Title: Mind Your Solver! On Adversarial Attack and Defense for Combinatorial Optimization. Abstract: Combinatorial optimization (CO) is a long-standing challenging task not only in its inherent complexity (e.g. NP-hard) but also the possible sensitivity to input conditions. In this paper, we take an initiative on developing the mechanisms for adversarial attack and defense towards combinatorial optimization solvers, whereby the solver is treated as a black-box function and the original problem's underlying graph structure (which is often available and associated with the problem instance, e.g. DAG, TSP) is attacked under a given budget. Experimental results on three real-world combinatorial optimization problems reveal the vulnerability of existing solvers to adversarial attack, including the commercial solvers like Gurobi. In particular, we present a simple yet effective defense strategy to modify the graph structure to increase the robustness of solvers, which shows its universal effectiveness across tasks and solvers. 