Analysis of Baseline Evolutionary Algorithms for the Packing While Travelling Problem
share
Although the performance of base-line Evolutionary Algorithms (EAs) on linear functions has been studied rigorously, the same theoretical analyses on non-linear objectives are still far behind. In this paper, variations of the Packing While Travelling (PWT), also known as a non-linear knapsack problem, is considered to address this gap. We investigate PWT for two cities with correlated weights and profits using single-objective and multi-objective algorithms. Our results show that RLS finds the optimal solution in O(n^3) expected time while the GSEMO enhanced with a specific selection operator to deal with exponential population size, calculates all the Pareto front solutions in the same expected time. In the case of uniform weights, (1+1) EA is able to find the optimal solution in expected time O(n^2({n,p_max})), where p_max is the largest profit of the given items. We also validate the theoretical results using practical experiments and present estimation for expected running time according to the experiments.
READ FULL TEXT
