Approximate Approaches to the Traveling Thief Problem

Abstract

This study addresses the recently introduced Traveling Thief Problem (TTP) which combines the classical Traveling Salesman Problem (TSP) with the 0-1 Knapsack Problem (KP). The problem consists of a set of cities, each containing a set of available items with weights and profits. It involves searching for a permutation of the cities to visit and a decision on items to pick. A selected item contributes its profit to the overall profit at the price of higher transportation cost incurred by its weight. The objective is to maximize the resulting profit.We propose a number of problem-specific packing strategies run on top of TSP solutions derived by the Chained Lin-Kernighan heuristic. The investigations provided on the set of benchmark instances prove their rapidity and efficiency when compared with an approximate mixed integer programming based approach and state-of-the-art heuristic solutions from the literature.

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

“…In practice, various algorithms are capable of producing superior tours for the TSP, and therefore many approaches to the TTP use this capability to succeed. Highperforming TTP algorithms are commonly two-stage heuristic approaches, like those proposed by Polyakovskiy et al [22], Faulkner et al [12], and El Yafrani and Ahiod [9]. Specifically, their first step generates a near-optimal TSP tour and the second step completes solution by selection of a subset of items.…”

A case study of algorithm selection for the traveling thief problem

“…Faulkner, Polyakovskiy, Schultz, and Wagner [12] investigated multiple operators and did a comprehensive comparison with existing approaches. They proposed a number of operators, such as Bitflip and PackIterative, for optimising the packing plan given a particular tour.…”

Exact Approaches for the Travelling Thief Problem

“…With the exact approaches being introduced, approximate approaches can be evaluated with respect to their accuracy to the optima. In the case of the TTP, most state-of-the-art approximate approaches are evolutionary algorithms and local searches, such as Memetic Algorithm with 2-OPT and Bit-flip (MA2B), CoSolver-based with 2-OPT, and Simulated Annealing (CS2SA) in [6], CoSolverbased with 2-OPT and Bit-flip (CS2B) in [5], and S1, S5, and C5 in [7].…”

“…attempts to solve the problem as a whole. In 2015, Faulkner et al [7] outperformed the existing approaches by their new operators and corresponding series of heuristics (named S1-S5 and C1-C6). Recently, Wagner [21] investigated the Max-Min Ant System (MMAS) [20] on the TTP, and El Yafrani and Ahiod [6] proposed a memetic algorithm (MA2B) and a simulated annealing algorithm (CS2SA).…”