A Review on Multi-Objective Mixed-Integer Non-Linear Optimization Programming Methods
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper reviews MO-MINLP problem and methods for solving it. It is a valuable work to contribute the application of different methods in MO-MINLP. This study, however, seems to be incomplete as a scientific review paper. Major revision is required to improve the paper suitably. Below I provide a list of specific issues, in no particular order of priority, that need to be revised, intending to help the authors in their effort.
1) This study assessed peer-reviewed journals and the others by the same weight. Thus, the authors need to certify the quality of the others, especially papers published in conference proceedings.
2) There is no description about the way to decide the target study.
3) There is no description about review’s validity.
4) The authors should clearly define the scope for this review.
5) No reasons were given for using this classification in the study. The authors should explain the reasons and the evidence to use this classification.
6) In the review methodology, the authors should demonstrate what kind of key word they used when searching relevant papers, and their standard for data washing. Such information will help future readers to reproduce the research easier.
7) Some important recent references (2020-2024) are missing, such as:
Khodashenas, M., Najafi, S. E., Kazemipoor, H., & Sobhani, M. (2023). Providing an integrated multi-depot vehicle routing problem model with simultaneous pickup and delivery and package layout under uncertainty with fuzzy-robust box optimization method. Decision Making: Applications in Management and Engineering, 6(2), 372–403. https://doi.org/10.31181/dmame622023640
Mzili, T., Mzili,I., Riffi, M.E., Pamucar, D., Simic, V., Kurdi, M. (2023). A novel discrete rat swarm optimization algorithm for the quadratic assignment problem. Facta Universitatis: Series Mechanical engineering, 21(3), 529-552. https://doi.org/10.22190/FUME230602024M
Ghaseminejad, A., Kazemipoor, H., & Fallah, M. (2023). Modeling the robust facility layout problem for unequal space considering health and environmental safety criteria under uncertain parameters. Decision Making: Applications in Management and Engineering, 6(2), 426–460.
Mzili, T., Mzili,I., Riffi, M.E., Pamucar, D., Simic, V., Abualigah, L. (2023). Hybrid genetic and penguin search optimization algorithm (GA-PSEOA) for efficient flow shop scheduling solutions. Facta Universitatis, Series: Mechanical Engineering. https://doi.org/10.22190/FUME230615028M
8) The far more significant concern this reviewer has is with the contribution of the paper. Only one citation to an article published in Eng. This raises the question for this reviewer as to why the authors chose to submit the paper to Eng. If the authors wish to make a contribution to the knowledge being generated in and by this top-tier journal, then the authors should find some related work published in Eng to link their work to. Finally, this reviewer thinks that it is crucial for the authors to connect their work more meaningfully to the work of authors in the Eng community and they should do so to improve their contribution.
Author Response
The authors would firstly thank the reviewer for taking the time to review our manuscript titled " A Review on Multi-Objective Mixed-Integer Non-Linear Optimization Programming Methods " and for providing valuable feedback. We have carefully considered your comments and suggestions and have made several revisions to address the concerns raised.
Comment 1: This study assessed peer-reviewed journals and the others by the same weight. Thus, the authors need to certify the quality of the others, especially papers published in conference proceedings.
Our response: The authors appreciate this notable comment, hence all references has been revised and modified as follows. Books and chapters are used for concept explanation ONLY. The Arxiv Preprint articles in the references have been replaced by the published version of the articles. All other references have been either removed or supported by peer-reviewed journal article references except the remaining two high quality conference papers (based on the number of citations).
Comment 2: There is no description about the way to decide the target study.
Our response: The authors added description about the way that they decided the target studies in Section 1.5: “From the resulted search, publications with recent publishing date and/or having more citation number have been more preferable”.
Comment 3: There is no description about review’s validity.
Our response: The authors appreciate the reviewer’s concern about the review’s validity, hence, they added a subsection in the Introduction section to clearly describe the methodology used to conduct this review: “Some paradigms are extensively discussed in the literature, so we highlight the review articles that focus on this particular domain. Other paradigms have less attention in the literature, hence, we provide a brief review about them. Some paradigms have not been discussed in the literature, thus, we highlight them as research gaps. Each set of methods that follow single paradigm has been discussed solely in this paper”.
Comment 4: The authors should clearly define the scope for this review.
Our response: The authors clearly stated the scope for the review in Section 1.5 as requested by the review: “The main scope of this paper is to describe and discuss all paradigms proposed in the literature to solve MO-MINLPs”. While the aim of the review is stated in Section 1.4: “This paper aims to contribute to the literature by providing a recent overview of the exact, approximate and hybrid optimization methods that handle MO-MINLP problems. This work aims to provide enough descriptive information for the newcomers in this area about the research that has been done and that is currently under way concerning the methods used to solve MO-MINLP problems”.
Comment 5: No reasons were given for using this classification in the study.
Our response: The authors appreciate this significant comment, accordingly, the authors have added the reason in Section 1.3: “This classification is based on the type of the resulting solution(s) by the method, i.e. exact (real) solution or approximate (estimated) solution. While hybrids gain their name from the hybridization of different methods to produce better performance.”
Comment 6: In the review methodology, the authors should demonstrate what kind of key word they used when searching relevant papers, and their standard for data washing. Such information will help future readers to reproduce the research easier.
Our response: The authors demonstrated the key words used in the search in Section 1.5 as requested from the reviewer: “To this aim, the literature has been reviewed using the Scopus database based on combination of five groups of specific keywords. The first group of keywords includes multi-objective, multi-criteria and many objectives. The second group consists of evolution, evolutionary, genetic, firefly, ant colony, bee colony, particle swarm, heuristic, and metaheuristic. The third group includes exact, deterministic and true front. The fourth group includes hybrid, tree search, combining metaheuristics and multi-criteria branch and bound. And the last group includes discrete, combinatorial and mixed-integer”.
Comment 7: Some important recent references (2020-2024) are missing, such as:
Khodashenas, M., Najafi, S. E., Kazemipoor, H., & Sobhani, M. (2023). Providing an integrated multi-depot vehicle routing problem model with simultaneous pickup and delivery and package layout under uncertainty with fuzzy-robust box optimization method. Decision Making: Applications in Management and Engineering, 6(2), 372–403. https://doi.org/10.31181/dmame622023640
Mzili, T., Mzili,I., Riffi, M.E., Pamucar, D., Simic, V., Kurdi, M. (2023). A novel discrete rat swarm optimization algorithm for the quadratic assignment problem. Facta Universitatis: Series Mechanical engineering, 21(3), 529-552. https://doi.org/10.22190/FUME230602024M
Ghaseminejad, A., Kazemipoor, H., & Fallah, M. (2023). Modeling the robust facility layout problem for unequal space considering health and environmental safety criteria under uncertain parameters. Decision Making: Applications in Management and Engineering, 6(2), 426–460.
Mzili, T., Mzili,I., Riffi, M.E., Pamucar, D., Simic, V., Abualigah, L. (2023). Hybrid genetic and penguin search optimization algorithm (GA-PSEOA) for efficient flow shop scheduling solutions. Facta Universitatis, Series: Mechanical Engineering. https://doi.org/10.22190/FUME230615028M
Our response: The suggested references have been integrated as suitable in the paper.
Comment 8: The far more significant concern this reviewer has is with the contribution of the paper. Only one citation to an article published in Eng. This raises the question for this reviewer as to why the authors chose to submit the paper to Eng. If the authors wish to make a contribution to the knowledge being generated in and by this top-tier journal, then the authors should find some related work published in Eng to link their work to. Finally, this reviewer thinks that it is crucial for the authors to connect their work more meaningfully to the work of authors in the Eng community and they should do so to improve their contribution.
Our response: The authors highly appreciate this significant concern. Consequently, they have related their work to four additional studies done by the authors in the ENG community.
- https://doi.org/10.3390/eng2030022
- https://doi.org/10.3390/eng5020049
- https://doi.org/10.3390/eng5020038
- https://doi.org/10.3390/eng5020050
Once again, we sincerely thank you for your valuable feedback. We have carefully addressed each of your comments, and we believe the revised manuscript now significantly improves upon the initial submission. We hope these revisions meet your expectations, and we look forward to your feedback on the updated version of the manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper reviews the methods for Multi-Objective Mixed-Integer Non-Linear Programming problems.
1. Abstract. The research questions should not be placed at the end of the abstract but in the first half.
2. I suggest further highlighting how different methods handle nonlinearities in optimization problems.
Author Response
The authors would firstly thank the reviewer for taking the time to review our manuscript titled " A Review on Multi-Objective Mixed-Integer Non-Linear Optimization Programming Methods " and for providing valuable feedback. We have carefully considered your comments and suggestions and have made several revisions to address the concerns raised.
Comment 1: Abstract. The research questions should not be placed at the end of the abstract but in the first half.
Our response: The abstract has been properly modified to suit the reviewer generous comment.
Comment 2: I suggest further highlighting how different methods handle nonlinearities in optimization problems.
Our response: Section 2.3 refer the reader to the suitable review articles that review each type of nonlinear problem, i.e. mono/multi-objective or convex/non-convex. However, the authors agree the reviewer’s precious comments, hence, Section 2.3 has been accordingly modified by adding some examples of different methods that handle nonlinear problems: “In [60], the authors mention six methods that can handle convex MINLPs, among them Outer Approximation and Extended Cutting Plane methods. In [61], the authors mentioned several techniques – such as factorization, under- and over-estimators and separable functions - in addition to various branch and bound based methods - such as spatial and a branch and bound - to solve non-convex MINLPs”.
Once again, we sincerely thank you for your valuable feedback. We have carefully addressed each of your comments, and we believe the revised manuscript now significantly improves upon the initial submission. We hope these revisions meet your expectations, and we look forward to your feedback on the updated version of the manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAs far as I am considered, the paper may be accepted for publishing as it is.
