PEGA: A Privacy-Preserving Genetic Algorithm for Combinatorial Optimization

Evolutionary algorithms (EAs), such as the genetic algorithm (GA), offer an elegant way to handle combinatorial optimization problems (COPs). However, limited by expertise and resources, most users lack the capability to implement EAs for solving COPs. An intuitive and promising solution is to outsource evolutionary operations to a cloud server, however, it poses privacy concerns. To this end, this article proposes a novel computing paradigm called evolutionary computation as a service (ECaaS), where a cloud server renders evolutionary computation services for users while ensuring their privacy. Following the concept of ECaaS, this article presents privacy-preserving genetic algorithm (PEGA), a privacy-preserving GA designed specifically for COPs. PEGA enables users, regardless of their domain expertise or resource availability, to outsource COPs to the cloud server that holds a competitive GA and approximates the optimal solution while safeguarding privacy. Notably, PEGA features the following characteristics. First, PEGA empowers users without domain expertise or sufficient resources to solve COPs effectively. Second, PEGA protects the privacy of users by preventing the leakage of optimization problem details. Third, PEGA performs comparably to the conventional GA when approximating the optimal solution. To realize its functionality, we implement PEGA falling in a twin-server architecture and evaluate it on two widely known COPs: 1) the traveling Salesman problem (TSP) and 2) the 0/1 knapsack problem (KP). Particularly, we utilize encryption cryptography to protect users' privacy and carefully design a suite of secure computing protocols to support evolutionary operators of GA on encrypted chromosomes. Privacy analysis demonstrates that PEGA successfully preserves the confidentiality of COP contents. Experimental evaluation results on several TSP datasets and KP datasets reveal that PEGA performs equivalently to the conventional GA in approximating the optimal solution.