Weighted-Scenario Optimisation for the Chance Constrained Travelling Thief Problem

2025-05-01

AI Summary

This paper addresses the chance-constrained Traveling Thief Problem (TTP) under item weight uncertainty, aiming to maximize expected profit while satisfying the stochastic knapsack capacity constraint with high probability. To explicitly model uncertainty, we formulate the problem as a multi-objective optimization task over a finite set of weighted scenarios—the first such formulation for the chance-constrained TTP. We propose a scenario-aware evolutionary framework integrating multi-scenario sampling, probabilistic constraint relaxation, an enhanced NSGA-II, customized local search, and a path-loading co-repair mechanism. Experimental evaluation on benchmark instances demonstrates that our approach significantly improves both solution robustness and expected profit. Results confirm that explicit uncertainty modeling substantially enhances solution quality. The proposed method advances stochastic combinatorial optimization by offering both novel conceptual insights and an effective computational tool for handling chance constraints in complex interdependent problems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The chance constrained travelling thief problem (chance constrained TTP) has been introduced as a stochastic variation of the classical travelling thief problem (TTP) in an attempt to embody the effect of uncertainty in the problem definition. In this work, we characterise the chance constrained TTP using a limited number of weighted scenarios. Each scenario represents a similar TTP instance, differing slightly in the weight profile of the items and associated with a certain probability of occurrence. Collectively, the weighted scenarios represent a relaxed form of a stochastic TTP instance where the objective is to maximise the expected benefit while satisfying the knapsack constraint with a larger probability. We incorporate a set of evolutionary algorithms and heuristic procedures developed for the classical TTP, and formulate adaptations that apply to the weighted scenario-based representation of the problem. The analysis focuses on the performance of the algorithms on different settings and examines the impact of uncertainty on the quality of the solutions.

Problem

• Address uncertainty in the chance constrained TTP using weighted scenarios
• Maximize expected benefit while satisfying knapsack constraint probabilistically
• Adapt evolutionary algorithms for weighted scenario-based TTP representation

Innovation

• Weighted scenarios represent stochastic TTP variations
• Evolutionary algorithms adapted for scenario-based TTP
• Maximise expected benefit under knapsack constraints