# Combinatorial Optimization Problems and Metaheuristics: Review, Challenges, Design, and Development
## 1 Introduction
### Research Objective and Questions  
This review paper aims to organize a body of knowledge by arranging the fundamental concepts and building blocks necessary to design and implement COPMH. Consequently, this paper has two main objectives. Section 1 provides a review of the field and Section 2 propose a standardization. In the review, two central points will be researched: in Section 1.1, the most important concepts and definitions (COPMH) and in Section 1.2 the main challenges of the field. For the second objective, this work must consider at least three classes of behavior: combinatorial optimization problem and its building blocks (Section 2.1), metaheuristics interface and interactions (Section 2.2), and typical operations that a framework structure should consider (Section 2.3). To address these objectives, we formulated five research questions. Before proceeding to the description of each research question, it is important to highlight that _RQ-1_ and _RQ-2_ are concerned with the review objectives of this paper. Moreover, they were designed, especially _RQ-1_, to provide essential inputs to the other research questions (_RQ-3_, _RQ-4_, and _RQ-5_).  
_RQ-1_: What are the fundamental concepts of COP (combinatorial optimization problem) and metaheuristics?  
_Rationale:_ The response to this question aims to offer the necessary knowledge to comprehend this research and its fundamental concepts. These concepts are vital for the reader and provide a broad perspective as a starting point in the COP and metaheuristics field. It also must support the understanding of the standard proposed and its definitions in this study.  
_RQ-2:_ What are the main challenges of the COP and metaheuristics research field?  
_Rationale:_ This question intends to draw attention to fundamental issues of the COP and metaheuristics research field by investigating several papers and other pieces of knowledge. Consequently, this question also can lead to future studies that may require community attention. Additionally, some of these open questions can provide valuable contributions to _RQ-3_, _RQ-4_, and _RQ-5_, considering that some issues can be treated through some guidelines and formalism.  
_RQ-3:_ What are the features of COP and metaheuristics that could be developed as independent methods in a framework structure?  
_Rationale:_ By answering this question, the main idea is to identify the elements that should be part of a framework structure because they can be reused in other situations by any COP or heuristic (without coding efforts in future problems). Consequently, avoiding the development of components that can be reused. Additionally, it also reduces the efforts to formulate a problem or develop a metaheuristic, make them leaner and simpler to define.  
_RQ-4:_ How can we develop a body of knowledge to formulate combinatorial optimization problems in a standard way?  
_Rationale:_ This question has many facets. It involves different aspects, which englobes the conceptual and practical perspectives to design and implement COP in a generic way. Therefore, a problem standard must consider a wide range of different problem specificities and several aspects of communication with heuristics and framework methods. The objective behind this is to provide guidelines to formulate COP in a standard way that can be manipulated by any method that knows its standard.  
_RQ-5:_ How can we define a standard design for metaheuristics completely without coding links to the problems?  
_Rationale:_ The answer to this question should provide a software pattern for metaheuristics, defining a set of behaviors and standard API (Application Programming Interface). Furthermore, a metaheuristics standard must follow a problem standard that also provides its own API. Therefore, it must know how to manipulate the COP by being aware of its behaviors. Consequently, the answer to _RQ-4_ will support the answer to this question.