Improved artificial bee colony algorithm for vehicle routing problem with time windows

<div><p>This paper investigates a well-known complex combinatorial problem known as the vehicle routing problem with time windows (VRPTW). Unlike the standard vehicle routing problem, each customer in the VRPTW is served within a given time constraint. This paper solves the VRPTW using an improved artificial bee colony (IABC) algorithm. The performance of this algorithm is improved by a local optimization based on a crossover operation and a scanning strategy. Finally, the effectiveness of the IABC is evaluated on some well-known benchmarks. The results demonstrate the power of IABC algorithm in solving the VRPTW.</p></div

Effect of number of random original food sources <i>m</i> on the performance of IABC.

<p>Effect of number of random original food sources <i>m</i> on the performance of IABC.</p

Comparison results for R2-01 with different parameter values.

<p>Comparison results for R2-01 with different parameter values.</p

Customer sorting by angles.

<p>Customer sorting by angles.</p

Six situations of two paths.

<p>Six situations of two paths.</p

Distribution of customers around the central depot (<i>c</i>₀) in the coordinate system of the scanning strategy.

<p>Distribution of customers around the central depot (<i>c</i>₀) in the coordinate system of the scanning strategy.</p

Point exchange in the crossover operation.

<p>Point exchange in the crossover operation.</p

Computational results using IABC, ABC-C and ABC-S.

<p>Computational results using IABC, ABC-C and ABC-S.</p

Behavior of honey bee foraging for nectar.

<p>Behavior of honey bee foraging for nectar.</p

Point selection in the crossover operations (clients <i>c</i>₂ and <i>c</i>₈ are selected).

<p>Point selection in the crossover operations (clients <i>c</i>₂ and <i>c</i>₈ are selected).</p