By Sbihi A.
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Additional info for A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem
However, the last row of Tab. 3 indicates that the use of the AIM strategies does not significantly improve the enclosures in the numerical case, in contrast to the symbolic approach from [RHA06]. Note also that even though the implementation of 24 ψ1 E. Auer et al. 4 t (a) Enclosure of the first state variable. 4 t (b) Enclosure of the second state variable. Fig. 5. Interval enclosures for the first and second state variable of the double pendulum Table 3. 4 VNODE vs. 564 ValEncIA: MVR vs. 8 ·10−8 Compared solvers VAL E NC IA-IVP in S MART MOBILE has not been optimized, the reduction of computing time in comparison to the VNODE-based integrator is considerable.
Corliss and Yu for interval arithmetic operations and elementary functions . Interval test suites should include many problems from existing test suites for approximate solvers and also problems intended to test existence and containment properties. – Software engineering publications related to the development of scientiﬁc software with respect to appropriate process models, methodologies and documentation. Software engineering has mostly ignored scientiﬁc software and placed most of the emphasis on research on safety critical systems and information systems.
To introduce VAL E NC IA-IVP into S MART MOBILE, we implement a new basic data type which helps to obtain the numerical reference solution and the required Jacobian. It contains members of the types double (the reference solution), INTERVAL (the solution), and FINTERVAL (the Jacobian). Note that the Jacobian is always evaluated even if only double or INTERVAL values are required. Besides, we cannot avoid multiple function evaluations with the help of this new data type TMoFInterval as it was done in VNODE with TMoInterval.