The performance of base-line Evolutionary Algorithms (EAs) on combinatorial problems has been studied rigorously. From the theoretical viewpoint, the literature extensively investigates the linear problems, while the theoretical analysis of the non-linear problems is still far behind. In this paper, variations of the Packing While Travelling (PWT) -- also known as the non-linear knapsack problem -- are studied as an attempt to analyse the behaviour of EAs on non-linear problems from theoretical perspective. We investigate PWT for two cities and $n$ items with correlated weights and profits, using single-objective and multi-objective algorithms. Our results show that RLS\_swap, which differs from the classical RLS by having the ability to swap two bits in one iteration, finds the optimal solution in $O(n^3)$ expected time. We also study an enhanced version of GSEMO, which a specific selection operator to deal with exponential population size, and prove that it finds the Pareto front in the same asymptotic expected time. In the case of uniform weights, (1+1)~EA is able to find the optimal solution in expected time $O(n^2\log{(\max\{n,p_{\max}\})})$, where $p_{\max}$ is the largest profit of the given items. We also perform an experimental analysis to complement our theoretical investigations and provide additional insights into the runtime behavior.
Comparing the Digital Annealer with Classical Evolutionary Algorithm
Fujitsu Research of Europe Ltd.（富士通欧洲研究有限公司）
在最近几年，已经有越来越多的研究兴趣，利用特定应用的硬件来解决优化问题。使用专用硬件的求解器的例子是IBM的Quantum System One和D-wave的Quantum Annealer（QA）和Fujitsu的Digital Annealer（DA）。这些求解器的开发是为了比在通用机器上实现的传统元算法更快地优化问题。以前的研究表明，这些求解器可以比精确求解器（如GUROBI和CPLEX）更快地优化许多问题。这样的结论还没有作出比较时，硬件求解器与经典的进化算法。传统的进化算法，如遗传算法（GA），和DA（或其他类似的求解器）之间进行公平的比较是具有挑战性的，因为后者受益于使用专用硬件，而进化算法往往是在通用机器上实现。此外，量子或量子启发的求解器仅限于以特定格式解决问题。二次无约束二进制优化（QUBO）。然而，许多优化问题是受约束的，并且具有非二进制的自然表示。将这样的问题转换为QUBO可能导致更多的问题难度和/或更大的搜索空间。在本文中解决的问题是量子或量子启发的求解器是否可以优化QUBO变换的组合优化问题的速度比经典的进化算法应用于相同的问题，在其自然表示。我们发现，DA往往提出更好的平均目标函数值比GA旅行推销员，二次分配和多维背包问题的实例。
LLM-Driven Instance-Specific Heuristic Generation and Selection
Southern University of Science and Technology（南方科技大学）；Zhongguancun Academy（中关村研究院）；Hong Kong University of Science and Technology（香港科技大学）；Hong Kong Polytechnic University（香港理工大学）；Advanced Micro Devices Inc.（超威半导体公司）；Institute of High Performance Computing, Agency for Science Technology and Research（新加坡科技研究局高性能计算研究所）；Nanyang Technological University（南洋理工大学）
