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Classical Optimization Methods
Published in A Vasuki, Nature-Inspired Optimization Algorithms, 2020
Geometric programming is an optimization method for solving non-linear programming problems. Duffin, Peterson, and Zener developed the geometric programming technique in 1967 [10]. The engineering design problem has to be stated in terms of polynomials. The objective function as well as the constraints have to be in polynomial form [11] and the algorithm finds the minimum of the function. The optimal minimum value can be obtained as the solution without the necessity of finding the values for the design variables. This is one of the advantages of geometric programming. Another advantage is the ability to reduce the problems into a set of simultaneous linear algebraic equations [12]. The disadvantage is having to express the problem and its constraints in terms of polynomials. Consider the example given below where the design problem is formulated as a polynomial:
Problem Formulation for Optimization
Published in Yogesh Jaluria, Design and Optimization of Thermal Systems, 2019
Geometric programming is an optimization method that can be applied if the objective function and the constraints can be written as sums of polynomials. The independent variables in these polynomials may be raised to positive or negative, integer or noninteger exponents, e.g., U=ax12+bx21.2+cx1x2−0.5+d
Fuzzy Geometric-Based Cost-Optimization Technique for Company
Published in Santosh Kumar Das, Massimiliano Giacalone, Fuzzy Optimization Techniques in the Areas of Science and Management, 2023
Neha Kumari, Arun Prasad Burnwal, Neha Keshri
In the current scenario, the total number of companies increases rapidly based on company strategy and competitors. Each company has its own strategy to meet the goals of the company [1–2]. In a decision-making situation, the strategy is two types: first is based on an increasing factor, the second on the decreasing factor. The first category indicates that if the factors are increased, then company profit also increases. The second category indicates that if the factors are decreased, then company profit increases. The combination of both helps predict and analyze the company's life cycle. In the proposed method, an intelligent technique is proposed based on the fusion of linear programming, geometric programming, and fuzzy logic. Linear programming is a numerical optimization technique which is used to optimize objective function based on related constraints depending on the situation. Geometric programming is a nonlinear programming which is used to efficiently optimize numerical problems based on related objective function and constraints in the posynomial environment instead of the polynomial environment. Sometimes, this is known as optimization purpose, which helps model the application based on different factors and information. It is also used to optimize nonlinear parameters efficiently as a nature-inspired optimization system [3]. The method used in this manuscript helps in several applications because it uses fuzzy logic to model the different parameters efficiently. Fuzzy logic is used to optimize imprecise information with the help of membership functions. Fuzzy logic is a type of soft computing methodology that produces soft results using an approximation method. Soft computing, in conjunction with wireless networks and wireless sensor networks, is utilized to tackle a variety of concerns and problems [4]. The suggested method's combination of the aforementioned strategies aids in the effective optimization of the proposed mathematical model based on restrictions.
MOS Amplifier Design Methodology for Optimum Performance
Published in IETE Journal of Research, 2020
Abir J. Mondal, Paromita Bhattacharjee, Pinaki Chakraborty, Bidyut K. Bhattacharyya
As a matter of fact that any circuit design problem is bound to be expressed in a mathematical form, many mathematical optimization methods, such as linear programming, NLP, quadratic programming, and geometric programming, which are widely used for constrained optimization problem [11, 12] can be incorporated into any analog design methodology. Most recent works in analog circuit optimization have been done using geometric programming [13–15]. Using their synthesis method [13], Mandal et al. proposed an op-amp sizing method using geometric programming formulation [15]. Hershenson et al. also proposed a similar optimal design approach for op-amp using geometric programming [14]. Geometric programming uses circuit equations in posynomial form and it can be transformed to a convex problem by using log transformation [12]. Geometric programming ensures a global optimum solution but also limits the form of objective function since it allows only minimization of the objective function. Henceforth, an objective to be maximized has to be converted to a minimization form, which may not be flexible to be done in every case. In view of these factors, an NLP-based approach has an edge over its other counterparts. It permits the objective to take any of the minimization or maximization form, does not restrict the constraint equations, and accepts convex as well as concave problem. The methodology presented in this paper based on NLP results in a global optimal solution and is extremely fast in computation.
An inventory model for non-instantaneous deteriorating items with credit period and carbon emission sensitive demand: a signomial geometric programming approach
Published in International Journal of Management Science and Engineering Management, 2019
Leyla Aliabadi, Reza Yazdanparast, Mohammad Mahdi Nasiri
Geometric Programming (GP) problem is a class of non-linear optimization problems that have particular objective functions and constraints. This method has very useful computational and theoretical properties to solve complex optimization problems in different fields such as engineering, management, science, etc. This technique was extended rapidly by researchers, especially engineering designers. Signomial geometric programming (SGP) problem was the first extension of GP problems. SGP problems are categorized in a class of non-convex optimization problems and NP-hard problems. SGP technique is well used for solving inventory models in the literature (Mandal, Roy, & Maiti, 2006; Sadjadi, Hesarsorkh, Mohammadi, & Naeini, 2015; Samadi, Mirzazadeh, & Pedram, 2013; Tabatabaei, Sadjadi, & Makui, 2017). In this technique degree of difficulty (DD1) has an important role. When , many researchers have applied dual geometric programming for solving inventory models. However, if , the inventory problem turns into a NP-hard one, which is difficult to solve. Therefore, solution approaches play an important role in SGP problems. In the following, a solution procedure for a SGP problem is proposed.
Optimising cutting conditions for minimising cutting time in multi-pass milling via weighted superposition attraction-repulsion (WSAR) algorithm
Published in International Journal of Production Research, 2021
Machining is still one of the most critical operations in the manufacturing industry and milling is one of the most frequently utilised machining operations. Therefore, optimisation of machining operations plays a critical role in achieving economic production and increasing company profits. Machining optimisation or cutting conditions optimisation is also an important and integral part of process planning (Dolgui, Levin, and Rozin 2020). Based on this motivation, extensive studies are performed in the literature in order to optimise various machining operations including milling with many different optimisation techniques. In the earlier studies, the focus was on the usage of classical mathematical programming techniques including geometric programming (Lambert and Walvekar 1978; Sönmez, Baykasoğlu, and Filiz 1996), dynamic programming (Sönmez et al. 1999) etc. for optimising cutting conditions in machining operations. Owing to the highly nonlinear structure of the machining operations and resultant mathematical models it was shown that classical mathematical programming approaches are not efficient in solving cutting conditions of optimisation problems including milling (Dereli, Filiz, and Baykasoğlu 2001; Dereli and Baykasoğlu 2005). Therefore, the focus of research shifted to utilisation of computational intelligence based algorithms specifically metaheuristic optimisation procedures for optimising cutting conditions. Many different metaheuristic techniques have been employed so far and successful results reported in the literature. Dereli, Filiz, and Baykasoğlu (2001) employed genetic algorithms for optimisation cutting conditions in the multi-pass milling operations. Baykasoğlu and Dereli (2002) employed a simulated annealing algorithm for optimising cutting parameters in milling processes. Wang et al. (2005) developed a parallel genetic simulated annealing (PGSA) approach without investigating the constraint limits for optimising cutting conditions in milling. Onwubolu (2006) developed a new approach, which is inspired from the particle swarm optimisation that is named as tribes for cutting conditions optimisation in milling. Deng et al. (2020) proposed a multi-objective particle swarm optimisation algorithm for optimising cutting conditions in milling operations by considering carbon utilisation efficiency. Some of the other successful metaheuristic optimisation techniques applied to cutting conditions optimisation in milling are cellular particle swarm optimisation algorithm of Gao, Huang, and Li (2012); artificial bee colony algorithm of Rao and Pawar (2010); imperialist competitive algorithm of Yang, Li, and Gao (2013); teaching-learning-based optimisation algorithm of Pawar and Rao (2013); hybrid teaching-learning-based optimisation and cuckoo search algorithm of Huang, Gao, and Li (2015); cuckoo search algorithm of Mellal and Williams (2016); grey wolf optimiser of Khalilpourazari and Khalilpourazary (2018).