Generic objective function

If the search is performed for an object from the lower levels, it is useful to limit the number of its iterations. For instance, suppose we want to solve a problem of maximum level that is a generic objective function bounds, linear, nonlinear equality and inequality constraints. The search for a new point that is better than the previous one can be performed with different strategies that can be used sequentially or in parallel, as required. The most important are the following ... 

Let us first consider the gradient vector of the weighted least square objective function (3.22), whose generic component has the form... 

Mujtaba and Macchietto (1996) presented a more general formulation for optimal design and operation, dealing in particular with multiple separation duties, multicomponent mixtures, more complex operations (involving off-cuts) and more general objective functions. The method utilises a dynamic model (Type IV, Chapter 4) of the column in the form of a generic system of DAEs. Models of various rigor (type III and V, etc. of Chapter 4) can therefore be used. 

Generically the models considered have a clear, quantitative way to compare feasible solutions. That is, they have single objective functions. In many applications single objectives reahstically model the true decision process. Decisions become much more confused when the problem arises in a complex engineering design, where more than one objective may be relevant. For such cases, as referred above, a multi-objective optimization model is required to capture all the possible perspectives. This is the case of the design of batch plants where two objectives are under consideration - one that maximizes the revenues (that is, production) and the other that minimizes the cost. 

As shown in Fig. 5, each layer considers two independent optimization sections the Solver and the Problem Formulation section. The former regards the optimization algorithm itself, while the latter regards the evaluation of the objective function (i.e., the function to be minimized and the constraints). Within the Generic Optimization layer, there are two abstract upper classes, which are the OptimizationAlgorithm and OptimizationProblem in the Solver and Problem Formulation sections. These two classes are connected in the sense that the OptimizationAlgorithm requires a defined... 

In a generic iteration, a feasible point is known together with the active variable bounds and inequality constraints. If the point is anything other than solution, a search direction must be determined to improve the objective function. In this search, all the active inequality constraints are treated as equality constraints, whereas the active bounds are used to simplify the problem. 

The following subsections define notation used to specify the generic supply chain configuration optimization model, and present the object function and constraints of this model. 

The generic formulation can be extended to multi-objective setting in various ways. Objectives associated with environmental issues, responsiveness, and reliability including customer service are considered most frequently. The generic supply chain configuration optimization model is extended to incorporate these additional objectives and the objective function (8.1) is reformulated as... 

Since an FE solver can calculate all modal parameters for all modes of interest at once, the computational cost to calculate one objective function is equal to the computational cost to calculate all objective functions. Generic non-linear optimisers use only one of these objective functions. Other results however can be useful for other optimisations, for instance to select a suitable start vector. In most cases some optima - especially these located on a vertex - can even be found without performing additional FE analyses. Especially for larger FE models, storing all EE analysis results can cut the computational cost significantly. 

The fundamental point developing a MOOP is that of evaluating the mean and variance of a conventional objective function. A widely nsed solntion for this problem, referred to the generic stochastic structural response R d) which depends on the uncertainty parameter vector d, is the linear approximation of the DPM that furnishes the mean value and variance ... 

Both MIPS are comprised of three main blocks of equations capacity limitations, demand satisfaction, and objective function-related equations. To formulate these constraints, we consider the generic SC structure depicted in Figure 13.2. The model contains two types of variables binary and continuous. The former are used to model the SC configuration (i.e., establishment of a new plant in a potential location), while the latter denote planning decisions (i.e., transportation flows). We describe next each of these equations in detail for both cases. 

Flowsheets can be built up from generic units and then evaluated using the operations for an extended type, T, which provides the information necessary for the global optimisation algorithm. The variable type being used is intervals. Each unit calculates the output streams (where the input and output streams are usually a vector) and the cost associated with the unit as intervals. The summation of the costs provides the objective function. The design constraints are added outside the module to the optimisation problem. 

In this step, the optimization problem is formulated as MILP or MINLP problem depending on the objective function definition and constraints using appropriate software, in this case GAMS. The ouQ)ut is the optimal biorefmery configuration. The generic models and stracture of the optimization problem (MIP/MINLP) organized and used in this study are presented and explained in the following text. 

The optimization formulation (presented in Eqs. I.II-I.I6) consists of the objective function (e.g., minimize TAG Eq. l.II) subjected to process constraints, the process models and constraints (Eqs. I.I-I.IO) of the generic model block mentioned earlier (x is a process variable, the mass flow rate), structural constraints (Eqs. 1.12 and 1.13) representing the superstructure which allows selection of only one process alternative in each step, and cost functions (Eqs. 1.14-1.16) to calculate the operating and capital costs using cost parameters (f l", waste treatment cost utility or chemicals cost , reactor... 

Kim, D., Nevatia, R. (1998). Recognition and localization of generic objects for indoor navigation using functionality. Image and Vision Computing, 729-743. doi 10.1016/... 

Java provides a light-weight serialization mechanism the implementor need do no additional work for objects to serialize and restore themselves correctly. The mechanism uses the underlying reflection services to implement generic save and restore functionality only once. 

OCL uses a Smalltalk-based block syntax to allow you to define some kinds of functions conveniently and inline, but it does not provide corresponding type rules for this based on generic types. For our discussion here, we treat blocks as first-class functions and use the syntax (T1 X T2 X T3 -> T ) for such a function. This is purely a syntactic convenience functions can be modeled as objects. Any function f (a,b) c can be described as an object with a single method eval (a, b) c. Thus,... 

Please note that use case modeling is not associated with any development process. It is even independent of object-oriented technologies. It is a generic tool for capturing functional requirements. I have used use case specifications in ISIS PL projects, and it worked perfectly. 

Generic is a mnemonic name, expressing the set of common features, behaviors or actions, relating to different aspects or elements of IT security system, like subjects, objects, assumptions for the security environment, organizational security policies, threats, security objectives for the TOE and its environment, security requirements for the environment, security functions, as well as vulnerabilities, risks and impacts. 

---