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Case Studies
Published in Michael Muhlmeyer, Shaurya Agarwal, Information Spread in a Social Media Age, 2021
Michael Muhlmeyer, Shaurya Agarwal
The simulation of a nonlinear coupled ordinary differential equation (ODE) system is typically performed by suitable ODE solvers such as ODE45 and ODE15 in MATLAB. In contrast, the parameter estimation problem is cast as an optimization problem that is much trickier and can be categorized into global or local optimization methods. Global optimization methods include random search, adaptive stochastic processes, evolutionary computation, and clustering techniques. Although the global methods are relatively stable, they come at a high computational cost. Local optimization methods, in contrast, including Newton methods and quasi-Newton methods, are computationally efficient, but they do not guarantee convergence to global minima. In the case of parameter identification in ODEs, the problem of convergence to local minima is predominant if the so-called initial value approach is considered.
Genetic Algorithms
Published in Anand Nayyar, Dac-Nhuong Le, Nhu Gia Nguyen, Advances in Swarm Intelligence for Optimizing Problems in Computer Science, 2018
Sandeep Kumar, Sanjay Jain, Harish Sharma
Global optimization methods concentrate on finding the best solution from all the local optima. It is a very tedious task to design a global optimization technique because there is no specific process or algorithm available for this designing process, and the criteria for optimum results are also not fixed. The literature contains a large number of heuristics and meta-heuristics to solve non-linear optimization problems. The approaches that presently exist in the literature for solving non-linear global optimization problems might be roughly categorized into two classes: deterministic and probabilistic methods. The deterministic strategies give us a guarantee of the global optimum. Probabilistic methods don’t give us a guarantee of optimum, but they provide the nearest to the optimum solution. This is attained by supposing that the better solutions are in proximity to the solution search space, and this is true for most of the real-world problems. These probabilistic methods use random components for fluctuations and are also referred to as stochastic algorithms. A balanced approach between exploration of search space and exploitation of best feasible solutions found so far is considered to be most successful in this class.
Memetic Algorithms with Extremal Optimization
Published in Yong-Zai Lu, Yu-Wang Chen, Min-Rong Chen, Peng Chen, Guo-Qiang Zeng, Extremal Optimization, 2018
Yong-Zai Lu, Yu-Wang Chen, Min-Rong Chen, Peng Chen, Guo-Qiang Chen
In general, most global optimization problems are intractable, especially when the optimization problem has complex landscape and the feasible region is concave and covers a very small part of the whole search space. Solution accuracy and global convergence are two important factors in the development of optimization techniques. Deterministic search methods are known to be very efficient with high accuracy. Unfortunately, they are easily trapped in local minima. It is hardly possible to design a deterministic algorithm that would outperform the exhaustive search in assuring the solution obtained to be the true global optimum. On the other hand, methods of CI (EAs, EO, ACO, etc.) are much more effective for traversing these complex surfaces and inherently better suited for avoiding local minima (Engelbrecht, 2007). However, CI has its weakness in slow convergence and providing a precise-enough solution because of the failure to exploit local information. Moreover, for constrained optimization problems, the given constraints must be met to have feasible solutions; CI methods often lack an explicit mechanism to bias the search in feasible regions.
A practical optimisation method of submarine base considering vibration reduction, light-weight and shock resistance
Published in Ships and Offshore Structures, 2022
Xinhao Zhao, Yuchao Yuan, Wenyong Tang
Common approximation models include the response surface model, RBF model, Kriging model, etc. Considering the complexity of the model and calculation, the RBF model is selected to approximate complex nonlinear functions in the paper. The RBF neural network is the feed-forward network with three layers: input layer, hidden layer and output layer (Wen et al. 2019). RBF has the advantages of fast training, global approximation ability, strong fault tolerance and simpler structure and can be used in nearly a vast nonlinear space (Zhang and Tao 2016). Global optimisation refers to finding the global optimal solution in nonlinear and discontinuous complex engineering problems. MIGA is efficient and reliable and has been applied to solve structural optimisation problems (Li et al. 2011; Ma et al. 2018). MIGA divides the population of GA into several subpopulations (islands) (Lin et al. 2019). It not only uses the GA method for population evolution in the island but also stipulates that a certain proportion of individuals will exchange and migrate between islands every certain algebra (Zhao et al. 2015). MIGA can properly use migration, selection, crossover, mutation and other operations to avoid falling into local optimal solutions and has better global optimisation ability than traditional GA (Pan et al. 2017).
A Comparative Study of Nature-Inspired Metaheuristic Algorithms in Search of Near-to-optimal Golomb Rulers for the FWM Crosstalk Elimination in WDM Systems
Published in Applied Artificial Intelligence, 2019
Due to highly nonlinearity and complexity of the problem of interest, design optimization in engineering fields tends to be very challenging. As conventional computing algorithms are local search algorithm, so they are not the best tools for highly nonlinear global optimization, and thus often miss the global optimality. In addition, design solutions have to be robust, low cost, subject to uncertainty in parameters and tolerance for the imprecision of available components and materials. Nature-inspired algorithms are now among the most widely used optimization algorithms. The guiding principle is to devise algorithms of computation that lead to an acceptable solution at low cost by seeking for an approximate solution to a precisely/imprecisely formulated problem (Cotta and Hemert 0000; Goldberg 1989; Koziel and Yang 2011; Mitchell 2004; Rajasekaran and Vijayalakshmi Pai 2004; Yang 2013a, 2010a, 2012a).
A hybrid Genetic Algorithm approach to minimize the total joint cost of a single-vendor multi-customer integrated scheduling problem
Published in Transportation Planning and Technology, 2019
Olivier Grunder, Zakaria Hammoudan, Benoit Beroule, Oussama Barakat
In this section, we develop a Hybrid Genetic Algorithm (HGA) to solve the MCLSDSP. A Genetic Algorithm (GA) is a general, robust and well-developed optimization method. As a global optimization method, they have been successfully used to find optimal or near-optimal solutions for a wide variety of optimization problems. For example, Holland (1975) proposed Genetic Algorithms (GAs) as a heuristic method based on ‘survival of the fittest’. In a GA, a population of strings (called chromosomes or the genotype of the genome), which encode candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem, evolve towards better solutions (Figure 2). The evolution usually starts from a population of randomly generated individuals and spreads to generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness) and modified (recombined and possibly randomly mutated) to form a new population. The new population is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. If the algorithm has been terminated due to a maximum number of generations, a good solution may or may not have been reached (Jat and Yang 2009). In the context of our paper, Wang, Grunder, and El Moudni (2013) used a GA approach to solve the Integrated Scheduling of Production Distribution-Inventory problem (ISPDI).