Abstract
The maximum k-coverage problem (MKCP) is a generalized covering problem which can be solved by genetic algorithms, but their operation is impeded by redundancy in the representation of solutions to MKCP. We introduce a normalization step for candidate solutions based on distance between genes which ensures that a standard crossover such as uniform and n-point crossovers produces a feasible solution and improves the solution quality. We present results from experiments in which this normalization was applied to a single crossover operation, and also results for example MKCPs.
Highlights
The maximum k-coverage problem (MKCP) is regarded as a generalization of several covering problems
Because MKCP selects a fixed number of columns, the representation of solutions is simpler than it is in other covering problems, and this favors the adoption of a genetic algorithm (GA)
Our experiments were conducted on 65 instances of 11 set cover problems with various size and densities, from the OR-library [43]. These benchmark data were designed as set cover problems, the data can be considered as maximum k-coverage problems, as in [27]
Summary
The maximum k-coverage problem (MKCP) is regarded as a generalization of several covering problems. We can consider a disaster management system in which n agencies are involved and m positions for Unmanned Aerial Vehicles (UAVs) are available to enable the communication between the agencies In this situation, it can be investigated whether or not each agency i is covered when a UAV is placed in each position j (meaning aij ). If only k UAVs are available for resource management, the problem of choosing exactly k positions of UAVs to cover as many agencies in the disaster area as possible can be formulated as MKCP. Because MKCP selects a fixed number of columns, the representation of solutions is simpler than it is in other covering problems, and this favors the adoption of a genetic algorithm (GA).
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