Abstract Notably, real problems are increasingly complex and require sophisticated models and algorithms capable of quickly dealing with large data sets and finding optimal solutions. However, there is no perfect method or algorithm; all of them have some limitations that can be mitigated or eliminated by combining the skills of different methodologies. In this way, it is expected to develop hybrid algorithms that can take advantage of the potential and particularities of each method (optimization and machine learning) to integrate methodologies and make them more efficient. This paper presents an extensive systematic and bibliometric literature review on hybrid methods involving optimization and machine learning techniques for clustering and classification. It aims to identify the potential of methods and algorithms to overcome the difficulties of one or both methodologies when combined. After the description of optimization and machine learning methods, a numerical overview of the works published since 1970 is presented. Moreover, an in-depth state-of-art review over the last three years is presented. Furthermore, a SWOT analysis of the ten most cited algorithms of the collected database is performed, investigating the strengths and weaknesses of the pure algorithms and detaching the opportunities and threats that have been explored with hybrid methods. Thus, with this investigation, it was possible to highlight the most notable works and discoveries involving hybrid methods in terms of clustering and classification and also point out the difficulties of the pure methods and algorithms that can be strengthened through the inspirations of other methodologies; they are hybrid methods.

This paper conducts a comprehensive literature review concerning hybrid techniques that combine optimization and machine learning approaches for clustering and classification problems. The aim is to identify the potential benefits of integrating these methods to address challenges in both fields. The paper outlines optimization and machine learning methods and provides a quantitative overview of publications since 1970. Additionally, it offers a detailed review of recent advancements in the last three years. The study includes a SWOT analysis of the top ten most cited algorithms from the collected database, examining their strengths and weaknesses as well as uncovering opportunities and threats explored through hybrid approaches. Through this research, the study highlights significant findings in the realm of hybrid methods for clustering and classification, showcasing how such integrations can enhance the shortcomings of individual techniques.

Abstract In engineering optimization with continuous variables, the use of Stochastic Global Optimization (SGO) algorithms is popular due to the easy availability of codes. All algorithms have a global and local search character, where the global behaviour tries to avoid getting trapped in local optima and the local behaviour intends to reach the lowest objective function values. As the algorithm parameter set includes a final convergence criterion, the algorithm might be running for a while around a reached minimum point. Our question deals with the local search behaviour after the algorithm reached the final stage. How fast do practical SGO algorithms actually converge to the minimum point? To investigate this question, we run implementations of well known SGO algorithms in a final local phase stage.

The provision of home health care services is becoming an important research area, mainly because in Portugal the population is ageing and it is necessary to perform home care services. Home care visits are organized taking into account the medical treatments and general support that elder/sick people need at home. This health service can be provided by nurses teams from Health Units, requiring some logistics for this purpose. Usually, the visits are manually planned and without computational support. The main goal of this work is to carry out the automatic nurse’s allocation of home care visits, of one Bragança Health Unit, in order to minimize the nurse’s workload balancing, spent time in all home care visits and, consequently, reduce the costs involved. The developed methodology was coded in MatLab Software and the problems were efficiently solved by the particle swarm optimization method. The nurse’s allocation solution of home care visits for the presented case study shows a significant improvement and reduction in the maximum time, in the nurse workload balancing, as well as the patients waiting time.

In logistics of home health care services in the Health Units, the managers and nurses need to carry out the schedule and the vehicles routes for the provision of care at the patients' homes. Currently, in Portugal, these services are increasingly used but the problem is still, usually, solved manually and without computational resources. The increased demand for home health care due to the boost of the elderly people number entails a high associated cost which, sometimes, does not guarantee the quality of the service. In this sense, the periodic vehicle routing problem is a generalization of the classical vehicle routing problem in which routes are determined for a time horizon of several days. In this work, it is provided a periodic vehicle routing problem applied in the Health Unit in Bragança. An integer linear programming formulation for the real database, allowed to solve the problem in an efficient and optimized way using the CPLEXR software.

Due to the increasing of life expectancy in the developed countries, the demand for home health care services is growing dramatically. Usually, home services are planned manually and lead to various optimization problems in their activities. In this sense, health units are confronted with appropriate scheduling which may contain multiple, often conflicting, objectives such as minimizing the costs related to the traveling distance while minimizing the traveling time. In order to analyze and discuss different trade-offs between these objectives, it is proposed a multi-objective approach to home health care scheduling in which the problem is solved using the Tchebycheff method and a Genetic algorithm. Different alternative solutions are presented to the decision maker that taking into account his/her preferences chooses the appropriate solution. A problem with real data from a home health care service is solved. The results highlight the importance of a multi-objective approach to optimize and support decision making in home health care services. Moreover, this approach provides efficient and good solutions in a reasonable time.

The head shaking that results from robot locomotion is important because it difficults stable image acquisition and the possibility to rely on that information to act accordingly, for instance, to achieve visually-guided locomotion.

This paper presents the implementation of a constraint-handling technique within the electromagnetism-like algorithm devised by Birbil and Fang, for solving real-world engineering design problems. A derivative-free elite-based descent search scheme is also included in the final stage of each iteration to accelerate convergence and improve accuracy. Numerical experiments with a set of engineering problems are carried out and a comparison with other stochastic methods is reported.