Generic feasible point

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 supernova models utilized below have all been generated by S. Woosley using the Kepler [7] supernova code. The evolution is followed with Kepler until the expansion becomes essentially homologous. At this point the Kepler information is transferred to the spectrum code. It is important to emphasize that once the supernova model has been selected the predicted spectra are generated without adjustable parameters. The adjustable parameters of the model are on the whole those with direct astrophysical relevance, for example the initial stellar mass and amount of mass loss. It is,.of course, feasible and useful to use the comparison of the observed and predicted spectra to refine the supernova model. This, however, has not yet been done except in a rough way. At present, the nebular spectra have been used only to choose broad classes of feasible models and mle out others. For example, the He detonation models for SNIa have been ruled out on the basis of the spectrum[8]. The results presented, therefore, must be viewed accordingly as generic to a whole class of models whose details are still unresolved. 

The above technological tools to aid process design indicate feasibility only (that is can it be done ). They do not compare process alternatives by a generic measure for efficiency (that is how well can it be done ). Again, a thermodynamic starting point can be taken to obtain a quantitative measure of process efficiency. 

In this research, a novel multi-objective PSO with ideal-point non-dominated sorting is designed to find the optimal solution of the proposed MCSCD model. Figure 3 demonstrates the PSO algorithm and repair process for this MCSCD model, four major steps, described as follows, are employed to search for a feasible solution then, a generic PSO process and a particle repair process are employed to... 

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