Constrained multi-objective optimization problems (CMOPs) are prevalent in real-world applications, dealing with multi-objective and constraint functions. Multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) has proven effective for unconstrained multi-objective optimization problems with complex Pareto front (PF). However, in CMOPs, the conflicting nature between objectives and constraints often makes it challenging to appropriately manage constraints while ensuring convergence, diversity, and feasibility of the solution set towards the PF. To address this issue, this paper proposes a bilayered decomposition technique. The proposed algorithm treats constraints as an additional objective function, separately decomposing the objective space and the constraint violation space. This method allows for the simultaneous attainment of convergence, diversity, and feasibility in the solution set while efficiently exploring the PF. Experimental results demonstrate that, within the MOEA/D-DE framework, our algorithm efficiently navigates complex PFs on challenging problems such as LIR-CMOPs and DAS-CMOPs, matching the performance of state-of-the-art constrained multi-objective evolutionary algorithms.

Presents corrections to the article "A Sub-Pixel Accurate Quantification of Joint Space Narrowing Progression in Rheumatoid Arthritis".

As systems become larger and more complex, real-world problems, such as system operation, require that quasi-optimal solutions with sufficient engineering optimality be obtained in practical time. Meta-heuristics have attracted attention as a framework for methods that seek quasi-optimal solutions. We focus on the issue of degeneracy in the Combinatorial optimization method with search strategy based on hierarchical interpretation of solution space, which has high performance and versatility compared to existing basic methods. The degeneracy is a phenomenon in which multiple search points follow the same path, which has negative effects such as wasting computational resources and weakening the interaction between search points. A new stochastic process is introduced with the main objective of improving search performance by dealing with the degeneracy. The occurrence of the degeneracy and search performance are compared and verified with the original method. We use the basic bench-mark problems: Knapsack Problem (KP), Traveling Salesman Problem (TSP), Flow-shop Scheduling Problem (FSP), and Quadratic Assignment Problem (QAP).

Differential Evolution (DE) is one of the effective metaheuristics for solving unconstrained optimization problems. Constraint Handling Technique (CHT) is needed to extend DE to constrained optimization. Feasibility Rule (FR) is one of the typical CHT. FR addresses constraints by using a simple rule that considers the objective function and constraint violation when comparing search individuals. However, since the solutions with small constraint violation, i.e., feasible solutions, are preferentially selected, the set of search individuals may be biased toward feasible regions and the improvement of the objective function value may stagnate. This paper overcomes this challenge by proposing a DE that uses a superior infeasible solution in an external archive. The external archive in the proposed DE stores search individuals that are superior in both objective function value and constraint violation and utilize them to generate mutant individuals. Finally, we verify the effectiveness of the proposed method using a benchmark problem where the feasible region is a convex set.

Rheumatoid arthritis (RA) is a chronic autoimmune disease that primarily affects peripheral synovial joints, like fingers, wrists and feet. Radiology plays a critical role in the diagnosis and monitoring of RA. Limited by the current spatial resolution of radiographic imaging, joint space narrowing (JSN) progression of RA for the same reason above can be less than one pixel per year with universal spatial resolution. Insensitive monitoring of JSN can hinder the radiologist/rheumatologist from making a proper and timely clinical judgment. In this paper, we propose a novel and sensitive method that we call partial image phase-only correlation which aims to automatically quantify JSN progression in the early RA. The majority of the current literature utilizes the mean error, root-mean-square deviation and standard deviation to report the accuracy at pixel level. Our work measures JSN progression between a baseline and its follow-up finger joint images by using the phase spectrum in the frequency domain. Using this study, the mean error can be reduced to 0.0130 mm when applied to phantom radiographs with ground truth, and 0.0519 mm standard deviation for clinical radiography. With the sub-pixel accuracy far beyond usual manual measurements, we are optimistic that the proposed work is a promising scheme for automatically quantifying JSN progression.

The spiral optimization (SPO) algorithm proposed by Tamura and Yasuda is a relatively novel and simple search concept inspired by natural spiral phenomena. This algorithm searches continuous space using no gradient and only spiral trajectories composed of spiral vectors generated by deterministic spiral models. The primary purpose of this paper is to propose conditions and settings that mathematically ensure the convergence of the SPO algorithm to a stationary point. The conditions relating to the sizes and directions of the spiral vectors and the initial search points are based on direct search theory and recent SPO algorithm theories. The presented convergence was numerically verified using test functions with different properties.

In this paper, we introduce a new expanded search mechanism, which pays attention to updating the group of solutions searched by same search point rather than just a solution. After confirming the affinities to “Hierarchical Interpretation of Solution Space which is also proposed by our research group, we adapt the expanded search mechanism to the search tactics based on the structure above. This assembly allows us to search solutions by expanding the explored area in the combinatorial optimization problem solution space, rather than searching in a route. In addition, remained issues in previous tactics can also be solved. To verify the basic performance of the expanded search mechanism, we propose a new combinatorial optimization method with previous strategies, and compare it with previous method by numerical experiment. Finally, the new mechanism's potentials are discussed.

Metaheuristic algorithms usually aim to solve nonconvex optimization problems in black-box and high-dimensional scenarios. Characterizing and understanding the properties of nonconvex problems is therefore important for effectively analyzing metaheuristic algorithms and their development, improvement and selection for problem solving. This paper establishes a novel analysis framework called nonconvex ratio analysis , which can characterize nonconvex continuous functions by measuring the degree of nonconvexity of a problem. This analysis uses two quantitative measures: the nonconvex ratio for global characterization and the local nonconvex ratio for detailed characterization. Midpoint convexity and Monte Carlo integral are important methods for constructing the measures. Furthermore, as a practical feature, we suggest a rapid characterization measure that uses the local nonconvex ratio and can characterize certain black-box high-dimensional functions using a much smaller sample. Throughout this paper, the effectiveness of the proposed measures is confirmed by numerical experiments using the COCO function set.

There is a multi-objective optimization problem that is very similar to the superior solution set search problem. Studies on multi-objective optimization problems have been very active recently and solution applications to the superior solution set search problem are to be expected. The superior solution set search problem contains parameters that provide constraints on evaluation value and distance. However, an optimization method for the superior solution set search problem explicitly incorporating these parameters has not yet been proposed. Therefore, in this paper, we propose an evaluation indicator that is inspired by a method based on a dominance relationships in multi-objective optimization problems and includes the aforementioned parameters. We also propose a search method based on this indicator and perform numerical experiments on unique superior solution set search problems. The proposed method finds more superior solutions than the conventional single-objective optimization method, which confirms its usefulness.

In conventional single objective optimization, presenting multiple alternatives is difficult because the aim is to search for only one global optimal or suboptimal solution. In this study, we propose a superior solution set search problem as an optimization problem to simultaneously find multiple excellent solutions in multimodal functions. In addition, we analyze the characteristics of the Firefly Algorithm (FA), which divides the search process into multiple clusters, and using this property, we efficiently search for the superior solution set. We interpret the metaheuristics strategy (i.e., diversification and intensification) of the superior solution set search problem and clarify the effects of parameters on the cluster search dynamics of FA in terms of the metaheuristics strategy. After the above analysis, we propose an Adaptive FA that preliminarily performs parameter adjustment according to set target value schedule, evaluate indicators of diversification and intensification for the superior solution set search problem, and verify their usefulness by conducting a numerical experiment using three typical benchmark functions.

In this paper, we focus on the idea of integral designing of problems/methods/distances in metaheuristics for combinatorial optimization problems. As a practical example of the above idea, we reconstruct and propose a method previously proposed by the authors. The above idea is important in combinatorial optimization, where it is necessary to consider the distance according to each problem. Furthermore, the idea is particularly important for methods that use distance for the movement strategy, which was proposed the authors. We report that, based on the above idea, when considering the distance, the proposed method has better search performance than the previous method in the flow shop scheduling problem.

A "basin of attraction" is a set of solutions arriving at the same local optimal solution by Best-improvement Local Search. By utilizing the concept of basin of attraction in the solution space of combinatorial optimization problem, the solution space is interpreted as a higher structure, which is a set of basin of attraction, and a lower structure, which is a set of solutions, in this paper. Based on the hierarchical interpretation of the solution space, which consists of the higher structure and the lower structure, and basic strategy in metaheuristics, an optimization method with search strategy to find a basin of attraction to which superior local optimal solution belongs is proposed. The search performance of this method was evaluated through numerical experiments using benchmark problems. In addition, the search situation and influence on search by parameter of this method are considered.

Recently, the development of high-performance metaheuristics has become an important subject. In this study, an adaptive Cuckoo Search based on ranking of search point is proposed. This study aims to improve the performance of Cuckoo Search by adjusting the parameter β to allow search points with good evaluation value to search nearby and those with poor evaluation value to search far away. Finally, the performance of the proposed method is evaluated by numerical experiments.

We analyzed the search characteristics of Firefly Algorithm (FA), which has a fundamental nature of a Superior Solution Set Search Problem, previously defined in our previous study for single-objective optimization problems. In this study, we proposed a new FA method based on the former problem. This method, which employs cluster information by K-means clustering, is tested for performance by fundamental numerical experiments.

In this paper, we propose a new search strategy based on functional specialization for multi-objective optimization and a new multi-objective optimization method. The proposed strategy is based on two ideas. The first idea is the state evaluation and classification of search points to realize an advanced search structure. The second idea is to use operations with different features to achieve an efficient search. The proposed method takes advantage of this search strategy to achieve high convergence and a well diversified solution set during multi-objective optimization. The performance of the proposed method was verified by a numerical simulation using typical benchmark problems.

This paper proposes a new formulation for single-objective optimization problems and a Firefly Algorithm (FA)-based optimization method for problem formulation. The formulated problem requires a set of solutions with approximately the same evaluation values and appropriate differences in relation to decision variables. In addition, the FA-based optimization method was developed based on an analysis of the FA search mechanism. Finally, the performance of the developed method is verified.

In this paper, we focus on Cuckoo Search (CS) that is one of metaheuristics, and propose an adaptive CS to improve its search performance and usability. First, we analyze basically and qualitatively the effects of CS's parameter on its search dynamics. Second, from the analysis results, we define an indicator that evaluates the search state of CS based on the effective metaheuristics strategy. Moreover, based on the indicator, we construct a new mechanism to control the search state by adaptively adjusting a parameter of CS. The performance of the proposed adaptive CS with the parameter adjustment mechanism is verified through numerical simulations for several types of typical benchmark problems.

A big valley structure is known to exist as the landscape of solution-objective function value spaces in a multitude of combinatorial optimization problems. However, this paper proposes new meta-heuristics for combinatorial optimization problems based on the degree of establishment of the big valley structure. The performance of the proposed combinatorial optimization method is verified through simulations by employing two types of typical benchmark problems.

A new smart strategy for supply-demand control in distributed energy systems, which strategy is based on Energy Management System (EMS) and Dynamic Pricing (DP) is proposed in this paper. This strategy can achieve both economical operation of customers by EMS and maintenance of the supply demand balance by the indirect control of a power company using DP. The effectiveness of the coordinative control for a distributed energy system, which has load, battery, photovoltaics and fuel cells as composition elements of a customer, is verified.

The primary study on feedback controlled Differential Evolution (FCDE) is presented. FCDE is a novel framework of DE with an automatic parameter adjustment mechanism, which controls its search situation (evaluation index) to be a promising situation (reference index) by the error feedback. Its adjustment mechanism consists of three parts: Estimator, Referencer, and Controller. Estimator calculates an evaluation index which quantitatively measures the search situation about the population diversity. Referencer generates a reference index being the ideal target of the evaluation index. Controller operates the DE parameters every generation to make the evaluation index follow the reference index. Further, this paper actually realizes a FCDE method using a typical DE by designing the three parts. The effectiveness of the proposed method is confirmed through computational experiment from viewpoint of the controllability and performance.

In recent years, the authors proposed a new multipoint metaheuristics, called Spiral Optimization (SPO), based on analogy of spiral phenomena for continuous optimization problems. The search points moving toward the common center with logarithmic spiral trajectories can find better solutions. In this paper, we propose a Cluster-structured SPO that aims to enhance diversification property to search the solution space more globally than the original SPO. The effectiveness and search performance of the proposed method are confirmed through simulation for typical benchmark functions.

This paper first completes Spiral Optimization (SPO), which is a new metaheuristics method proposed by the authors based on analogy of spiral phenomena in nature, by refining our previous studies and adding some new matters. Secondary, we point out that the SPO model has a dynamic equilibrium point and strictly analyze its asymptotic stability and ε-stability. In addition, the stability analysis results are applied to a simple setting method for a parameter of SPO. Finally, we evaluate the effectiveness and peculiarity of SPO through numerical experiments for some benchmark problems and comparing other representative methods PSO and DE.

In this paper, we focus on one of the Meta-Heuristics Differential Evolution (DE) and propose an adaptive parameter adjustment method to improve its search performance and usability. First, we define a scalar index based on numerical analysis according which diversification and intensification of search in DE can be executed. Moreover, we set an ideal target schedule for the index to reach a high level of search performance. Then we propose an adaptive parameter adjustment method to adjust the parameters properly so that the index can follow the ideal target schedule during the search process. Finally, we use several classic benchmark problems for the numerical experiment to verify the effectiveness of this newly proposed method.

In this paper, the authors propose a new practical multi-objective optimization framework that combines optimization method, modeling and simulation technologies organically. The new framework is called Multi-Objective Integrated Optimization that combines Multi-Objective Differential Evolution and Radial Basis Function Network. This new framework is used to reduce the number of accesses to a simulator or a sensing system with heavy computational load. According to the numerical experiment on typical benchmark problems, it is shown that the proposed Multi-Objective Integrated Optimization obtains good Pareto solutions with drastic reduction in the number of function calls for evaluating the performance index values of systems.

In this paper, we introduce a new concept into solution space of combinatorial optimization problems, and propose an optimization method algorithm based on hierarchical structure in solution space. The introduced new concept: "basin of attraction" is a set binding solutions by utilizing properties of local optimal solution. We become able to construe solution space as not only set of solutions but also set of basins of attraction hierarchically. The proposed method clarifies the search policy by relating hierarchical structure in solution space with intensification and diversification. We inspect performance of the proposed method by numerical experiment using typical benchmark problems.

In recent years, the authors proposed an effective metaheuristics method for continuous optimization problems based on analogy of spiral phenomena in nature which is called Spiral Optimization (SPO). The SPO has two setting parameters: the convergence rate and the rotation rate. Their values affect the search performance depending on computational and/or problem conditions. However, their effective setting methods without trial and error have not studied so far including analyses of its search dynamics which are needed for making such methods. This paper especially focuses on the convergence rate and proposes 1 its effective setting method from analyzing stability of dynamic equilibrium point of the SPO model. The effectiveness of the proposed method is confirmed thorough simulation for some benchmark functions and comparison with other representative metaheuristics methods.

Recently, the authors proposed a new metaheuristics method for continuous optimization problems based on analogy of spiral phenomena in nature which is called Spiral Optimization. The focused spiral phenomena are spirals which are approximated to logarithmic spirals. The Spiral Optimization utilizes a feature of the logarithmic spirals for global optimization. The Spiral Optimization has two tuning parameters: the convergence rate r and the rotation angle θ. However, any tuning methods and policies for them were not studied and referred in our previous works. This paper especially focuses on the convergence rate r and quantitatively analyzes its properties. Furthermore, by using the analysis result, a simple the convergence rate tuning law which can match various computational conditions and problems is proposed.

In this paper, a new optimization method based on a combination of Differential Evolution (DE) and Evolution Strategy (ES), which belong to both Meta-Heuristics and Evolutionary Computation, are developed as a fast approximation optimization method. A weak point of DE is weak local search ability and considerable computation time for obtaining a good approximate solution. The proposed method aims at compensation for the weak points of DE by connecting ES with strong local search capacity. The effectiveness of the proposed method is confirmed through the numerical experiments.

This paper deals with autonomous decentralized operation for a distributed energy system composed of a number of customers with dispersed generation and storage systems. The distributed energy system studied in this paper has the following operation structures: (1) Operation for customer's energy storage which is decided by production rules with learning function, and (2) Operation for power flow on distribution network which is determined by a successive approximation method. In this paper, we especially study the autonomous decentralized operation in (1). To enhance the autonomy and effectiveness of the autonomous decentralized operation a distributed energy system, Genetic Algorithm is applied to learning of production rules.

Recently we proposed a new multipoint search method in metahuristics for only 2-dimensional continuous optimization problems based on analogy of spiral phenomena in nature which is called 2-dimensional spiral optimization. The focused spiral phenomena which appear frequently in nature are approximated to logarithmic spirals. The 2-dimensional spiral optimization utilizes a feature of logarithmic spirals. In this paper, we propose n-dimensional spiral optimization by extending 2-dimensional one. The n-dimensional spiral model is constructed based on rotation matrices defined in n-dimensional space. Simulation results for various benchmark problems show effectiveness of the proposed method in comparison with other metaheuristics.

This paper presents a hierarchical optimization method for determining optimal operation of a distributed energy system which consists of a distribution network and customers with dispersed generation and storage systems. The optimal operation problem of a distributed energy system is divided into two subproblems; optimal operation of a dispersed energy system for a customer and optimal operation of power flow on distribution network. While Dynamic Programming (DP) is used for solving optimal operation of a dispersed energy system for a customer, successive approximation method is applied for obtaining optimal operation of power flow on distribution network. The practicability and generality of the developed hierarchical optimization method for determining optimal operation of a distributed energy system are evaluated through some simulations using some simple models of a distributed energy system consisting of a distribution network and customers with dispersed generation and storage systems.

This paper proposes a new method for solving combinatorial optimization problems on the basis of Proximate Optimality Principle (POP). The proposed method has higher optimality and lower computational complexity than conventional methods. The proposed method is applied to several typical combinatorial optimization problems in order to verify the performance of the proposed method.

Differential Evolution (DE) is based on both an evolutionary strategy and a parallel direct search method employing a population. DE is an effective optimization method available for solving global optimization problem over continuous space. DE has a few control parameters that have to be set by users. This paper describes a new DE using Down-hill Simplex Method. Then we consider and examine average distance of a new DE. In addition we append a mechanism, using a proposed method or the other proposed method according to the average distance, to the new DE. The feasibility and advantage of the proposed DE are demonstrated through some numerical simulations using four different typical global optimization test problems.

In order to meet the high requirement of practical optimization, it is essential to construct an integrated optimization system for real systems, which is a new paradigm of optimization system based on combining optimization technique with modeling and simulation technologies. From the viewpoint of optimality and computational efficiency, this paper examines some strategies for arranging sample points adaptively in an integrated optimization system that combines Particle Swarm Optimization and Radial Basis Function Network. The proposed strategies for arranging sample points are examined through numerical simulations using four types of typical benchmark problems.