2 research outputs found
The -vehicle exploration problem is NP-complete
The -vehicle exploration problem (NVEP) is a combinatorial optimization
problem, which tries to find an optimal permutation of a fleet to maximize the
length traveled by the last vehicle. NVEP has a fractional form of objective
function, and its computational complexity of general case remains open. We
show that Hamiltonian Path NVEP, and prove that NVEP is NP-complete.Comment: 5 pages, 6 figure
A polynomial-time algorithm to solve the large scale of airplane refueling problem
Airplane refueling problem is a nonlinear combinatorial optimization problem
with feasible feasible solutions. Given a fleet of airplanes with
mid-air refueling technique, each airplane has a specific fuel capacity and
fuel consumption rate. The fleet starts to fly together to a same target and
during the trip each airplane could instantaneously refuel to other airplanes
and then be dropped out. The question is how to find the best refueling policy
to make the last remaining airplane travels the farthest. To solve the large
scale of the airplane refueling problem in polynomial-time, we propose the
definition of the sequential feasible solution by employing the data structural
properties of the airplane refueling problem. We prove that if an airplane
refueling problem has feasible solutions, it must have sequential feasible
solutions, and its optimal feasible solution must be the optimal sequential
feasible solution. Then we present the sequential search algorithm which has a
computational complexity that depends on the number of sequential feasible
solutions referred to , which is proved to be upper bounded by
as an exponential bound that lacks of applicability on larger input for worst
case. Therefore we investigate the complexity behavior of the sequential search
algorithm from dynamic perspective, and find out that is bounded by
when the input is greater than . Here is a
constant and is regarded as the "inflection point" of the complexity of
the sequential search algorithm from exponential-time to polynomial-time.
Moreover, we build an efficient computability scheme according to which we
shall predict the specific complexity of the sequential search algorithm to
choose a proper algorithm considering the available running time for decision
makers or users.Comment: 18 pages, 2 figure