SIAM Journal on Optimization, Volume 30, Issue 4, Page 3122-3145, January 2020.
Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we build linear outer approximations of the image set in an adaptive way. We are able to guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. As far as we know, the procedure we present is the first non-scalarization-based deterministic algorithm devised to handle this class of problems. Our numerical experiments show results on biobjective and triobjective mixed integer convex instances.

中文翻译：

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解决多目标混合整数凸优化问题

SIAM优化杂志，第30卷，第4期，第3122-3145页，2020年1月。
多目标混合整数凸优化是指数学编程问题，其中多个凸目标函数需要同时进行优化，并且某些变量被约束为采用整数值。我们提出了一种使用正确定义的下限的分支定界方法。我们不仅仅依赖于凸弛豫，而是以自适应方式建立图像集的线性外部近似。我们可以根据规定的精度，在检测有效和非支配的多目标混合整数凸问题方面保证正确性。据我们所知，我们提出的过程是第一个设计用于处理此类问题的基于非标量的确定性算法。