In continuous multiple criteria problems, finding a distinct preferred solution for a decision maker (DM) is not straightforward. There are few recent studies proposed for this task, and the algorithms developed are cognitively difficult and complex for the DM in general. We propose a novel interactive algorithm to guide the DM in converging highly-preferred solutions in continuous multiple criteria problems. We test our algorithm on portfolio optimization problems formed with the stocks included in the S&P 100 index using expected return, liquidity, conditional value at risk, and mean absolute deviation as criteria. We simulate DM responses with linear and nonlinear preference functions and use various weights for the criteria. The experiments show that our algorithm is able to find highly-preferred solutions in considerably low number of iterations. We also test our algorithm against benchmark algorithms and demonstrate that our algorithm produces superior or comparable results.

中文翻译：

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连续多准则问题的一种新的交互式算法：投资组合优化示例

在连续多标准问题中，为决策者 (DM) 找到一个明显的首选解决方案并非易事。最近很少有针对这项任务提出的研究，并且开发的算法对于一般的 DM 来说在认知上是困难和复杂的。我们提出了一种新颖的交互式算法来指导 DM 在连续多标准问题中收敛高度优选的解决方案。我们使用预期收益、流动性、条件风险价值和平均绝对偏差作为标准，针对标准普尔 100 指数中包含的股票形成的投资组合优化问题测试我们的算法。我们使用线性和非线性偏好函数模拟 DM 响应，并为标准使用各种权重。实验表明，我们的算法能够在相当少的迭代次数中找到高度优选的解决方案。我们还针对基准算法测试我们的算法，并证明我们的算法产生了优越或可比的结果。