Abstract We consider a non-linear version of the Generalized Assignment Problem, a well-known strongly NP -hard combinatorial optimization problem. We assume that the variables are continuous and that objective function and constraints are defined by non-linear functions of the variables. A mathematical model is introduced and used to derive upper bounds on the optimal solution value. We present constructive heuristics, obtained from decomposition and non-linear programming tools, and a binary linear programming model that provides approximate solutions. By combining the various methods and a local search framework, we finally obtain a hybrid heuristic approach. Extensive computational experiments show that the proposed methods outperform the direct application of non-linear solvers and provide high quality solutions in a reasonable amount of time.

中文翻译：

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非线性广义分配问题的上下界

摘要 我们考虑广义分配问题的非线性版本，这是一个众所周知的强 NP 难组合优化问题。我们假设变量是连续的，并且目标函数和约束由变量的非线性函数定义。数学模型被引入并用于推导出最优解值的上限。我们提出了从分解和非线性规划工具中获得的建设性启发式方法，以及提供近似解的二元线性规划模型。通过结合各种方法和局部搜索框架，我们最终获得了一种混合启发式方法。大量的计算实验表明，所提出的方法优于非线性求解器的直接应用，并在合理的时间内提供高质量的解决方案。