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The intended audience of this guide is developers who seek to optimize their interactive 3D rendering applications for Intel® Processor Graphics Xe-LP. It is assumed that the developer has a fundamental understanding of the graphics API pipelines for Microsoft DirectX 12, Vulkan*, and/or Metal 2. Intel® Processor Graphics Xe-LP also supports the DirectX 11 and OpenGL* graphics APIs; however, there are performance benefits and lower CPU overhead for applications that use the newer and lower level APIs such as DirectX 12, Vulkan*, and Metal 2, and also new graphics architecture features that are only available in these APIs.

The game or 3D application must ensure that its rendering swap chain implements asynchronous buffer flips. On displays that support Adaptive Sync, this results in smooth interactive rendering, with the display refresh dynamically synchronized with the asynchronous swap chain flips. If application and platform conditions are met, the Xe-LP driver enables Adaptive Sync by default. There is also an option to disable it using the Intel graphics control panel. For more information on enabling Adaptive Sync, please refer to Enabling Intel® Adaptive Sync guide.

Intel® GPA Framework is a cross-platform, cross-API suite of tools and interfaces, which allows users to capture, playback and analyze graphics applications.In a nutshell, an Intel® GPA Framework user can do a real time analysis of a running application using custom layers, capture a multi frame stream of a running application starting either from application startup or an arbitrary point of time, playback the stream to recreate the application graphics execution or create a script that can play back a stream up to a given frame, get a list of API calls, get metrics, and produce a performance regression report.

While the scope of this guide is only limited to performance optimizations on Xe-LP, this guide provides an overview of key features that are helpful for developers when tuning performance on workloads that are more graphical in nature, such as gaming applications.

Modern graphics APIs like DirectX 12, Metal, and Vulkan* give developers more control over lower level choices that were once handled in driver implementations. Although each API is different, there are general recommendations for application developers that are API independent.

Mobile and ultra-mobile computing are ubiquitous. On these platforms, power is shared between CPU and GPU, so optimizing for CPU can frequently result in GPU performance gains.As a result, battery life, device temperature, and power-limited performance have become significant issues. As manufacturing processes continue to shrink and improve, we see improved performance per-watt characteristics of CPUs and processor graphics. However, there are many ways that software can reduce power use on mobile devices, as well as improve power efficiency. In the following sections, you will find insights and recommendations illustrating how to best recognize these performance gains.

The latest graphics APIs (DirectX 12, Vulkan*, and Metal 2) can dramatically reduce CPU overhead, resulting in lower CPU power consumption given a fixed frame rate (33 fps), as shown on the left side in the figure below. When unconstrained by frame rate the total power consumption is unchanged, but there is a significant performance boost due to increased GPU utilization. See the Asteroids* and DirectX* 12 white paper for full details.

While some graphics optimizations focus on reducing geometric level of detail, checkerboard rendering (CBR) reduces the amount of shading done that is imperceptible. The technique produces full resolution pixels that are compatible with modern post processing techniques and can be implemented for both forward and deferred rendering. More information, implementation details, and sample code can be found in the white paper Checkerboard Rendering for Real-Time Upscaling on Intel Integrated Graphics.

The GPU Detect sample demonstrates how to get the vendor and ID from the GPU. For Intel® Processor Graphics, the sample also demonstrates a default graphics quality preset (low, medium, or high), support for DirectX 9 and DirectX 11 extensions, and the recommended method for querying the amount of video memory. If supported by the hardware and driver, it also shows the recommended method for querying the minimum and maximum frequencies.

Register below to download and run the SolverSetup program that installs Premium Solver Platform (aka Analytic Solver Optimization) with a free 15-day trial license. You can use every feature of the software, solve real problems, examine the full User Guide and Help, and get expert technical support -- all without any obligation. You can download immediately, or return later for your free trial.

You can also download precompiled executables of SCIP with which you can solve MIP, MIQCP, CIP, SAT, or PBO instances in MPS, LP, RLP, ZIMPL, flatzinc, CNF, OPB, WBO, PIP, or CIP format. Note that these executables do not include the readline features (i.e., command line editing and history) due to license issues. However, you can download the free readline wrapper rlwrap to provide this missing feature to the executables.

The number of SCIP downloads is tracked and used to generate statistics about the downloads and to generate the world map of download locations.The personal information is used to distinguish the number of downloads from the number of users per year that might download more than one version or archive.In addition to the privacy statements of ZIB, we hereby declare that your name and affiliation recorded for the SCIP download is used for purposes of granting licenses and for statistics about software downloads, and is processed and stored on our server for the duration of a year.

Deterministic Modeling:Linear Optimization with ApplicationsPara mis visitantes del mundo de habla hispana,este sitio se encuentra disponible en español en: Versión en Español Sitio Espejo para América Latina A mathematical optimization model consists of an objective function and a set of constraints in the form of a system of equations or inequalities. Optimization models are used extensively in almost all areas of decision-making, such as engineering design and financial portfolio selection. This site presents a focused and structured process for optimization problem formulation, design of optimal strategy, and quality-control tools that include validation, verification, and post-solution activities.Professor Hossein Arsham To search the site, try Edit | Find in page [Ctrl + f]. Enter a word or phrase in the dialogue box, e.g. "parameter " or "linear " If the first appearance of the word/phrase is not what you are looking for, try Find Next. MENUIntroduction & SummaryOptimization-Modeling ProcessIngredients of Optimization Problems and Their ClassificationLinear Programming (LP)Dual Problem: Its Construction and Economics ImplicationsLearning From the Optimal StrategyGoal-Seeking ProblemExercise Your Knowledge to Enhance What You Have Learned (PDF)Linear Optimization Solvers to Download (free-of-charge)Companion Sites:Success Science Leadership Decision Making Linear Optimization Software to Download Artificial-variable Free LP Solution Algorithms Integer Optimization and the Network Models Tools for LP Modeling Validation The Classical Simplex Method Zero-Sum Games with ApplicationsComputer-assisted Learning Concepts and Techniques Linear Algebra and LP Connections From Linear to Nonlinear Optimization with Business Applications Construction of the Sensitivity Region for LP Models Zero Sagas in Four Dimensions Probabilistic Modeling Systems Simulation Compendium of Web Site Review Keywords and Phrases Collection of JavaScript E-labs Learning Objects Decision Science Resources Ingredients of Optimization Problems and Their ClassificationIntroduction Bilevel Optimization Combinatorial Optimization Constraint Satisfaction Convex Program Data Envelopment Analysis Dynamic ProgrammingEvolutionary & Genetic TechniquesFractional Program Games TheoryGeometric ProgramGlobal Optimization Heuristic Optimization Linearly Constrained Global OptimizationLinear ProgramMetaheuristics Multilevel Optimization Multiobjective Program Non-Binary Constraints ProgramNonconvex Program Nonsmooth ProgramOnline Optimization Particle Swarm OptimizationQuadratic Program Separable ProgramSwarm Intelligence Linear Programming (LP)Introduction LP Problem Formulation Process and Its Applications The Carpenter's Problem: Allocating scarce resources among competitive means A Product-Replacement ProblemA Diet ProblemA Blending ProblemOther Common Applications of LPGraphical Solution Method (two-dimensional decisions)Links Between LP and Systems of Equations: Algebraic MethodExtension to Higher Dimensions Numerical Example: The Transportation ProblemHow to Solve a Linear System of Equations by LP Solvers?The Dual Problem: Its Construction and Economics Implications Dual Problem: Construction and Its MeaningsThe Dual Problem of the Carpenter's ProblemManagerial Roundoff ErrorComputation of Shadow PricesBehavior of Changes in the RHS Values of the Optimal ValueLearning From the Optimal Strategy: Sensitivity, Specificity, Structural, and the "What-if" AnalysisDealing with Uncertainties and Scenario ModelingComputation of Sensitivity Ranges for Small Size ProblemsMarginal Analysis & Factors Prioritization What Is the 100% Rule (sensitivity region)Adding a New ConstraintDeleting a ConstraintReplacing a ConstraintChanges in the Coefficients of ConstraintsAdding a Variable (e.g., Introducing a new product)Deleting a Variable (e.g., Terminating a product)Optimal Resource Allocation ProblemDetermination of Product's Least Net ProfitMin Max & Max Min Computation in a Single-RunFeasibility Problem: Goal-Seeking IndicatorsIntroduction & SummaryDecision-making problems may be classified into two categories: deterministic and probabilistic decision models. In deterministic models good decisions bring about good outcomes. You get that what you expect; therefore, the outcome is deterministic (i.e., risk-free). This depends largely on how influential the uncontrollable factors are in determining the outcome of a decision, and how much information the decision-maker has in predicting these factors.Those who manage and control systems of men and equipment face the continuing problem of improving (e.g., optimizing) system performance. The problem may be one of reducing the cost of operation while maintaining an acceptable level of service, and profit of current operations, or providing a higher level of service without increasing cost, maintaining a profitable operation while meeting imposed government regulations, or "improving" one aspect of product quality without reducing quality in another. To identify methods for improvement of system operation, one must construct a synthetic representation or model of the physical system, which could be used to describe the effect of a variety of proposed solutions.A model is a representation of the reality that captures "the essence" of reality. A photograph is a model of the reality portrayed in the picture. Blood pressure may be used as a model of the health of an individual. A pilot sales campaign may be used to model the response of individuals to a new product. In each case the model captures some aspect of the reality it attempts to represent. Since a model only captures certain aspects of reality, it may be inappropriate for use in a particular application for it may capture the wrong elements of the reality. Temperature is a model of climatic conditions, but may be inappropriate if one is interested in barometric pressure. A photograph of a person is a model of that individual, but provides little information regarding his or her academic achievement. An equation that predicts annual sales of a particular product is a model of that product, but is of little value if we are interested in the cost of production per unit. Thus, the usefulness of the model is dependent upon the aspect of reality it represents. If a model does capture the appropriate elements of reality, but capture the elements in a distorted or biased manner, then it still may not be useful. An equation predicting monthly sales volume may be exactly what the sales manager is looking for, but could lead to serious losses if it consistently yields high estimates of sales. A thermometer that reads too high or too low would be of little use in medical diagnosis. A useful model is one that captures the proper elements of reality with acceptable accuracy. Mathematical optimization is the branch of computational science that seeks to answer the question `What is best?' for problems in which the quality of any answer can be expressed as a numerical value. Such problems arise in all areas of business, physical, chemical and biological sciences, engineering, architecture, economics, and management. The range of techniques available to solve them is nearly as wide. A mathematical optimization model consists of an objective function and a set of constraints expressed in the form of a system of equations or inequalities. Optimization models are used extensively in almost all areas of decision-making such as engineering design, and financial portfolio selection. This site presents a focused and structured process for optimization analysis, design of optimal strategy, and controlled process that includes validation, verification, and post-solution activities. If the mathematical model is a valid representation of the performance of the system, as shown by applying the appropriate analytical techniques, then the solution obtained from the model should also be the solution to the system problem. The effectiveness of the results of the application of any optimization technique, is largely a function of the degree to which the model represents the system studied.To define those conditions that will lead to the solution of a systems problem, the analyst must first identify a criterion by which the performance of the system may be measured. This criterion is often referred to as the measure of the system performance or the measure of effectiveness. In business applications, the measure of effectiveness is often either cost or profit, while government applications more often in terms of a benefit-to-cost ratio. The mathematical (i.e., analytical) model that describes the behavior of the measure of effectiveness is called the objective function. If the objective function is to describe the behavior of the measure of effectiveness, it must capture the relationship between that measure and those variables that cause it to change. System variables can be categorized as decision variables and parameters. A decision variable is a variable, that can be directly controlled by the decision-maker. There are also some parameters whose values might be uncertain for the decision-maker. This calls for sensitivity analysis after finding the best strategy. In practice, mathematical equations rarely capture the precise relationship between all system variables and the measure of effectiveness. Instead, the OR/MS/DS analyst must strive to identify the variables that most significantly affect the measure of effectiveness, and then attempt to logically define the mathematical relationship between these variables and the measure of effectiveness. This mathematical relationship is the objective function that is used to evaluate the performance of the system being studied. Formulation of a meaningful objective function is usually a tedious and frustrating task. Attempts to develop the objective function may fail. Failure could result because the analyst chose the wrong set of variables for inclusion in the model, because he fails to identify the proper relationship between these variables and the measure of effectiveness. Returning to the drawing board, the analyst attempts to discover additional variables that may improve his model while discarding those which seem to have little or no bearing. However, whether or not these factors do in fact improve the model, can only be determined after formulation and testing of new models that include the additional variables. The entire process of variable selection, rejection, and model formulation may require multiple reiteration before a satisfactory objective function is developed. The analyst hopes to achieve some improvement in the model at each iteration, although it is not usually the case. Ultimate success is more often preceded by a string of failures and small successes. At each stage of the development process the analyst must judge the adequacy and validity of the model. Two criteria are frequently employed in this determination. The first involves the experimentation of the model: subjecting the model to a variety of conditions and recording the associated values of the measure of effectiveness given by the model in each case. For example, suppose a model is developed to estimate the market value of single-family homes. The model will express market value in dollars as a function of square feet of living area, number of bedrooms, number of bathrooms, and lot size. After developing the model, the analyst applies the model to the valuation of several homes, each having different values for the characteristics mentioned above. For this, the analyst finds market value tends to decrease as the square feet of living area increases. Since this result is at variance with reality, the analyst would question the validity of the model. On the other hand, suppose the model is such that home value is an increasing function of each of the four characteristics cited, as we should generally expect. Although this result is encouraging, it does not imply that the model is a valid representation of reality, since the rate of increase with each variable may be inappropriately high or low. The second stage of model validation calls for a comparison of model results with those achieved in reality.A mathematical model offers the analyst a tool that he can manipulate in his/her analysis of the system under study, without disturbing the system itself. For example, suppose that a mathematical model has been developed to predict annual sales as a function of unit selling price. If the production cost per unit is known, total annual profit for any given selling price can easily be calculated. However, to determine the selling price to yield the maximum total profit, various values for the selling price can be introduced into the model one at a time. The resulting sales are noted and the total profit per year are computed for each value of selling price examined. By trial and error, the analyst may determine the selling price that will maximize total annual profit. Unfortunately, this approach does not guarantee that one obtained the optimal or best price, because the possibilities are enormous to try them all. The trial-and-error approach is a simple example for sequential thinking. Optimization solution methodologies are based on simultaneous thinking that result in the optimal solution. The step-by-step approach is called an optimization solution algorithm. Progressive Approach to Modeling: Modeling for decision making involves two distinct parties, one is the decision-maker and the other is the model-builder known as the analyst. The analyst is to assist the decision-maker in his/her decision-making process. Therefore, the analyst must be equipped with more than a set of analytical methods.Specialists in model building are often tempted to study a problem, and then go off in isolation to develop an elaborate mathematical model for use by the manager (i.e., the decision-maker). Unfortunately the manager may not understand this model and may either use it blindly or reject it entirely. The specialist may feel that the manager is too ignorant and unsophisticated to appreciate the model, while the manager may feel that the specialist lives in a dream world of unrealistic assumptions and irrelevant mathematical language.Such miscommunication can be avoided if the manager works with the specialist to develop first a simple model that provides a crude but understandable analysis. After the manager has built up confidence in this model, additional detail and sophistication can be added, perhaps progressively only a bit at a time. This process requires an investment of time on the part of the manager and sincere interest on the part of the specialist in solving the manager's real problem, rather than in creating and trying to explain sophisticated models. This progressive model building is often referred to as the bootstrapping approach and is the most important factor in determining successful implementation of a decision model. Moreover the bootstrapping approach simplifies otherwise the difficult task of model validating and verification processes.The purpose of this site is not to make the visitor an expert on all aspects of mathematical optimization, but to provide a broad overview of the field. We introduce the terminology of optimization and the ways in which problems and their solutions are formulated and classified. Subsequent sections consider the most appropriate methods for dealing with linear optimization, with emphasis placed on the formulation, solution algorithm, and the managerial implication of the optimal solution, with sensitivity analysis.Further Readings:Ackoff R., Ackoff's Best: His Classic Writings on Management, Wiley, 1999. Bender E., An Introduction to Mathematical Modeling, Dover Pubns, 2000. Fdida S., and G. Pujolle, Modeling Techniques and Performance Evaluation, Elsevier Science, 1987.Gershenfeld N., The Nature of Mathematical Modeling, Cambridge Univ. Pr., 1998. Optimization-Modeling ProcessOptimization problems are ubiquitous in the mathematical modeling of real world systems and cover a very broad range of applications. These applications arise in all branches of Economics, Finance, Chemistry, Materials Science, Astronomy, Physics, Structural and Molecular Biology, Engineering, Computer Science, and Medicine.Optimization modeling requires appropriate time. The general procedure that can be used in the process cycle of modeling is to: (1) describe the problem, (2) prescribe a solution, and (3) control the problem by assessing/updating the optimal solution continuously, while changing the parameters and structure of the problem. Clearly, there are always feedback loops among these general steps. Mathematical Formulation of the Problem: As soon as you detect a problem, think about and understand it in order to adequately describe the problem in writing. Develop a mathematical model or framework to re-present reality in order to devise/use an optimization solution algorithm. The problem formulation must be validated before it is offered a solution. A good mathematical formulation for optimization must be both inclusive (i.e., it includes what belongs to the problem) and exclusive (i.e., shaved-off what does not belong to the problem).Find an Optimal Solution: This is an identification of a solution algorithm and its implementation stage. The only good plan is an implemented plan, which stays implemented!Managerial Interpretations of the Optimal Solution: Once you recognize the algorithm and determine the appropriate module of software to apply, utilize software to obtain the optimal strategy. Next, the solution will be presented to the decision-maker in the same style and language used by the decision-maker. This means providing managerial interpretations of the strategic solution in layman's terms, not just handing the decision-maker a computer printout.Post-Solution Analysis: These activities include updating the optimal solution in order to control the problem. In this ever-changing world, it is crucial to periodically update the optimal solution to any given optimization problem. A model that was valid may lose validity due to changing conditions, thus becoming an inaccurate representation of reality and adversely affecting the ability of the decision-maker to make good decisions. The optimization model you create should be able to cope with changes.The Importance of Feedback and Control: It is necessary to place heavy emphasis on the importance of thinking about the feedback and control aspects of an optimization problem. It would be a mistake to discuss the context of the optimization-modeling process and ignore the fact that one can never expect to find a never-changing, immutable solution to a decision problem. The very nature of the optimal strategy's environment is changing, and therefore feedback and control are an important part of the optimization-modeling process. The above process is depicted as the Systems Analysis, Design, and Control stages in the following flow chart, including the validation and verification activities: Further Readings:Beroggi G., Decision Modeling in Policy Management: An Introduction to the Analytic Concepts, Boston, Kluwer Academic Publishers, 1999. Camm J., and J. Evans, Management Science: Modeling, Analysis, and Interpretation, South-Western College Pub., 1999. Ingredients of Optimization Problems and Their ClassificationThe essence of all businesslike decisions, whether made for a firm, or an individual, is finding a course of action that leaves you with the largest profit. Mankind has long sought, or professed to seek, better ways to carry out the daily tasks of life. Throughout human history, man has first searched for more effective sources of food and then later searched for materials, power, and mastery of the physical environment. However, relatively late in human history general questions began to quantitatively formulate first in words, and later developing into symbolic notations. One pervasive aspect of these general questions was to seek the "best" or "optimum". Most of the time managers seek merely to obtain some improvement in the level of performance, or a "goal-seeking" problem. It should be emphasized that these words do not usually have precise meanings.Efforts have been made to describe complex human and social situations. To have meaning, the problem should be written down in a mathematical expression containing one or more variables, in which the value of variables are to be determined. The question then asked, is what values should these variables have to ensure the mathematical expression has the greatest possible numerical value (maximization) or the least possible numerical value (minimization). This process of maximizing or minimizing is referred to as optimization.Optimization, also called mathematical programming, helps find the answer that yields the best result--the one that attains the highest profit, output, or happiness, or the one that achieves the lowest cost, waste, or discomfort. Often these problems involve making the most efficient use of resources--including money, time, machinery, staff, inventory, and more. Optimization problems are often classified as linear or nonlinear, depending on whether the relationship in the problem is linear with respect to the variables. There are a variety of software packages to solve optimization problems. For example, LINDO or your WinQSB solve linear program models and LINGO and What'sBest! solve nonlinear and linear problems. Mathematical Programming, solves the problem of determining the optimal allocations of limited resources required to meet a given objective. The objective must represent the goal of the decision-maker. For example, the resources may correspond to people, materials, money, or land. Out of all permissible allocations of the resources, it is desired to find the one or ones that maximize or minimize some numerical quantity such as profit or cost. Optimization models are also called Prescriptive or Normative models since they seek to find the best possible strategy for decision-maker.There are many optimization algorithms available. However, some methods are only appropriate for certain types of problems. It is important to be able to recognize the characteristics of a problem and identify an appropriate solution technique. Within each class of problems, there are different minimization methods, which vary in computational requirements, convergence properties, and so on. Optimization problems are classified according to the mathematical characteristics of the objective function, the constraints, and the controllable decision variables. Optimization problems are made up of three basic ingredients: An objective function that we want to minimize or maximize. That is, the quantity you want to maximize or minimize is called the objective function. Most optimization problems have a single objective function, if they do not, they can often be reformulated so that they do. The two interesting exceptions to this rule are: The goal seeking problem: In most business applications the manager wishes to achieve a specific goal, while satisfying the constraints of the model. The user does not particularly want to optimize anything so there is no reason to define an objective function. This type of problem is usually called a feasibility problem. Multiple objective functions: Often, the user would actually like to optimize many different objectives at once. Usually, the different objectives are not compatible. The variables that optimize one objective may be far from optimal for the others. In practice, problems with multiple objectives are reformulated as single-objective problems by either forming a weighted combination of the different objectives or else by placing some objectives as "desirable" constraints.The controllable inputs are the set of decision variables which affect the value of the objective function. In the manufacturing problem, the variables might include the allocation of different available resources, or the labor spent on each activity. Decision variables are essential. If there are no variables, we cannot define the objective function and the problem constraints. The uncontrollable inputs are called parameters. The input values may be fixed numbers associated with the particular problem. We call these values parameters of the model. Often you will have several "cases" or variations of the same problem to solve, and the parameter values will change in each problem variation. Constraints are relations between decision variables and the parameters. A set of constraints allows some of the decision variables to take on certain values, and exclude others. For the manufacturing problem, it does not make sense to spend a negative amount of time on any activity, so we constrain all the "time" variables to be non-negative. Constraints are not always essential. In fact, the field of unconstrained optimization is a large and important one for which a lot of algorithms and software are available. In practice, answers that make good sense about the underlying physical or economic problem, cannot often be obtained without putting constraints on the decision variables. Feasible and Optimal Solutions: A solution value for decision variables, where all of the constraints are satisfied, is called a feasible solution. Most solution algorithms proceed by first finding a feasible solution, then seeking to improve upon it, and finally changing the decision variables to move from one feasible solution to another feasible solution. This process is repeated until the objective function has reached its maximum or minimum. This result is called an optimal solution. The basic goal of the optimization process is to find values of the variables that minimize or maximize the objective function while satisfying the constraints. This result is called an optimal solution. There are well over 4000 solution algorithms for different kinds of optimization problems. The widely used solution algorithms are those developed for the following mathematical programs: convex programs, separable programs, quadratic programs and the geometric programs. Linear Program Linear programming deals with a class of optimization problems, where both the objective function to be optimized and all the constraints, are linear in terms of the decision variables.A short history of Linear Programming:In 1762, Lagrange solved tractable optimization problems with simple equality constraints.In 1820, Gauss solved linear system of equations by what is now call Causssian elimination. In 1866 Wilhelm Jordan refinmened the method to finding least squared errors as ameasure of goodness-of-fit. Now it is referred to as the Gauss-Jordan Method.In 1945, Digital computer emerged.In 1947, Dantzig invented the Simplex Methods.In 1968, Fiacco and McCormick introduced the Interior Point Method.In 1984, Karmarkar applied the Interior Method to solve Linear Programs adding his innovative analysis. Linear programming has proven to be an extremely powerful tool, both in modeling real-world problems and as a widely applicable mathematical theory. However, many interesting optimization problemsare nonlinear. The study of such problems involves a diverse blend of linear algebra, multivariatecalculus, numerical analysis, and computing techniques. Important areas include the design ofcomputational algorithms (including interior point techniques for linear programming), the geometryand analysis of convex sets and functions, and the study of specially structured problems such asquadratic programming. Nonlinear optimization provides fundamental insights into mathematicalanalysis and is widely used in a variety of fields such as engineering design, regression analysis, inventory control, geophysical exploration, and economics.Quadratic Program Quadratic Program (QP) comprises an area of optimization whose broad range of applicability is second only to linear programs. A wide variety of applications fall naturally into the form of QP. The kinetic energy of a projectile is a quadratic function of its velocity. The least-square regression with side constraints has been modeled as a QP. Certain problems in production planning, location analysis, econometrics, activation analysis in chemical mixtures problem, and in financial portfolio management and selection are often treated as QP. There are numerous solution algorithms available for the case under the restricted additional condition, where the objective function is convex. Constraint Satisfaction Many industrial decision problems involving continuous constraints can be modeled as continuous constraint satisfaction and optimization problems. Constraint Satisfaction problems are large in size and in most cases involve transcendental functions. They are widely used in chemical processes and cost restrictions modeling and optimization.Convex Program Convex Program (CP) covers a broad class of optimization problems. When the objective function is convex and the feasible region is a convex set, both of these assumptions are enough to ensure that local minimum is a global minimum.Data Envelopment Analysis The Data Envelopment Analysis (DEA) is a performance metric that is grounded in the frontier analysis methods from the economics and finance literature. Frontier efficiency (output/input) analysis methods identify best practice performance frontier, which refers to the maximal outputs that can be obtained from a given set of inputs with respect to a sample of decision making units using a comparable process to transform inputs to outputs. The strength of DEA relies partly on the fact that it is a non-parametric approach, which does not require specification of any functional form of relationships between the inputs and the outputs. DEA output reduces multiple performance measures to a single one to use linear programming techniques. The weighting of performance measures reacts to the decision-maker's utility.Dynamic ProgrammingDynamic programming (DP) is essentially bottom-up recursion where you store the answers in a table starting from the base case(s) and building up to larger and larger parameters using the recursive rule(s). You would use this technique instead of recursion when you need to calculate the solutions to all the sub-problems and the recursive solution would solve some of the sub-problems repeatedly. While generally DP is capable of solving many diverse problems, it may require huge computer storage in most cases.Separable Program Separable Program (SP) includes a special case of convex programs, where the objective function and the constraints are separable functions, i.e., each term involves just a single variable.Geometric Program Geometric Program (GP) belongs to Nonconvex programming, and has many applications in particular in engineering design problems.Fractional Program In this class of problems, the objective function is in the form of a fraction (i.e., ratio of two functions). Fractional Program (FP) arises, for example, when maximizing the ratio of profit capital to capital expended, or as a performance measure wastage ratio.Heuristic Optimization A heuristic is something "providing aid in the direction of the solution of a problem but otherwise unjustified or incapable of justification." So heuristic arguments are used to show what we might later attempt to prove, or what we might expect to find in a computer run. They are, at best, educated guesses.Several heuristic tools have evolved in the last decade that facilitate solving optimizationproblems that were previously difficult or impossible to solve. These tools include evolutionarycomputation, simulated annealing, tabu search, particle swarm, etc.Common approaches include, but are not limited to: comparing solution quality to optimum on benchmark problems withknown optima, average difference from optimum, frequency with which theheuristic finds the optimum. comparing solution quality to a best knownbound for benchmark problems whose optimal solutions cannot be determined. comparing your heuristic to published heuristics for the sameproblem type, difference in solution quality for a given run time and,if relevant, memory limit. profiling average solution quality as a function of run time, forinstance, plotting mean and either min and max or 5th and 95thpercentiles of solution value as a function of time -- this assumes thatone has multiple benchmark problem instances that are comparable.Global Optimization The aim of Global Optimization (GO) is to find the best solution of decision models, in presence of the multiple local solutions. While constrained optimization is dealing with finding the optimum of the objective function subject to constraints on its decision variables, in contrast, unconstrained optimization seeks the global maximum or minimum of a function over its entire domain space, without any restrictions on decision variables.Nonconvex Program A Nonconvex Program (NC) encompasses all nonlinear programming problems that do not satisfy the convexity assumptions. However, even if you are successful at finding a local minimum, there is no assurance that it will also be a global minimum. Therefore, there is no algorithm that will guarantee finding an optimal solution for all such problem.Nonsmooth Program Nonsmooth Programs (NSP) contain functions for which the first derivative does not exist. NSP are arising in several important applications of science and engineering, including contact phenomena in statics and dynamics or delamination effects in composites. These applications require the consideration of nonsmoothness and nonconvexity.Metaheuristics Most metaheuristics have been created for solving discrete combinatorial optimization problems. Practical applications in engineering, however, usually require techniques, which handle continuous variables, or miscellaneous continuous and discrete variables. As a consequence, a large research effort has focused on fitting several well-known metaheuristics, like Simulated Annealing (SA), Tabu Search (TS), Genetic Algorithms (GA), Ant Colony Optimization (ACO), to the continuous cases. The general metaheuristics aim at transforming discrete domains of application into continuous ones, by means of: Methodological developments aimed at adapting some metaheuristics, especially SA, TS, GA, ACO, GRASP, variable neighborhood search, guided local search, scatter search, to continuous or discrete/continuous variable problems.Theoretical and experimental studies on metaheuristics adapted to continuous optimization, e.g., convergence analysis, performance evaluation methodology, test-case generators, constraint handling, etc.Software implementations and algorithms for metaheuristics adapted to continuous optimization.Real applications of discrete metaheuristics adapted to continuous optimization.Performance comparisons of discrete metaheuristics (adapted to continuous optimization) with that of competitive approaches, e.g., Particle Swarm Optimization (PSO), Estimation of Distribution Algorithms (EDA), Evolutionary Strategies (ES), specifically created for continuous optimization.Multilevel Optimization In many decision processes there is a hierarchy of decision makers and decisions are taken at different levels in thishierarchy. Multilevel Optimization focuses on the whole hierarchystructure. The field of multilevel optimization has become a well known and important research field. Hierarchical structures can be found in scientific disciplines such as environment,ecology, biology, chemical engineering, mechanics, classification theory, databases, network design, transportation, supply chain, game theory and economics. Moreover, new applications are constantly being introduced.Multiobjective Program Multiobjective Program (MP) known also as Goal Program, is where a single objective characteristic of an optimization problem is replaced by several goals. In solving MP, one may represent some of the goals as constraints to be satisfied, while the other objectives can be weighted to make a composite single objective function.Multiple objective optimization differs from the single objective case in several ways:The usual meaning of the optimum makes no sense in the multiple objective case because the solution optimizing all objectives simultaneously is, in general, impractical; instead, a search is launched for a feasible solution yielding the best compromise among objectives on a set of, so called, efficient solutions; The identification of a best compromise solution requires taking into account the preferences expressed by the decision-maker; The multiple objectives encountered in real-life problems are often mathematical functions of contrasting forms.A key element of a goal programming model is the achievement function; that is, the function that measures the degree of minimisation of the unwanted deviation variables of the goals considered in the model. A Business Application: In credit card portfolio management, predicting the cardholder's spending behavior is a key to reduce the risk of bankruptcy. Given a set of attributes for major aspects of credit cardholders and predefined classes for spending behaviors, one might construct a classification model by using multiple criteria linear programming to discover behavior patterns of credit cardholders.Non-Binary Constraints Program Over the years, the constraint programming community has paid considerable attention to modeling and solving problems by using binary constraints. Only recently has non-binary constraints captured attention, due to growing number of real-life applications. A non-binary constraint is a constraint that is defined on k variables, where k is normally greater than two. A non-binary constraint can be seen as a more global constraint. Modeling a problem as a non-binary constraint has two main advantages: It facilitates the expression of the problem; and it enables more powerful constraint propagation as more global information becomes available. Success in timetabling, scheduling, and routing, has proven that the use of non-binary constraints is a promising direction of research. In fact, a growing number of OR/MS/DS workers feel that this topic is crucial to making constraint technology a realistic way to model and solve real-life problems. Bilevel Optimization Most of the mathematical programming models deal with decision-making with a single objective function. The bilevel programming on the other hand is developed for applications in decentralized planning systems in which the first level is termed as the leader and the second level pertains to the objective of the follower. In the bilevel programming problem, each decision maker tries to optimize its own objective function without considering the objective of the other party, but the decision of each party affects the objective value of the other party as well as the decision space. Bilevel programming problems are hierarchical optimization problems where the constraints of one problem are defined in part by a second parametric optimization problem. If the second problem has a unique optimal solution for all parameter values, this problem is equivalent to usual optimization problem having an implicitly defined objective function. However, when the problem has non-unique optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are being applied.Combinatorial Optimization Combinatorial generally means that the state space is discrete (e.g., symbols, not necessarilynumbers). This space could be finite or denumerable sets. For example, a discrete problem is combinatorial. Problems where the state space is totally ordered can often be solved by mapping them to the integers and applying "numerical" methods. If the state space is unordered or only partially ordered, these methods fail. This means that the heuristics methods becomes necessary, such as simulated annealing.Combinatorial optimization is the study of packing, covering, and partitioning, which are applications of integer programs. They are the principle mathematical topics in the interface between combinatorics and optimization. These problems deal with the classification of integer programming problems according to the complexity of known algorithms, and the design of good algorithms for solving special subclasses. In particular, problems of network flows, matching, and their matroid generalizations are studied. This subject is one of the unifying elements of combinatorics, optimization, operations research, and computer science.Evolutionary Techniques Nature is a robust optimizer. By analyzing nature's optimization mechanism we may find acceptable solution techniques to intractable problems. Two concepts that have most promise are simulated annealing and the genetic techniques. Scheduling and timetabling are amongst the most successful applications of evolutionary techniques.Genetic Algorithms (GAs) have become a highly effective tool for solving hard optimization problems. However, its theoretical foundation is still rather fragmented.Particle Swarm Optimization Particle Swarm Optimization (PSO) is a stochastic, population-based optimization algorithm. Instead of competition/selection, like say in Evolutionary Computation, PSO makes use of cooperation, according to a paradigm sometimes called "swarm intelligence". Such systems are typically made up of a population of simple interacting agents without any centralized control, and inspired by cases that can be found in nature, such as ant colonies, bird flocking, animal herding, bacteria molding, fish schooling, etc.There are many variants of PSO including constrained, multiobjective, and discrete or combinatorial versions, and applications have been developed using PSO in many fields.Swarm Intelligence Biologists studied the behavior of social insects for a long time. After millions of years of evolution all these species have developed incredible solutions for a wide range of problems. The intelligent solutions to problems naturally emerge from the self-organization and indirect communication of these individuals. Indirect interactions occur between two individuals when one of them modifies the environment and the other responds to the new environment at a later time.Swarm Intelligence is an innovative distributed intelligent paradigm for solving optimization problems that originally took its inspiration from the biological examples by swarming, flocking and herding phenomena in vertebrates. Data Mining is an analytic process designed to explore large amounts of data in search of consistent patterns and/or systematic relationships between variables, and then to validate the findings by applying the detected patterns to new subsets of data.Online Optimization Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision-making. In online optimization, the main issue is incomplete data and the scientific challenge: how well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In real-time optimization there is an additional requirement: decisions have to be computed very fast in relation to the time frame we are considering.Further Readings:Abraham A., C. Grosan and V. Ramos, Swarm Intelligence, Springer Verlag, 2006. It deals with the applications of swarm intelligence in data mining, using different intelligent approaches.Charnes A., Cooper W., Lewin A., and L. Seiford, Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Academic Publications, 1994.Dempe S., Foundations of Bilevel Programming, Kluwer, 2002.Diwekar U., Introduction to Applied Optimization, Kluwer Academic Publishers, 2003. Covers almost all the above techniques.Liu B., and A. Esogbue, Decision Criteria and Optimal Inventory Processes, Kluwer, 1999.Luenberger D., Linear and Nonlinear Programming, Kluwer Academic Publishers, 2003.Miller R., Optimization: Foundations and Applications, Wiley, 1999.MigdalasA., Pardalos p., and P. Varbrand, Multilevel Optimization: Algorithms and Applications, Kluwer, 1998.Reeves C., and J. Rowe, Genetic Algorithms: Principles and Perspectives, Kluwer, 2002. Rodin R., Optimization in Operations Research, Prentice Hall, New Jersey, 2000.For more books and journal articles on optimization visit the Web site Decision Making ResourcesLinear Programming Linear programming is often a favorite topic for both professors and students. The ability to introduce LP using a graphical approach, the relative ease of the solution method, the widespread availability of LP software packages, and the wide range of applications make LP accessible even to students with relatively weak mathematical backgrounds. Additionally, LP provides an excellent opportunity to introduce the idea of "what-if" analysis, due to the powerful tools for post-optimality analysis developed for the LP model.Linear Programming (LP) is a mathematical procedure for determining optimal allocation of scarce resources. LP is a procedure that has found practical application in almost all facets of business, from advertising to production planning. Transportation, distribution, and aggregate production planning problems are the most typical objects of LP analysis. In the petroleum industry, for example a data processing manager at a large oil company recently estimated that from 5 to 10 percent of the firm's computer time was devoted to the processing of LP and LP-like models. Linear programming deals with a class of programming problems where both the objective function to be optimized is linear and all relations among the variables corresponding to resources are linear. This problem was first formulated and solved in the late 1940's. Rarely has a new mathematical technique found such a wide range of practical business, commerce, and industrial applications and simultaneously received so thorough a theoretical development, in such a short period of time. Today, this theory is being successfully applied to problems of capital budgeting, design of diets, conservation of resources, games of strategy, economic growth prediction, and transportation systems. In very recent times, linear programming theory has also helped resolve and unify many outstanding applications.It is important for the reader to appreciate, at the outset, that the "programming" in Linear Programming is of a different flavor than the "programming" in Computer Programming. In the former case, it means to plan and organize as in "Get with the program!", it programs you by its solution. While in the latter case, it means to write codes for performing calculations. Training in one kind of programming has very little direct relevance to the other. In fact, the term "linear programming" was coined before the word "programming" became closely associated with computer software. This confusion is sometimes avoided by using the term linear optimization as a synonym for linear programming. Any LP problem consists of an objective function and a set of constraints. In most cases, constraints come from the environment in which you work to achieve your objective. When you want to achieve the desirable objective, you will realize that the environment is setting some constraints (i.e., the difficulties, restrictions) in fulfilling your desire or objective. This is why religions such as Buddhism, among others, prescribe living an abstemious life. No desire, no pain. Can you take this advice with respect to your business objective? What is a function: A function is a thing that does something. For example, a coffee grinding machine is a function that transform the coffee beans into powder. The (objective) function maps and translates the input domain (called the feasible region) into output range, with the two end-values called the maximum and the minimum values.When you formulate a decision-making problem as a linear program, you must check the following conditions:The objective function must be linear. That is, check if all variables have power of 1 and they are added or subtracted (not divided or multiplied)The objective must be either maximization or minimization of a linear function. The objective must represent the goal of the decision-makerThe constraints must also be linear. Moreover, the constraint must be of the following forms ( £, ³, or =, that is, the LP-constraints are always closed).For example, the following problem is not an LP: Max X, subject to X 2b1af7f3a8