This particular challenge arises in many semi-automatic surveillance systems which alert a human operator to potential abnormalities in the scene. Low-level, spatio-temporally local motion features are sparse (and thus require comparatively little storage space) and sufficiently powerful in the context of video abnormality detection to reduce the need for human intervention by more than 100-fold. This paper introduces three significant contributions: (i) we describe a dense algorithm for perspective estimation which uses motion features to estimate the perspective distortion at each image locus and then polls all such local estimates to arrive at the globally best estimate, (ii) we also present an alternative coarse algorithm which subdivides the image frame into blocks, and uses motion features to derive block-specific motion characteristics and constrain the relationships between these characteristics, with the perspective estimate emerging as a result of a global optimization scheme, and (iii) we report the results of an evaluation using nine large sets acquired using existing close-circuit television (CCTV) cameras, not installed specifically for the purposes of this work. Our findings demonstrate that both of the proposed methods are successful, their accuracy matching that of human labelling using complete visual data (by the constraints of the setup unavailable to our algorithms).

Nowadays, the fashion industry is moving towards fast fashion, offering a large selection of garment products in a quicker and cheaper manner. Machine learning is completely changing the trends in the fashion industry. From big to small every brand is using machine learning techniques in order to improve their revenue, increase customers and stay ahead of the trend. People are into fashion and they want to know what looks best and how they can improve their style and elevate their personality. Traditional recommendations for clothes consisted of lexical methods. However, visual-based recommendations have gained popularity over the past few years. This involves processing a multitude of images using different image processing techniques. In order to handle such a vast quantity of images, deep neural networks have been used extensively. With the help of fast pre trained algorithms, these networks provide results which are extremely accurate, within a small amount of time. However, there are still ways in which recommendations for clothes can be improved. In this paper, we propose a deep learning based system which operates as a personal assistant to a fashion user. The system’s architecture and all its components are presented, with emphasis on the data collection and data clustering subsystems. In our use case scenario, datasets of garment products are retrieved from Kaggle website which contains different outfit which includes t-shirt, shirts, shoes, dress, etc nearly 20 + categories. With this dataset, we trained our CNN model and the performance of it is over 84%. And our model can also recommend daily outfit to users.

Distribution and finding intervals contained of the zeros of the Riemann Zeta function. Abstract.. One of the most celebrated problems of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line s = 1/2. all the non trivial zeros lie in the critical strip, the number of such zeros with ordinate less than T is proportional to T log T, most zeros concentrate along the critical line s = 1/2, there exists an infinity of zeros on the critical line and moreover, more than two fifth of the zeros are on the critical line.Finding the roots by Lagrange method demarcating the intervals whose are not trivial zeros of the Zeta-function.

Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here we explore a new technique for combined physical system and control design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinitedimensional control design problems into finite dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and finegrained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to a new problem structures and new challenges. Here we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing codesign methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations.

The present paper is  concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex
subset  of a locally convex space  and taking values in a locally convex space ordered by a normal cone.
One proves also equi-Lipschitz properties for  pointwise bounded families of continuous convex mappings, provided the source space  is barrelled.
Some results  on Lipschitz properties  of continuous convex functions defined on metrizable topological vector spaces are included as well.

The objective of this research thesis is to investigate the effect of managerial skill on
operational performance in case of National Cement Share Company at dire dawa
administration. A combination of descriptive& explanatory research designs used to analyze
and interpret data collected through questionnaire. A Mixed strategy of qualitative and
quantitative research approach methods was used. Stratified random sampling technique was
used to collect questionnaire among different departments distributed for managers and
subordinates based on slovins sample size determination formulas. The target population
comprised of all the 317 employees in both in the managerial positions and subordinates in
which 290 response rates was used for data analysis. For the purpose of data collection, the
researcher used closed-ended questionnaires and both structured and semi structured
interviews. To analysis the data both descriptive statistics (measure of central tendency,
measure of dispersion and measure of location (e.g. percentages, frequencies; mean and
standard deviations)) and inferential statistics (correlation (spearman correlation) and
regression (ordinal logistic regression)) was used. T-tests used to test the significant of the
relationship between managerial skills and operational performance and to establish the
extent to which the predictor variable (managerial skills) explains the variation in dependent
variable (operational performance). . In the study, the researcher expected to afford Research
implications for cement manufacturing industries, Particularly National Cement Share
Company (NCSC) to improve the effect of managerial skill on operational performance
measured in terms of quality, cost, delivery and flexibility to achieve managerial goals. The
result of this study offers valuable inputs and directions for the cement industries to
consolidate their organizational productivity and knowledge management in order to increase
their operational performance. After all, research contributes for both educational and applied
knowledge in the context of Ethiopia in cement manufacturing industry. The finding of the
study shows that management skills (technical, human and cognitive) have a significant and
positive influence on Operational Performance.
The study recommended that measures must be undertaken to ensure that managers had
acquired some basic technical, human and conceptual skills to maximize the operational
performance of the company.
Key words: Managerial skills, operational performance, National Cement share company

This paper proposes the use of an improved version of the ɛ-constraint method for the design and optimization of a rectangular micro-channel heat sink. This study aims to optimize the geometric parameters describing the micro-channel, namely its width, its fin width and its depth. The thermal resistance and the pumping power, considered as indicators of the thermal performance, have been approximated by surrogated models based on Response Surface Approximation. The optimization task is formulated as a nonlinear programming problem. This approach has been implemented in GAMS. Sufficient details on both the single-criterion and multi-criteria formulation of the problem have been provided. The implications of the mathematical modelling formulation and the interrelationship between criteria and estimated quantities have been clarified. The use of the augmented ε-constraint method for the multi-objective optimization of a rectangular micro-channel heat sink constitutes the main contribution of this work.

The Golden Ratio(aka “golden mean”, “golden section” or “divine section”: standardly denoted with the capital Greek letter Phi) is the only positive (irrational) quadratic solution of the (minimal polynomial) x^2-x-1=0 equation, so that: Phi=[sqrt(5)+1]/2.
The purpose of this paper is to demonstrate some aspects recently discovered by the author of this paper:
(0) a recursive geometrical method for constructing  Phi (inspired from the Taoist religious iconography), which is more simple and elegant than Odom’s method;
(1) an occurrence of Phi  in the water molecule geometry;
(2) a quasi-Pythagorean property of the (Phi,e,PI)  triad;
(3) some other interesting quasi-exact relations between the elements of the (Phi,e,PI) triad;
(4) the tendency of the human systolic/diastolic blood pressure ratio to stabilize to a value close to  Phi with age

Keywords: Golden Ratio/section/mean (Phi), Odom’s method, Taoist religious iconography, water molecule geometry, quasi-Pythagorean property, human blood pressure

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A grid computing environment provides a type of distributed computation that is unique because it is not centrally managed and it has the capability to connect heterogeneous resources. A grid system provides location-independent access to the resources and services of geographically distributed machines. An essential ingredient for supporting location-independent computations is the ability to discover resources that have been requested by the users. Because the number of grid users can increase and the grid environment is continuously changing, a scheduler that can discover decentralized resources is needed. Grid resource scheduling is considered to be a complicated, NP-hard problem because of the distribution of resources, the changing conditions of resources, and the unreliability of infrastructure communication. Various artificial intelligence algorithms have been proposed for scheduling tasks in a computational grid. This paper uses the imperialist competition algorithm (ICA) to address the problem of independent task scheduling in a grid environment, with the aim of reducing the makespan. Experimental results compare ICA with other algorithms and illustrate that ICA finds a shorter makespan relative to the others.  Moreover, it converges quickly, finding its optimum solution in less time than the other algorithms.

We present a particular theorem of the alternative for finite systems of linear inequalities. The theorem is universal in the sense that other classical theorems of the alternative (Motzkin's Theorem and Tucker's Theorem) are implicit in it; the theorem itself is an extension of Farkas' Lemma. The presented result also generalizes and unifies both Dax's new theorem the alternative [Dax, A. (1993). Annals of Operations Research, 46, 11-60] and Rohn's residual existence theorem for linear equations [Rohn, J. (2010). Optimization Letters, 4, 287-292]. The universal theorem of the alternative is established by using Farkas' Lemma in the setting of a vector space over a linearly ordered (commutative or skew) field.

Programimi Linear(PL) është një degë e matematikës që lidhet me zgjidhjen e një morie problemash praktike: posacërisht me gjetjen e zgjidhjeve optimale të tyre. Raste speciale të problemave të tilla janë problemat me rrjedhje në një rrjet dhe ato të fushave ekonomike (për planifikime optimale të prodhimit apo për shpërndarje optimale të produkteve). PL është e lidhur ngushtësisht edhe me sajimin e algoritmeve të shpejtë dhe sa më efektivë si dhe të programeve kompjuterike përkatës që përdoren për zgjidhjen e problemave PL. Si rezultat i përpjekjeve të bëra për këto algoritme ka lindur dega e vecante e matematikës: teoria e optimizimit e cila përfshin dualitetin, dekompozimin, konveksitetin dhe përgjithësimet e tyre. Idea e përgjithshme e probemave nga fusha ekonomike është maksimizimi i fitimit dhe minimizimi i kostove në mjedisin material me burime të kufizuara.

This paper propose a practical optimization problem of product-mix based on labor
capacity, machine capacity, raw materials and demand constrains in a Sri Lankan tea
producing company. The objective is to profit maximization, satisfying all constraints.
In this paper, the problem is formulated as a linear programming model. As a case
study, a software package (LINGO 9.0) is applied to solve the optimization problem.
As with any LP model, the reduced costs for decision variables and dual prices and
allowable fluctuation for constraints are used to conduct detailed sensitivity analysis.
Eventually, this paper comes up with a set of policy making suggestions which might
be helpful for the production planning and detailed scheduling.

One of the most challenging tasks in today's food industry is controlling the product quality throughout the food supply chain. In this paper, we integrate food quality in decision-making on production and distribution in a food supply chain. We provide a methodology to model food quality degradation in such a way that it can be integrated in a mixed-integer linear programming model used for production and distribution planning. The resulting model is applied in an illustrative case study, and can be used to design and operate food distribution systems, using both food quality and cost criteria.

This paper proposes a logic-based approach to optimization that combines solution methods from mathematical programming and logic programming. From mathematical programming it borrows strategies for exploiting structure that have logic-based analogs. From logic programming it borrows methods for extracting information that are unavailable in a traditional mathematical programming framework. Logic-based methods also provide a unified approach to solving optimization problems with both quantitative and logical constraints.

Artificial intelligence research is a rapidly growing field. Here we provide a brief survey of artificial neural networks, an essential component of AI research. We briefly introduce the way neural networks work, along with several types of neural networks currently used. Then, we explore an evolutionary method of creating neural networks. Several of these are implemented in silico, and results are analyzed.

In this paper we approach a typical warehouse problem that is common to most industrial businesses, were efficiency is given by the best arrangement of items in the warehouse (slotting) and the best picking routes selected for each order (picking). Yet, when implementing picking and slotting optimization techniques, the information used is historical data that, in most cases, would fail to work given the many factors that affect daily warehousing operations. On the other hand, simulation models have been used to make virtual scenarios of a warehouse and can predict, with some accuracy, what would happen if a specific decision was made, but these models also fail to work, due to the fact that the data collected is not a reliable one. Given the complexity of most warehouses, we have designed a Warehouse Management System (WMS) that functions dynamically with real-time data, through the use of RFID technology and the integration of simulation and optimization models.