A microbial kinetic optimization approach

2021 ◽  
pp. 1-17
Author(s):  
Xiong Ding ◽  
Yan Lu
Keyword(s):  
Culture System ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Culture Fluid ◽  
Microbial Populations ◽  
Optimization Approach ◽  
Toxic Substances ◽  
Global Optimal ◽  
Growth Changes ◽  
The Impact

In order to solve some optimization problems with many local optimal solutions, a microbial dynamic optimization (MDO) algorithm is proposed by the kinetic theory of hybrid food chain microorganism cultivation with time delay. In this algorithm, it is assumed that multiple microbial populations are cultivated in a culture system. The growth of microbial populations is not only affected by the flow of culture fluid injected into the culture system, the concentration of nutrients and harmful substances, but also by the interaction between the populations. The influence of culture medium which is injected regularly will suddenly increase the concentration of nutrients and toxic substances, it will suddenly increase the impact on the population. These characteristics are used to construct absorption operators, grabbing operators, hybrid operators, and toxin operators; the global optimal solution of the optimization problem can be quickly solved by these operators and the population growth changes. The simulation experiment results show that the MDO algorithm has certain advantages for solving optimization problems with higher dimensions.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

scholarly journals Hybrid GA-SOCP Approach for Placement and Sizing of Distributed Generators in DC Networks

2020 ◽  
Vol 10 (23) ◽  
pp. 8616 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Luis Fernando Grisales-Noreña
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Mathematical Optimization ◽  
Optimal Solution ◽  
Distribution Networks ◽  
Optimization Approach ◽  
Global Optimal Solution ◽  
Distributed Generators ◽  
Second Order Cone ◽  
Global Optimal

This research addresses the problem of the optimal location and sizing distributed generators (DGs) in direct current (DC) distribution networks from the combinatorial optimization. It is proposed a master–slave optimization approach in order to solve the problems of placement and location of DGs, respectively. The master stage applies to the classical Chu & Beasley genetic algorithm (GA), while the slave stage resolves a second-order cone programming reformulation of the optimal power flow problem for DC grids. This master–slave approach generates a hybrid optimization approach, named GA-SOCP. The main advantage of optimal dimensioning of DGs via SOCP is that this method makes part of the exact mathematical optimization that guarantees the possibility of finding the global optimal solution due to the solution space’s convex structure, which is a clear improvement regarding classical metaheuristic optimization methodologies. Numerical comparisons with hybrid and exact optimization approaches reported in the literature demonstrate the proposed hybrid GA-SOCP approach’s effectiveness and robustness to achieve the global optimal solution. Two test feeders compose of 21 and 69 nodes that can locate three distributed generators are considered. All of the computational validations have been carried out in the MATLAB software and the CVX tool for convex optimization.

scholarly journals An Efficient Hybrid Optimization Approach Using Adaptive Elitist Differential Evolution and Spherical Quadratic Steepest Descent and Its Application for Clustering

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
T. Nguyen-Trang ◽  
T. Nguyen-Thoi ◽  
T. Truong-Khac ◽  
A. T. Pham-Chau ◽  
HungLinh Ao
Keyword(s):  
Differential Evolution ◽  
Clustering Analysis ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Internal Validity ◽  
Optimal Solution ◽  
Population Based ◽  
Steepest Descent ◽  
Optimization Approach ◽  
Global Optimal

In this paper, a hybrid approach that combines a population-based method, adaptive elitist differential evolution (aeDE), with a powerful gradient-based method, spherical quadratic steepest descent (SQSD), is proposed and then applied for clustering analysis. This combination not only helps inherit the advantages of both the aeDE and SQSD but also helps reduce computational cost significantly. First, based on the aeDE’s global explorative manner in the initial steps, the proposed approach can quickly reach to a region that contains the global optimal value. Next, based on the SQSD’s locally effective exploitative manner in the later steps, the proposed approach can find the global optimal solution rapidly and accurately and hence helps reduce the computational cost. The proposed method is first tested over 32 benchmark functions to verify its robustness and effectiveness. Then, it is applied for clustering analysis which is one of the problems of interest in statistics, machine learning, and data mining. In this application, the proposed method is utilized to find the positions of the cluster centers, in which the internal validity measure is optimized. For both the benchmark functions and clustering problem, the numerical results show that the hybrid approach for aeDE (HaeDE) outperforms others in both accuracy and computational cost.

Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 526-530 ◽  
Author(s):  
Hong Wei Jiao ◽  
Jing Ben Yin ◽  
Yun Rui Guo
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Linearization Method ◽  
Equivalent Transformation ◽  
Engineering System ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Multiplicative Problems

Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.

A Deterministic Method for a Class of Fractional Programming Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 531-536
Author(s):  
Jing Ben Yin ◽  
Kun Li
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Deterministic Algorithm ◽  
Linear Relaxation ◽  
Convex Programming Problem ◽  
Global Optimal Solution ◽  
Deterministic Method ◽  
Equivalent Problem ◽  
Linear Programming Problems ◽  
Global Optimal

The sum of linear fractional functions problem has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are non-convex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms are only for the case that sum of linear ratios problem without coefficients, and may be difficult to be solved. In this paper, a deterministic algorithm is proposed for globally solving the sum of linear fractional functions problem with coefficients. By utilizing an equivalent problem and linear relaxation technique, the initial non-convex programming problem is reduced to a sequence of linear relaxation programming problems. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Mean–Variance Portfolio Management with Functional Optimization

2021 ◽  
pp. 2050055
Author(s):  
Ka Wai Tsang ◽  
Zhaoyi He
Keyword(s):  
Portfolio Management ◽  
Optimization Problems ◽  
Empirical Studies ◽  
Optimal Solution ◽  
Weight Vector ◽  
Optimization Approach ◽  
Functional Optimization ◽  
Mean And Variance ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean–variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.

Artificial Intelligence Application in Modern Management

2010 ◽  
Vol 37-38 ◽  
pp. 203-206
Author(s):  
Rong Jiang
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Local Optimum ◽  
Efficient Operation ◽  
Modern Management ◽  
Global Optimal ◽  
Annealing Algorithm

Modern management is a science of technology that adopts analysis, test and quantification methods to make a comprehensive arrangement of the limited resources to realize an efficient operation of a practical system. Simulated annealing algorithm has become one of the important tools for solving complex optimization problems, because of its intelligence, widely used and global search ability. Genetic algorithm may prevent effectively searching process from restraining in local optimum, thus it is more possible to obtains the global optimal solution.This paper solves unconstrained programming by simulated annealing algorithm and calculates constrained nonlinear programming by genetic algorithm in modern management. So that optimization process was simplified and the global optimal solution is ensured reliably.

scholarly journals The Impact of Manufacturing Flexibility and Multi-Criteria Optimization on the Sustainability of Manufacturing Systems

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 157 ◽  
Author(s):  
Robert Ojstersek ◽  
Borut Buchmeister
Keyword(s):  
Manufacturing Systems ◽  
Optimization Problems ◽  
Time Profile ◽  
Environmental Benefits ◽  
New Method ◽  
Optimization Approach ◽  
Manufacturing Flexibility ◽  
Time Investment ◽  
Benchmark Datasets ◽  
The Impact

The presented manuscript deals with the impact of manufacturing flexibility on cost-time investment as a function of sustainable production, which addresses the company’s sustainable social and environmental impact adequately. The impact of manufacturing flexibility on cost-time investment in the research sphere is not described, despite the fact that we know its key role in the high-mix low-volume production types. Recently, researchers have been addressing intensively the impacts of various parameters on the sustainable aspect and its dependence on manufacturing flexibility. The complexity of the influence parameters is reflected in the multi-criteria nature of optimization problems that can be solved with appropriate use of the evolutionary computation methods. The manuscript presents a new method of manufacturing flexibility modelling, with respect to the four-level architectural model, which reflected as a symmetry phenomena influence on the cost-time profile diagram. The solution to a complex optimization problem is derived using the proposed improved heuristic Kalman algorithm method. A new method is presented of optimization parameters’ evaluation with respect to the manufacturing flexibility impacts on cost-time investment. The large impact of appropriate multi-criteria optimization on a sustainably justified production system is presented, with the experimental work on benchmark datasets and an application case. The new method allows a comprehensive optimization approach, and validation of the optimization results by which we can provide more sustainable products, manufacturing processes, and increase the company’s total, social and environmental benefits.

A novel PGSA–PSO hybrid algorithm for structural optimization

2019 ◽  
Vol 37 (1) ◽  
pp. 144-160 ◽  
Author(s):  
Zhengrong Jiang ◽  
Quanpan Lin ◽  
Kairong Shi ◽  
Wenzhi Pan
Keyword(s):  
Structural Optimization ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Initial Growth ◽  
Global Optimal Solution ◽  
Content Type ◽  
Dome Structure ◽  
Global Optimal ◽  
Optimization Efficiency

Purpose The purpose of this paper is to propose a new hybrid algorithm, named improved plant growth simulation algorithm and particle swarm optimization hybrid algorithm (PGSA–PSO hybrid algorithm), for solving structural optimization problems. Design/methodology/approach To further enhance the optimization efficiency and precision of this algorithm, the optimization solution process of PGSA–PSO comprises two steps. First, an excellent initial growth point is selected by PSO. Then, the global optimal solution can be obtained quickly by PGSA and its improved strategy called growth space adjustment strategy. A typical mathematical example is provided to verify the capacity of the new hybrid algorithm to effectively improve the global search capability and search efficiency of PGSA. Moreover, PGSA–PSO is applied to the optimization design of a suspended dome structure. Findings Through typical mathematical example, the improved strategy can improve the optimization efficiency of PGSA considerably, and an initial growth point that falls near the global optimal solution can be obtained. Through the optimization of the pre-stress of a suspended dome structure, compared with other methods, the hybrid algorithm is effective and feasible in structural optimization. Originality/value Through the examples of suspended dome structure, it shows that the optimization efficiency and precision of PGSA–PSO are better than those of other algorithms and methods. PGSA–PSO is effective and feasible in structural optimization problems such as pre-stress optimization, size optimization, shape optimization and even topology optimization.

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