Fermat's Last Theorem—which we shall abbreviate to FLT—is the (as yet unproved) assertion that the Diophantine equation x" + y" — z" has no solutions in positive integers if 11 ^ 3. It would suffice to deal with the case in which n is prime, and this is where the most significant work has been done. None the less it is not yet known even whether FLT is true for infinitely many prime exponents. ...

this paper presents a new mathematical model for the problem of scheduling part families and jobs within each part family in a flow line manufacturing cell where the setup times for each family are sequence dependent and it is desired to minimize the maximum completion time of the last job on the last machine (makespan) while processing parts (jobs) in each family together. gaining an optimal s...

Criteria containing a barrier function i.e., an unbounded function at the boundary of the feasible solution domain are frequently encountered in the optimization framework, in particular in interior point methods for constrained optimization. Barrier function has to be carefully handled in the optimization algorithm. When an iterative descent method is used for the minimization, a search along ...

We present a novel, generic model of the grid that emphasises the roles of individual organizations that form the system. The model allows us to study the global behaviour of the system without introducing external forms of recompense. Using game-theory and equitable multicriteria optimization, we study three diverse types of computational grids: an off-line system with dedicated uniprocessors,...

A hybrid neural network model based on-line re-optimization control strategy is developed for a batch polymerization reactor. To address the difficulties in batch polymerization reactor modeling, the hybrid neural network model contains a simplified mechanistic model covering material balance assuming perfect temperature control, and recurrent neural networks modeling the residuals of the simpl...

Increasing environmental awareness in today's society and stricter regulations have forced manufacturing firms to take necessary actions for the recovery of end-of-life (EOL) products through different options (e.g., recycling, remanufacturing,). Disassembly is regarded as a critical operation EOL treatment used since all product require disassembly at certain levels. This generally carried out...