距離に基づく相互作用を用いた多点探索型組合せ最適化手法

In this study, we propose a new global optimization method in which the simultaneous perturbation gradient approximation is introduced into a multi-point type chaotic optimization method. The multi-point type chaotic optimization method, which has been proposed recently, is a global optimization method to solve unconstrained optimization problems in which multiple search points which implement global search driven by a chaotic gradient dynamic model are synchronized to their elite search points. The chaotic optimization method uses gradient as a driving force for search points. Hence, its application is confined to a class of problems in which gradient of the objective function can be computed. In this study, we introduce the simultaneous perturbation gradient approximation into the multi-point type chaotic optimization method in order to compute gradient approximately so that the chaotic optimization method can be applied to a class of problems whose objective function values only can be computed. Then, we confirm effectiveness of the proposed method through applications to several unconstrained multi-peaked optimization problems with 100 variables comparing to other major meta-heuristics.

In this study, we transform an optimization problem into a game problem by multiple decision makers. This transformation is called gamification of the optimization problem. Then, we discuss correspondence of the dynamics to search the rational solution of the game problem with the multi-point type optimization method to search the optimal solution of the original problem. Specifically, we propose a condition to compose objective functions of multiple decision makers who interfere with each other from the objective function of the original problem so that equivalence of the Nash equilibrium solution of the game problem to the optimal solution of the original problem is guaranteed. Then, correspondence of the gradient dynamics to solve the game problem with the multi-point type optimization method is discussed. We also show some numerical examples in order to explain the gamification of the optimization problem.

We propose a multipoint combinatorial optimization method that aims to realize efficient search in consideration of intensification and diversification in higher structure solution space by sharing information between search points. We evaluated the performance of the proposed method through numerical experiments using benchmark problems.

PurposeTo develop a postprocessing algorithm for multiecho chemical‐shift encoded water–fat separation that estimates proton density fat fraction (PDFF) maps over the full dynamic range (0‐100%) using multipeak fat modeling and multipoint search optimization. To assess its accuracy, reproducibility, and agreement with state‐of‐the‐art complex‐based methods, and to evaluate its robustness to artefacts in abdominal PDFF maps.MethodsWe introduce MAGO (MAGnitude‐Only), a magnitude‐based reconstruction that embodies multipeak liver fat spectral modeling and multipoint optimization, and which is compatible with asymmetric echo acquisitions. MAGO is assessed first for accuracy and reproducibility on publicly available phantom data. Then, MAGO is applied to N = 178 UK Biobank cases, in which its liver PDFF measures are compared using Bland‐Altman analysis with those from a version of the hybrid iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL) algorithm, LiverMultiScan IDEAL (LMS IDEAL, Perspectum Diagnostics Ltd, Oxford, UK). Finally, MAGO is tested on a succession of high field challenging cases for which LMS IDEAL generated artefacts in the PDFF maps.ResultsPhantom data showed accurate, reproducible MAGO PDFF values across manufacturers, field strengths, and acquisition protocols. Moreover, we report excellent agreement between MAGO and LMS IDEAL for 6‐echo, 1.5 tesla human acquisitions (bias = −0.02% PDFF, 95% confidence interval = ±0.13% PDFF). When tested on 12‐echo, 3 tesla cases from different manufacturers, MAGO was shown to be more robust to artefacts compared to LMS IDEAL.ConclusionMAGO resolves the water–fat ambiguity over the entire fat fraction dynamic range without compromising accuracy, therefore enabling robust PDFF estimation where phase data is inaccessible or unreliable and complex‐based and hybrid methods fail.

Purpose. To develop a new approach to the design of mining production processes with limited resources. Methods. Combinatorial optimisation methods were used to develop a new approach. The problem of designing technological processes can be solved by interpreting the problem “knapsack problem” with a private solution “backpack 0-1”. Dynamic programming algorithms are used to find the optimal solution. Findings. A new approach to the design of mining production management processes with limited resources has been developed. If the target goal is to obtain the maximum effect at minimum costs, then the direct run method is used. If there are restrictions on bandwidth, energy characteristics, specific cost, then the reverse run method is used. In the final part of the study, the proposed approach was verified. The task consisted in the development of recommendations regarding the choice of the structure of the technological chain of the cleaning pit under the given technological and mining-geological development parameters. The amount of specific production cost was imposed as a limitation. As a result of solving the design problem by the reverse run method, recommendations for replacing the cleaning equipment were developed. This made it possible to ensure the specified level of productivity and reduce the unit cost by 10.6%. The use of combinatorial optimisation methods made it possible to obtain an optimal solution in the field of given parameters. Originality. The scientific novelty of the work consists in establishing regularities in the formation of the efficiency of mineral deposit development processes. For the first time, combinatorial optimization methods were used to design the processes that accompany the development of mineral deposits, and the scope of their application was determined, as well as a number of dynamic programming tasks and algorithms were formalised: backtracking, spanning tree. Practical implication. Verification of the developed approach was carried out in relation to the design of mining production processes with limited resources. The obtained approach makes it possible to find optimal solutions under the constraints set at the design stage. As limitations can be: throughput capacity of the transport chain, energy characteristics of technological processes accompanying mining, specific cost of mining, etc. The design problem can be solved in a direct order – if the objective function is to maximise the parameter, or in the opposite way – if there are restrictions.

A of 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.

The object of research is the analysis of the state of development of methods of optimal planning of multifactorial experiment on cost and time indicators. The subject of the research is the methods of optimization of multifactor experiment plans in terms of cost and time indicators. The objective: the development of practical recommendations for the application of existing optimization methods of multifactorial experiment plans in terms of cost and time criteria based on their comparative analysis. The tasks are the comparing of optimization methods of multifactorial experiment plans by characteristics: the allowable number of factors for effective optimization, type of plan, accuracy of the method, the number of optimization criteria, speed; development of practical recommendations for the use of these methods; the determine of directions for further development of the research topic. Methods: method of comparative analysis, optimization methods based on the study of nature, combinatorial optimization methods, graph optimization methods, approximate optimization methods. The results of study. The 20 methods of multifactorial experiment plans in terms of cost and time criteria are analyzed. The 6 practical recommendations for their application in the range of factors number 2 < k ≤ 16 are given. Conclusions. The scientific novelty of the obtained results is the improved comparative analysis of existing methods of multifactorial experiment plans based on 5 characteristics in terms of the experimenter's choice, namely: the allowable number of factors for effective optimization, type of plan, method accuracy, number of optimization criteria; speed-code. In the future, it is planned to study the classification of methods of multifactorial experiment plans, the development and improvement of two-criteria optimization methods for cost and time characteristics, the speed analysis of approximate optimization methods for k > 7 and their improvement.

In the intelligent era, combinatorial optimization problems—such as those in logistics scheduling, resource allocation, and intelligent transportation—have become increasingly prominent as core issues in numerous fields. Meanwhile, the rapid development of intelligent technologies has brought new opportunities for solving combinatorial optimization problems. This paper first introduces the basic concepts and classifications of combinatorial optimization problems. It then uses the bibliometric tool Citespace to analyze literature on digital-intelligent combinatorial optimization. Additionally, it comprehensively reviews and analyzes recent research progress from two core dimensions: intelligent optimization algorithms and artificial intelligence algorithms. The paper also summarizes application cases of combinatorial optimization methods in the intelligent era, such as logistics supply chain optimization, transportation route planning, manufacturing optimization, and financial prediction optimization, and discusses the shortcomings of current research. Finally, it prospects future research directions, providing important references for the theoretical development of combinatorial optimization.

A combinatorial optimization method is proposed for finding the optimal stacking sequence and the ply drop-offs of a blended composite structure. This method assumes that the thicknesses of the regions of the structure are fixed in advance. It is able to handle efficiently design and manufacturing rules which are of combinatorial type. The optimization problem is formulated as a constrained binary programming problem and it is solved by applying both a primal and a dual backtracking procedures with a local search method. Some numerical experiments are carried out to show the efficiency of the optimization method with respect to both computational time and quality criteria.

In a parts recycling system, reusable parts in the collected waste products are employed to produce new products with new parts. Two assembly methods are considered in the parts recycling system. The primary method is random assembly, in which new parts are selected randomly from the entire population and assembled. The remaining method is selective assembly based on the combinatorial optimization method, in which a combination of reusable parts and new parts is optimized so that high quality assembled units are obtained in a lot unit at the maximum assembly rate while dimensions of each part are referred to appropriately. The assembly methods are applied to the parts recycling system where hole parts are combined with shaft parts. In this paper the effectiveness of parts mix, reusable parts and new parts, is clarified in various situations.

On‐fault earthquake magnitude distributions are calculated for northern Caribbean faults using estimates of fault slip and regional seismicity parameters. Integer programming, a combinatorial optimization method, is used to determine the optimal spatial arrangement of earthquakes sampled from a truncated Gutenberg‐Richter distribution that minimizes the global misfit in slip rates on a complex fault system. Slip rates and their uncertainty on major faults are derived from a previously published GPS block model for the region, with fault traces determined from offshore geophysical mapping and previously published onshore studies. The optimal spatial arrangement of the sampled earthquakes is compared with the 500‐year history of earthquake observations. Rupture segmentation of the subduction interface along the Hispaniola‐Puerto Rico Trench (PRT) fault and seismic coupling on the PRT fault appear to exert the primary control over this spatial arrangement. Introducing a rupture barrier for the Hispaniola‐PRT fault northwest of Mona Passage, based on geophysical and seismicity observations, and assigning a low slip rate of 2 mm/yr on the PRT fault are most consistent with historical earthquakes in the region. The addition of low slip‐rate secondary faults as well as segmentation of the Hispaniola and Septentrional strike‐slip fault improves the consistency with historical seismicity. An important observation from the modeling is that varying the slip rate on the PRT fault and different segmentation scenarios result in significant changes to the optimal magnitude distribution on faults farther away. In general, optimal on‐fault magnitude distributions are more complex and inter‐dependent than is typically assumed in probabilistic seismic hazard analysis and probabilistic tsunami hazard analysis.

This chapter illustrates the use of the combinatorial optimization models presented in Chapter 19 for the Feature Set selection and Gene Ordering problems to find genetic signatures for diseases using micro-array data. We demonstrate the quality of this approach by using a microarray dataset from a mouse model of Parkinson's disease. The results are accompanied by a description of the currently known molecular functions and biological processes of the genes in the signatures.

4 - Evolution Strategies-Based Metaheuristics in Structural Design Optimization

Due to the dynamic process of maximum power point tracking (MPPT) caused by turbulence and large rotor inertia, variable-speed wind turbines (VSWTs) cannot maintain the optimal tip speed ratio (TSR) from cut-in wind speed up to the rated speed. Therefore, in order to increase the total captured wind energy, the existing aerodynamic design for VSWT blades, which only focuses on performance improvement at a single TSR, needs to be improved to a multi-point design. In this paper, based on a closed-loop system of VSWTs, including turbulent wind, rotor, drive train and MPPT controller, the distribution of operational TSR and its description based on inflow wind energy are investigated. Moreover, a multi-point method considering the MPPT dynamic process for the aerodynamic optimization of VSWT blades is proposed. In the proposed method, the distribution of operational TSR is obtained through a dynamic simulation of the closed-loop system under a specific turbulent wind, and accordingly the multiple design TSRs and the corresponding weighting coefficients in the objective function are determined. Finally, using the blade of a National Renewable Energy Laboratory (NREL) 1.5 MW wind turbine as the baseline, the proposed method is compared with the conventional single-point optimization method using the commercial software Bladed. Simulation results verify the effectiveness of the proposed method.

Data processing in high-dimensional spaces is a challenging task. In order to effectively classify the data in a high-dimensional space, a quantum particle swarm optimization classification algorithm (QPSOCA) for high-dimensional datasets is proposed in this paper. In QPSOCA, an uncorrelated discriminant analysis algorithm is utilized to reduce the dimension of the data, which is implemented automatically and no extra parameters are needed. In addition, to avoid the randomness of the swarm and improve the convergence speed, quantum computation is introduced into particle swarm optimization (PSO). In the experimental section, a detailed comparison of three different combinatorial optimization methods is given to demonstrate the efficiency of the proposed algorithm. Comparative experiments show that the proposed algorithm can improve the classification accuracy.