By Mark Sh. Levin (auth.)
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Extra info for Combinatorial Engineering of Decomposable Systems
We will take into account compatibility for multiple-choice knapsack problem, and for composition problems based on morphological analysis in further sections. The consideration of compatibility for KP leads to the search for a clique with the maximum total profit and a restricted total weight (profit clique). 2 present an example for the following problems: KP, profit clique (KP, and compatibility of selected items), limited clique (maximizing the number of selected compatible items, and constraint to total item weight as in KP) ; and maximal clique (maximizing the number of selected compatible items) .
U. , ideal decisions (of the best DA's), Pareto-effective by N DA's, etc. Trivially, a basic solving scheme is: Step 1. To construct feasible compositions. Step 2. To select Pareto-effective composite DA's. Evidently, the problem is NP-hard . Usually for constructing the feasible compositions there are used backtracking, and the following two operations (, ): (a) rejecting the infeasible DA's; and (b) revealing the situation when the composite decision does not exist. In our case, more complex scales for DA's, Ins, and S allow to apply a direct solving scheme both from w = u, and r = I.
Is a convex quadratic function), quadratic BPP (F and! are convex quadratic functions) . ) . , minimax problems, linear integer problems, bilinear and quadratic problems) can be rewritten as a linear BPP . , network design/management, facility location) have discrete nature, and are similar to combinatorial synthesis. ): (1) extreme point algorithms (linear BPPs, linear-quadratic BPPs); (2) branch and bound algorithms (convex BP, integer linear BPP, integer quadratic BPP); (3) complimentary pivot algorithms (linear BPPs, linear-quadratic BPPs); (4) descent methods (convex BP, nonlinear BPPs); (5) penalty function methods; and (6) artificial intelligent based approaches.
Combinatorial Engineering of Decomposable Systems by Mark Sh. Levin (auth.)