*Article* **Ranking Multi-Metric Scientific Achievements Usinga Concept of Pareto Optimality**

#### **Shahryar Rahnamayan 1, Sedigheh Mahdavi 1, Kalyanmoy Deb 2 and Azam Asilian Bidgoli 1,\***


Received: 18 April 2020; Accepted: 2 June 2020; Published: 11 June 2020

**Abstract:** The ranking of multi-metric scientific achievements is a challenging task. For example, the scientific ranking of researchers utilizes two major types of indicators; namely, number of publications and citations. In fact, they focus on how to select proper indicators, considering only one indicator or combination of them. The majority of ranking methods combine several indicators, but these methods are faced with a challenging concern—the assignment of suitable/optimal weights to the targeted indicators. Pareto optimality is defined as a measure of efficiency in the multi-objective optimization which seeks the optimal solutions by considering multiple criteria/objectives simultaneously. The performance of the basic Pareto dominance depth ranking strategy decreases by increasing the number of criteria (generally speaking, when it is more than three criteria). In this paper, a new, modified Pareto dominance depth ranking strategy is proposed which uses some dominance metrics obtained from the basic Pareto dominance depth ranking and some sorted statistical metrics to rank the scientific achievements. It attempts to find the clusters of compared data by using all of indicators simultaneously. Furthermore, we apply the proposed method to address the multi-source ranking resolution problem which is very common these days; for example, there are several world-wide institutions which rank the world's universities every year, but their rankings are not consistent. As our case studies, the proposed method was used to rank several scientific datasets (i.e., researchers, universities, and countries) for proof of concept.

**Keywords:** Pareto optimality; *h*-index; ranking; dominance; Pareto-front; multi-indicators; multi-metric; multi-resources; citation; universities ranking
