Many optimization problems in reality involve both continuous and discrete decision variables, and these problems are called mixed-variable optimization problems (MVOPs). The mixed decision variables of MVOPs increase the complexity of search space and make them difficult to be solved. The Particle Swarm Optimization (PSO) algorithm is easy to implement due to its simple framework and high speed of convergence, and has been successfully applied to many difficult optimization problems. Many existing PSO variants have been proposed to solve continuous or discrete optimization problems, which make it feasible and promising for solving MVOPs. In this paper, a new PSO algorithm for solving MVOPs is proposed, namely P S O m v , which can deal with both continuous and discrete decision variables simultaneously. To efficiently handle mixed variables, the P S O m v employs a mixed-variable encoding scheme. Based on the mixed-variable encoding scheme, two reproduction methods respectively for continuous variables and discrete variables are proposed. Furthermore, an adaptive parameter tuning strategy is employed and a constraints handling method is utilized to improve the overall efficiency of the P S O m v .The experimental results on 28 artificial MVOPs and two practical MVOPs demonstrate that the proposed P S O m v is a competitive algorithm for MVOPs.

A Particle Swarm Optimization Algorithm for Mixed-Variable Optimization Problems

A large number of intelligent algorithms based on social intelligent behavior have been extensively researched in the past few decades, through the study of natural creatures, and applied to various optimization fields. The learning-based intelligent optimization algorithm (LIOA) refers to an intelligent optimization algorithm with a certain learning ability. This is how the traditional intelligent optimization algorithm combines learning operators or specific learning mechanisms to give itself some learning ability, thereby achieving better optimization behavior. We conduct a comprehensive survey of LIOAs in this paper. The research includes the following sections: Statistical analysis about LIOAs, classification of LIOA learning method, application of LIOAs in complex optimization scenarios, and LIOAs in engineering applications. The future insights and development direction of LIOAs are also discussed.

A Survey of Learning-Based Intelligent Optimization Algorithms

Swarm intelligence (SI) is the collective behavior of decentralized, self-organized natural or artificial systems. Monarch butterfly optimization (MBO) algorithm is a class of swarm intelligence metaheuristic algorithm inspired by the migration behavior of monarch butterflies. Through the migration operation and butterfly adjusting operation, individuals in MBO are updated. MBO can outperform many state-of-the-art optimization techniques when solving global numerical optimization and engineering problems. This paper presents a comprehensive review of the MBO algorithm including its modifications, hybridizations, variants, and applications. Additionally, further research directions for MBO are discussed. This review study serves as a solid reference for future studies in the arena of SI and in particular the MBO algorithm.

Monarch butterfly optimization: A comprehensive review

Hybrid many-objective particle swarm optimization algorithm for green coal production problem

Portfolio optimization is the process of determining the best combination of securities and proportions with the aim of having less risk and obtaining more profit in an investment. Utilizing covariance as a risk measure, mean-variance portfolio optimization model has brought a revolutionary approach to quantitative finance. Since then, along with the advancements in computational power and algorithmic enhancements, a lot of efforts have been made on improving this model by considering real-life conditions and solving model variants with various methodologies tested on various data and performance measures. A comprehensive literature review of recent and novel papers is crucial to establish a pattern of the past, and to pave the way on future directions. In this paper, a total of 175 papers published in the last two decades are selected within the scope of operations research community and reviewed in detail. Thus, a comprehensive survey on the deterministic models and applications suggested for mean-variance portfolio optimization in which several variants of this model as well as additional real-life constraints are studied. The review classifies the approaches according to exact and approximate attempts and analyzes the proposed algorithms based on various data and performance indicators in depth. Areas of future research are outlined.

A comprehensive review of deterministic models and applications for mean-variance portfolio optimization

A hybrid particle swarm optimization algorithm using adaptive learning strategy

Recently, multi-objective evolutionary algorithms (MOEAs) have been widely explored and applied to many real-world problems. Particularly, preference-based MOEAs are among the mostly studied. Several preference-based optimization algorithms have already been proposed in literature. However, most existing studies focus on how to locate the region of interest (ROI) and how to control the size of ROI, and overlook the relationship between preference information and distribution of the final solutions. Given that the distribution of the final solutions is also an important factor, in this paper, we propose a new preference-based MOEAs called MOEA/D-AWV using an adaptive weight vector generation strategy (AWV). The weight vectors are generated adaptively by the decision maker’s preference, and finally guide the solutions to converge to a preferred distribution. Solutions will converge to the reference point as close as possible with the AWV strategy, which will lead to the loss of diversity. In order to prevent the search process from being trapped at local optima, we propose an adaptive parameter tuning scheme (APT) to maintain diversity during the search process. In addition, since the distribution of weight vectors should adapt to the changes of decision makers’ preference, the APT scheme can help algorithm find desired results in different scenarios. Compared with five state-of-the-art preference-based MOEAs on 23 test instances, MOEA/D-AWV achieves the best performance. Especially, in many-objective optimization problems with high-dimensional objective space, our proposed MOEA/D-AWV still shows a competitive performance.

An adaptive weight vector guided evolutionary algorithm for preference-based multi-objective optimization

A simple PID-based strategy for particle swarm optimization algorithm

Multiobjective evolutionary algorithms based on decomposition (MOEA/D) decompose a multiobjective optimization problem (MOP) into a group of subproblems and optimizes them at the same time The reproduction method in MOEA/D, which generates offspring solutions, has crucial effect on the performance of algorithm As the difficulties of MOPs increases, it requires much higher efficiency for the reproduction methods in MOEA/D However, for the complex optimization problems whose PS shape is complicated, the original reproduction method used in MOEA/D might not be suitable to generate excellent offspring solutions In order to improve the property of the reproduction method for MOEA/D, this paper proposes an external archive matching strategy which selects solutions’ most matching archive solutions as parent solutions The offspring solutions generated by this strategy can maintain a good convergence ability To balance convergence and diversity, a perturbed learning scheme is used to extend the search space of the solutions The experimental results on three groups of test problems reveal that the solutions obtained by MOEA/D-EAM have better convergence and diversity than the other four state-of-the-art algorithms

Heng Zhang

Papers

A hybrid particle swarm optimization algorithm using adaptive learning strategy

A Particle Swarm Optimization Algorithm for Mixed-Variable Optimization Problems

An adaptive weight vector guided evolutionary algorithm for preference-based multi-objective optimization

A simple PID-based strategy for particle swarm optimization algorithm

External archive matching strategy for MOEA/D