Core Concepts
Symbolic regression is used to learn useful features of near-optimal packing plans, which are then used to design efficient metaheuristic genetic algorithms for the traveling thief problem.
Abstract
The paper presents a novel approach to designing heuristics for the Traveling Thief Problem (TTP), an NP-hard combination of the Traveling Salesman and 0-1 Knapsack problems.
The key insights are:
- Analysis of near-optimal packing plans reveals a smooth, regular relationship between the standardized item profitability ratio (IPR) and the standardized distance to the end of the tour (rDist) of packed items.
- Symbolic regression is used to discover combinations of IPR and rDist that are important to this relationship.
- These feature combinations are used to define a family of metaheuristic genetic algorithms, where each individual encodes a boundary line separating packed and unpacked items.
- Symbolic regression is again used to directly predict the parameter values of the optimal individuals produced by the metaheuristic GA, greatly accelerating the algorithm and stabilizing its performance.
- Experiments show that the proposed heuristics outperform previous state-of-the-art initialization schemes in terms of both solution quality and computational efficiency.
Stats
The knapsack capacity is determined based on a capacity factor C ∈ {1...10} as W = C/11 * Σ(i=1 to n) Σ(k=0 to m) wik.
The renting ratio is calculated as the optimal profit of the KP subproblem divided by the time taken to traverse the linkern tour while collecting the items in that optimal packing.
Quotes
"Symbolic regression is used to learn useful features of near-optimal packing plans, which are then used to design efficient metaheuristic genetic algorithms for the traveling thief problem."
"Analysis of near-optimal packing plans reveals a smooth, regular relationship between the standardized item profitability ratio (IPR) and the standardized distance to the end of the tour (rDist) of packed items."
"Symbolic regression is again used to directly predict the parameter values of the optimal individuals produced by the metaheuristic GA, greatly accelerating the algorithm and stabilizing its performance."