Constraint handling techniques

Coello Coello, C.A. (2002) Theoretical and numerical constraint handling techniques used with evolutionary algorithms A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 191 (11—12), 1245-1287. 

As indicated before, this section is devoted to review works whose main goal is to propose a new MOEA (or an important component of it). Among these novel contributions we can find, for instance, an evolutionary operator, a constraint-handling technique and a proposal to... 

This constraint-handling technique is based on z. (ju,X ) evolutionary strategy. Each... 

Constraints Interpretable as another form of nonlinearity. Requiring controller design techniques with explicit and intelligent constraints handling capabilities ... 

Some people prefer to use the multiple time step approach to handle fast degrees of freedom, while others prefer to use constraints, and there are situations in which both techniques are applicable. Constraints also find an application in the study of rare events, where a system may be studied at the top of a free energy barrier (see later), or for convenience when it is desired to fix a thennodynamic order parameter or ordering direction... 

Syntheses of radioactive tracers involve all of the classical biochemical and synthetic chemical reactions used in the synthesis of nonradio active chemicals. There are, however, specialized techniques and considerations required for the safe handling of radioactive chemicals, strategic synthetic considerations in terms of their relatively high cost, and synthesis scale constraints governed by specific activity requirements. 

Table 13.17 lists some of the important considerations for the different fume capture techniques. From the point of view of cost effectiveness, the usual preference is source collection or a low-level hood, provided an acceptable scheme can be developed within the process, operating, and layout constraints. The cost of fume control systems is almost a direct function of the gas volume being handled. Flence, the lower volume requirements for the source capture or low-level hood approach often results in significant capital and operating cost savings for the fume control system. 

Significant progress has recently been made in several areas which will have a profound effect on the ability of molecular dynamics to handle more complex problems. In this section we speculate on several areas which appear to hold promise for advancing computer modeling studies. In section 4.1, recent progress in both analytic potential energy expressions and first principles calculations are briefly mentioned. Recent advances in computational techniques are discussed in section 4.2. These include the use of constraints within the classical equations of motion to model thermostats in the surface region, and the incorporation of Monte Carlo techniques into molecular dynamics simulations. 

These tools may assist the scientist in two ways. First, the design process can be optimized with the nse of more complex constraints than could otherwise be handled. Second, in some cases the need for time-consuming and costly physical or chemical property measurements can be eliminated with the use of estimation techniques for properties of interest. 

The results presented below were obtained by multivariate curve resolution-alternating least squares (MCR-ALS). MCR-ALS was selected because of its flexibility in the application of constraints and its ability to handle either one data matrix (two-way data sets) or several data matrices together (three-way data sets). MCR-ALS has been applied to the folding process monitored using only one spectroscopic technique and to a row-wise augmented matrix, obtained by appending spectroscopic measurements from several different techniques. 

The first step is to describe the basic scenario for the purification. General considerations answer questions such as What is the intended use of the product What kind of starting material is available and how should it be handled What are the purity issues in relation to the source material and intended use of the final product What has to be removed What must be removed completely What will be the final scale of purification If there is a need for scale-up, what consequences will this have on the chosen purification techniques What are the economical constraints and what resources and equipment are available ... 

This graphical technique is adequate for the two variables investigated in this problem. This problem can also be solved using optimization techniques such as linear programming, a technique that can handle numerous constraints and variables... 

Least squares fitting techniques now in use are not necessarily the best way of handling large data sets. The lack of resistance to small changes in the data (or in the weights and constraints) is a significant drawback. 

---