Evolutionary computation plus dynamic programming for the bi-objective travelling thief problem

Abstract

This research proposes a novel indicator-based hybrid evolutionary approach that combines approximate and exact algorithms. We apply it to a new bi-criteria formulation of the travelling thief problem, which is known to the Evolutionary Computation community as a benchmark multi-component optimisation problem that interconnects two classical N P-hard problems: the travelling salesman problem and the 0-1 knapsack problem. Our approach employs the exact dynamic programming algorithm for the underlying Packing-While-Travelling problem as a subroutine within a bi-objective evolutionary algorithm. This design takes advantage of the data extracted from Pareto fronts generated by the dynamic program to achieve better solutions. Furthermore, we develop a number of novel indicators and selection mechanisms to strengthen synergy of the two algorithmic components of our approach. The results of computational experiments show that the approach is capable to outperform the state-of-the-art results for the single-objective case of the problem.

A Non-Dominated Sorting Based Customized Random-Key Genetic Algorithm for the Bi-Objective Traveling Thief Problem

“…Yafrani et al (2017) created an approach that generates diverse sets of TTP/TTP1 solutions, while being competitive with the stateof-the-art single-objective algorithms; the objectives were travel time and total profit of items. Wu et al (2018) considered a bi-objective version of the TTP1; the objectives were the weight and the TTP objective score. This hybrid approach makes use of the dynamic programming approach for fixed tours and then searches over the space of tours only.…”

“…As we consider that the thief travels on a symmetric map, where both these tours result in the same overall traveling time. Note that achieving near-optimal TSP tours is not a guarantor for near-optimal TTP solutions, and it has been observed that slightly longer tours have the potential to yield overall better TTP solutions (Wagner 2016;Wu et al 2018). However, we observed that near-optimal TSP tours combined with KP packing with lighter items generate BI-TTP solutions very close to the Pareto front regarding the traveling time objective.…”

A Specialized Evolutionary Approach to the bi-objective Travelling Thief Problem

“…A multi-objective approach to TTP is considered less common in literature. However, authors of [15] used a combination of evolutionary computation and dynamic programming for the bi-objective TTP. Additionally, novel indicators were proposed, and the approach was compared to state-of-the-art methods.…”

A weighted-sum method for solving the bi-objective traveling thief problem

“…For example, created a fully-heuristic approach that generates diverse sets of solutions, while being competitive with the state-of-the-art single-objective algorithms. Wu et al (2018) considered a bi-objective version of the TTP, which used dynamic programming as an optimal subsolver, where the objectives were the total weight and the TTP objective score. At two recent competitions 2,3 , a bi-objective TTP (BITTP) variant has been used that trades off the total profit of the items and the travel time.…”