Mohamed Tawhid - Academia.edu (original) (raw)

Papers by Mohamed Tawhid

Nature-Inspired Methods for Metaheuristics Optimization, 2020

This chapter introduces the basic concepts of biogeography based optimization (BBO) algorithm and... more This chapter introduces the basic concepts of biogeography based optimization (BBO) algorithm and its application to a combinatorial water switching problem. Water switching optimization is a pump scheduling problem which considers minimization of total electrical energy requirement as an objective function. Pump status (switch on/switch off) of pumping stations are considered as a discrete (binary) decision variables for the optimization problem. Suction and discharge pressure are considered as constraints in the procedure. A case study with 10 pumping station and 40 pumps is presented for the experimentation. The performance of BBO is tested against other state-of-the art algorithms that includes genetic algorithm (GA), branch & bound method (B&B), harmony search (HS) algorithm, particle swarm optimization (PSO) and ant colony optimization (ACO) algorithms. Water pump switching problem is also investigated by using different constraint handling techniques and by considering different pump situations in a pumping station. The Computational results indicate that BBO is an appropriate algorithm to solve water pump switching problem and is effective over other optimization methods. Moreover, 20 alternative optimum solutions are presented to demonstrate water switching problem as a multi-modal problem with different optimum solutions and the search capability of BBO to find alternate optimum solutions.

Adaptive Structures and Material Systems, 1999

An electromechanical model for a circular piezoelectric actuator is developed. A critical challen... more An electromechanical model for a circular piezoelectric actuator is developed. A critical challenge in certain applications employing piezoceramic actuators is to maximize the displacement provided by the actuator while minimizing it power consumption. This problem is addressed here by developing an electromechanical model which can be used to optimize the volume displacement to admittance ratio for various circular actuator designs. The model includes multiple layers with independent radii which can be varied to optimize performance. The piezoceramic, bonding, plating, and mounting materials can be varied to accommodate various design criteria. An advantage of the model lies in the property that for a variety of material configurations, analytic solutions can be obtained. Numerical examples demonstrating the properties of the model are presented.

Thermal System Optimization, 2019

There are a few thermal components which can play an important role in power-generating systems, ... more There are a few thermal components which can play an important role in power-generating systems, refrigeration systems, or any such system. Similarly, there are few thermal systems which can be operated with solar energy. In this chapter, thermal modeling of few such systems like the cooling tower, heat pipe, micro-channel heat sink, solar air heater, solar water heater, solar chimney, and other systems of such type is presented. The objective function for each of these systems is derived from the thermal model. The optimization of a derived objective is performed by implementing 11 different metaheuristic algorithms for each system, and then the comparative results are tabulated and discussed. In this chapter, a thermal modeling of components which can play an important role in systems such as the power-generating system and refrigerating system is carried out. Apart from the conventional system, the thermal modeling of few solar-assisted systems is also performed in this chapter. The objective function of each component/system is derived based on the thermal modeling and optimization of the derived objective (which is carried out by implementing different metaheuristic algorithms). 7.1 Cooling Tower A cooling tower is a device used in thermal power plant refrigeration plants, air conditioning plants, and chemical and petrochemical industries to dissipate processed heat. The large quantities of processed heat must be removed to maintain standard operating parameters. The cooling tower works based on a combination of heat and mass transfers to cool water by direct contact between air and water. The water to be cooled is distributed in the tower by spray nozzles, fills, and splash bars in such a way that it exposes a large quantity of surface water to atmospheric air (Kröger 2004). The movement of the air is accomplished by fans, natural draft, or the induction effect from the water sprays. A portion of the water is evaporated

Swarm Intelligence Algorithms, 2020

Journal of Computational Design and Engineering, 2018

In this study, we propose a new hybrid algorithm consisting of two meta-heuristic algorithms; Dif... more In this study, we propose a new hybrid algorithm consisting of two meta-heuristic algorithms; Differential Evolution (DE) and the Monarch Butterfly Optimization (MBO). This hybrid is called DEMBO. Both of the meta-heuristic algorithms are typically used to solve nonlinear systems and unconstrained optimization problems. DE is a common metaheuristic algorithm that searches large areas of candidate space. Unfortunately, it often requires more significant numbers of function evaluations to get the optimal solution. As for MBO, it is known for its time-consuming fitness functions, but it traps at the local minima. In order to overcome all of these disadvantages, we combine the DE with MBO and propose DEMBO which can obtain the optimal solutions for the majority of nonlinear systems as well as unconstrained optimization problems. We apply our proposed algorithm, DEMBO, on nine different, unconstrained optimization problems and eight well-known nonlinear systems. Our results, when compare...

Thermal System Optimization, 2019

Heat exchangers are energy conservation equipment used to transfer heat between hot and cold flui... more Heat exchangers are energy conservation equipment used to transfer heat between hot and cold fluid. In this chapter, thermal modeling of different types of heat exchangers like shell and tube heat exchanger, plate-fin heat exchanger, fin and tube heat exchanger, plate heat exchanger, and rotary regenerator is presented. The objective function for each of the heat exchanger is derived from the thermal model. Optimization of a derived objective is performed by implementing 11 different metaheuristic algorithms for each heat exchanger, and comparative results are tabulated and discussed.

Journal of the Operations Research Society of Japan, 2011

We consider an unconstrained minimization reformulation of the generalized complementarity proble... more We consider an unconstrained minimization reformulation of the generalized complementarity problem GCP(f, g) when the underlying functions f and g are H-differentiable, We describe H-differentials of some GCP functions based on the min function and the penalized Fischer-Burmeister function, and their merit functions. Under appropriate semimonotone (Eo), strictly semimonotone (E) regularit)r-conditions on the H-differentials of f and g, we show that a locallglobal minimum of a merit function (or a `stationary point' of a merit function) is coincident; with the solution of the given generalized complementarity problem, When specialized GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but alse extend/unify various similar results proved for Ci , semismooth, and locaily Lipschitzian.

Journal of Computational Design and Engineering, 2017

In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-obj... more In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-objective engineering design problems is presented. This algorithm is developed to solve multi-objective optimization problems by evaluating a set of single objective sub-problems. The effectiveness of the proposed algorithm is checked by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as discrete, convex, and non-convex. This algorithm is also tested for several distinctive multi-objective engineering design problems, such as four bar truss problem, gear train problem, multi-plate disc brake design, speed reducer problem, welded beam design, and spring design problem. Moreover, the numerical experimentation shows that the proposed algorithm generates the solution to represent true Pareto front. Highlights A novel multi-objective optimization (MOO) algorithm is proposed. Proposed algorithm is presented to obtain the Pareto-optimal...

Modelling and Simulation in Engineering, 2017

Most of the modern multiobjective optimization algorithms are based on the search technique of ge... more Most of the modern multiobjective optimization algorithms are based on the search technique of genetic algorithms; however the search techniques of other recently developed metaheuristics are emerging topics among researchers. This paper proposes a novel multiobjective optimization algorithm named multiobjective heat transfer search (MOHTS) algorithm, which is based on the search technique of heat transfer search (HTS) algorithm. MOHTS employs the elitist nondominated sorting and crowding distance approach of an elitist based nondominated sorting genetic algorithm-II (NSGA-II) for obtaining different nondomination levels and to preserve the diversity among the optimal set of solutions, respectively. The capability in yielding a Pareto front as close as possible to the true Pareto front of MOHTS has been tested on the multiobjective optimization problem of the vehicle suspension design, which has a set of five second-order linear ordinary differential equations. Half car passive ride...

Numerical Algebra, Control and Optimization, 2017

In this paper, we propose a new hybrid grey wolf optimizer (GWO) algorithm with simplex Nelder-Me... more In this paper, we propose a new hybrid grey wolf optimizer (GWO) algorithm with simplex Nelder-Mead method in order to solve integer programming and minimax problems. We call the proposed algorithm a Simplex Grey Wolf Optimizer (SGWO) algorithm. In the the proposed SGWO algorithm, we combine the GWO algorithm with the Nelder-Mead method in order to refine the best obtained solution from the standard GWO algorithm. We test it on 7 integer programming problems and 10 minimax problems in order to investigate the general performance of the proposed SGWO algorithm. Also, we compare SGWO with 10 algorithms for solving integer programming problems and 9 algorithms for solving minimax problems. The experiments results show the efficiency of the proposed algorithm and its ability to solve integer and minimax optimization problems in reasonable time.

Engineering Applications of Artificial Intelligence, 2017

This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method ... more This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method for solving multi-objective problems. Most of the multi-objective optimization algorithms use different search techniques inspired by different optimization techniques such as genetic algorithms, differential evolutions, particle swarm optimization, cuckoo search etc., but search techniques of recently developed metaheuristics have hardly been investigated. Non-dominated moth-flame optimization algorithm (NS-MFO) is based on the search technique of moth-flame optimization algorithm (MFO) algorithm and utilizes the elitist non-dominated sorting and crowding distance approach for obtaining different non domination levels and to preserve the diversity among the optimal set of solutions respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems and multi-objective engineering design problems with distinctive features. It is shown in this paper that this method effectively generates the Pareto front and also, this method is easy to implement and algorithmically simple.

East Asian Journal on Applied Mathematics, 2016

A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Ne... more A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms, and the numerical results show the optimal or near optimal solution is obtained faster.

Soft Computing, 2016

The minimization of the molecular potential energy function is one of the most important real-lif... more The minimization of the molecular potential energy function is one of the most important real-life problems which can help to predict the 3D structure of the protein by knowing the steady (ground) state of the molecules of the protein. In this paper, we propose a new hybrid algorithm between the social spider algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by hybrid social spider optimization and genetic algorithm (HSSOGA). The HSSOGA comprises of three main steps. In the first step, we apply the social spider optimization algorithm to balance between the exploration and the exploitation processes in the proposed algorithm. In the second step, we use the dimensionality reduction process and the population partitioning process by dividing the population into subpopulations and applying the arithmetical crossover operator for each subpopulation order to increase the diversity of the search in the algorithm. In the last steps, we use the genetic mutation operator in the whole population to avoid the premature convergence and avoid trapping in local minima. The combination of three steps helps the proposed algorithm to solve the molecular potential energy function with different molecules size, especially when the problem dimension Communicated by V. Loia.

Applied Mathematics & Information Sciences, 2016

In this paper, we propose a new hybrid algorithm for solving global optimization problems, namely... more In this paper, we propose a new hybrid algorithm for solving global optimization problems, namely, integer programming and minimax problems. The main idea of the proposed algorithm, Direct Search Firefly Algorithm (DSFFA), is to combine the firefly algorithm with direct search methods such as pattern search and Nelder-Mead methods. In the proposed algorithm, we try to balance between the global exploration process and the local exploitation process. The firefly algorithm has a good ability to make a wide exploration process while the pattern search can increase the exploitation capability of the proposed algorithm. In the final stage of the proposed algorithm, we apply a final intensification process by applying the Nelder-Mead method on the best solution found so far, in order to accelerate the search instead of letting the algorithm running with more iterations without any improvement of the results. Moreover, we investigate the general performance of the DSFFA algorithm on 7 integer programming problems and 10 minimax problems, and compare it against 5 benchmark algorithms for solving integer programming problems and 4 benchmark algorithms for solving minimax problems. Furthermore, the experimental results indicate that DSFFA is a promising algorithm and outperforms the other algorithms in most cases.

SpringerPlus, 2016

Background Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed b... more Background Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed by Yang et al. (2007). CS (Garg 2015a, d) and other meta-heuristic algorithms such as ant colony optimization (ACO)

INFOR: Information Systems and Operational Research, 2015

In this article, we propose a new hybrid algorithm by combining the particle swarm optimization a... more In this article, we propose a new hybrid algorithm by combining the particle swarm optimization and genetic arithmetical crossover operator. We adjust the proposed algorithm in order to avoid the problem of stagnation and premature convergence of the population. Invoking the modified arithmetical crossover operator improves the exploration process of the proposed algorithm. We call the new proposed algorithm hybrid particle swarm optimization with a modified arithmetical crossover (HPSOAC). Also, we test HPSOAC on 26 functions (16 unconstrained optimization benchmark functions and 10 CEC05 special session functions). Furthermore, we compare the general performance of the proposed algorithm against 6 various particle swarm optimization algorithms. Moreover, we show the efficiency of the proposed algorithm and its ability to solve unconstrained optimization problems by giving several computational results.

Australian Journal of Mathematical Analysis and Applications

Computational Optimization, 1999

Given a continuous P 0-function F : R n → R n , we describe a method of constructing trajectories... more Given a continuous P 0-function F : R n → R n , we describe a method of constructing trajectories associated with the P 0-equation F (x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P 0-function lead to P 0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P 0-equations when the underlying function is P 0. To generate the trajectories, we perturb the given P 0-function F to a P-function F (x, ε); unique solutions of F (x, ε) = 0 as ε varies over an interval in (0, ∞) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.

2009 7th IEEE International Conference on Industrial Informatics, 2009

ABSTRACT The nonlinear complementarity problem (NCP) has been served as a general framework for l... more ABSTRACT The nonlinear complementarity problem (NCP) has been served as a general framework for linear, quadratic, and nonlinear programming, linear complementarity problem, and some equilibrium problems. Applications of the NCP can be found in many important fields such as economics, mathematical programming, operations research, engineering and mechanics. In this article, we consider smooth NCP on the basis of the square penalized Fischer-Burmeister function. We show under certain assumptions, any stationary point of the unconstrained minimization problem is already a solution of smooth NCP. Furthermore, a derivative-free descent algorithm is suggested and conditions for its convergence are given. Finally, some preliminary numerical results are presented.

Abstract and Applied Analysis, 2014

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeiste... more We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

Nature-Inspired Methods for Metaheuristics Optimization, 2020

This chapter introduces the basic concepts of biogeography based optimization (BBO) algorithm and... more This chapter introduces the basic concepts of biogeography based optimization (BBO) algorithm and its application to a combinatorial water switching problem. Water switching optimization is a pump scheduling problem which considers minimization of total electrical energy requirement as an objective function. Pump status (switch on/switch off) of pumping stations are considered as a discrete (binary) decision variables for the optimization problem. Suction and discharge pressure are considered as constraints in the procedure. A case study with 10 pumping station and 40 pumps is presented for the experimentation. The performance of BBO is tested against other state-of-the art algorithms that includes genetic algorithm (GA), branch & bound method (B&B), harmony search (HS) algorithm, particle swarm optimization (PSO) and ant colony optimization (ACO) algorithms. Water pump switching problem is also investigated by using different constraint handling techniques and by considering different pump situations in a pumping station. The Computational results indicate that BBO is an appropriate algorithm to solve water pump switching problem and is effective over other optimization methods. Moreover, 20 alternative optimum solutions are presented to demonstrate water switching problem as a multi-modal problem with different optimum solutions and the search capability of BBO to find alternate optimum solutions.

Adaptive Structures and Material Systems, 1999

An electromechanical model for a circular piezoelectric actuator is developed. A critical challen... more An electromechanical model for a circular piezoelectric actuator is developed. A critical challenge in certain applications employing piezoceramic actuators is to maximize the displacement provided by the actuator while minimizing it power consumption. This problem is addressed here by developing an electromechanical model which can be used to optimize the volume displacement to admittance ratio for various circular actuator designs. The model includes multiple layers with independent radii which can be varied to optimize performance. The piezoceramic, bonding, plating, and mounting materials can be varied to accommodate various design criteria. An advantage of the model lies in the property that for a variety of material configurations, analytic solutions can be obtained. Numerical examples demonstrating the properties of the model are presented.

Thermal System Optimization, 2019

There are a few thermal components which can play an important role in power-generating systems, ... more There are a few thermal components which can play an important role in power-generating systems, refrigeration systems, or any such system. Similarly, there are few thermal systems which can be operated with solar energy. In this chapter, thermal modeling of few such systems like the cooling tower, heat pipe, micro-channel heat sink, solar air heater, solar water heater, solar chimney, and other systems of such type is presented. The objective function for each of these systems is derived from the thermal model. The optimization of a derived objective is performed by implementing 11 different metaheuristic algorithms for each system, and then the comparative results are tabulated and discussed. In this chapter, a thermal modeling of components which can play an important role in systems such as the power-generating system and refrigerating system is carried out. Apart from the conventional system, the thermal modeling of few solar-assisted systems is also performed in this chapter. The objective function of each component/system is derived based on the thermal modeling and optimization of the derived objective (which is carried out by implementing different metaheuristic algorithms). 7.1 Cooling Tower A cooling tower is a device used in thermal power plant refrigeration plants, air conditioning plants, and chemical and petrochemical industries to dissipate processed heat. The large quantities of processed heat must be removed to maintain standard operating parameters. The cooling tower works based on a combination of heat and mass transfers to cool water by direct contact between air and water. The water to be cooled is distributed in the tower by spray nozzles, fills, and splash bars in such a way that it exposes a large quantity of surface water to atmospheric air (Kröger 2004). The movement of the air is accomplished by fans, natural draft, or the induction effect from the water sprays. A portion of the water is evaporated

Swarm Intelligence Algorithms, 2020

Journal of Computational Design and Engineering, 2018

In this study, we propose a new hybrid algorithm consisting of two meta-heuristic algorithms; Dif... more In this study, we propose a new hybrid algorithm consisting of two meta-heuristic algorithms; Differential Evolution (DE) and the Monarch Butterfly Optimization (MBO). This hybrid is called DEMBO. Both of the meta-heuristic algorithms are typically used to solve nonlinear systems and unconstrained optimization problems. DE is a common metaheuristic algorithm that searches large areas of candidate space. Unfortunately, it often requires more significant numbers of function evaluations to get the optimal solution. As for MBO, it is known for its time-consuming fitness functions, but it traps at the local minima. In order to overcome all of these disadvantages, we combine the DE with MBO and propose DEMBO which can obtain the optimal solutions for the majority of nonlinear systems as well as unconstrained optimization problems. We apply our proposed algorithm, DEMBO, on nine different, unconstrained optimization problems and eight well-known nonlinear systems. Our results, when compare...

Thermal System Optimization, 2019

Heat exchangers are energy conservation equipment used to transfer heat between hot and cold flui... more Heat exchangers are energy conservation equipment used to transfer heat between hot and cold fluid. In this chapter, thermal modeling of different types of heat exchangers like shell and tube heat exchanger, plate-fin heat exchanger, fin and tube heat exchanger, plate heat exchanger, and rotary regenerator is presented. The objective function for each of the heat exchanger is derived from the thermal model. Optimization of a derived objective is performed by implementing 11 different metaheuristic algorithms for each heat exchanger, and comparative results are tabulated and discussed.

Journal of the Operations Research Society of Japan, 2011

We consider an unconstrained minimization reformulation of the generalized complementarity proble... more We consider an unconstrained minimization reformulation of the generalized complementarity problem GCP(f, g) when the underlying functions f and g are H-differentiable, We describe H-differentials of some GCP functions based on the min function and the penalized Fischer-Burmeister function, and their merit functions. Under appropriate semimonotone (Eo), strictly semimonotone (E) regularit)r-conditions on the H-differentials of f and g, we show that a locallglobal minimum of a merit function (or a `stationary point' of a merit function) is coincident; with the solution of the given generalized complementarity problem, When specialized GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but alse extend/unify various similar results proved for Ci , semismooth, and locaily Lipschitzian.

Journal of Computational Design and Engineering, 2017

In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-obj... more In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-objective engineering design problems is presented. This algorithm is developed to solve multi-objective optimization problems by evaluating a set of single objective sub-problems. The effectiveness of the proposed algorithm is checked by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as discrete, convex, and non-convex. This algorithm is also tested for several distinctive multi-objective engineering design problems, such as four bar truss problem, gear train problem, multi-plate disc brake design, speed reducer problem, welded beam design, and spring design problem. Moreover, the numerical experimentation shows that the proposed algorithm generates the solution to represent true Pareto front. Highlights A novel multi-objective optimization (MOO) algorithm is proposed. Proposed algorithm is presented to obtain the Pareto-optimal...

Modelling and Simulation in Engineering, 2017

Most of the modern multiobjective optimization algorithms are based on the search technique of ge... more Most of the modern multiobjective optimization algorithms are based on the search technique of genetic algorithms; however the search techniques of other recently developed metaheuristics are emerging topics among researchers. This paper proposes a novel multiobjective optimization algorithm named multiobjective heat transfer search (MOHTS) algorithm, which is based on the search technique of heat transfer search (HTS) algorithm. MOHTS employs the elitist nondominated sorting and crowding distance approach of an elitist based nondominated sorting genetic algorithm-II (NSGA-II) for obtaining different nondomination levels and to preserve the diversity among the optimal set of solutions, respectively. The capability in yielding a Pareto front as close as possible to the true Pareto front of MOHTS has been tested on the multiobjective optimization problem of the vehicle suspension design, which has a set of five second-order linear ordinary differential equations. Half car passive ride...

Numerical Algebra, Control and Optimization, 2017

In this paper, we propose a new hybrid grey wolf optimizer (GWO) algorithm with simplex Nelder-Me... more In this paper, we propose a new hybrid grey wolf optimizer (GWO) algorithm with simplex Nelder-Mead method in order to solve integer programming and minimax problems. We call the proposed algorithm a Simplex Grey Wolf Optimizer (SGWO) algorithm. In the the proposed SGWO algorithm, we combine the GWO algorithm with the Nelder-Mead method in order to refine the best obtained solution from the standard GWO algorithm. We test it on 7 integer programming problems and 10 minimax problems in order to investigate the general performance of the proposed SGWO algorithm. Also, we compare SGWO with 10 algorithms for solving integer programming problems and 9 algorithms for solving minimax problems. The experiments results show the efficiency of the proposed algorithm and its ability to solve integer and minimax optimization problems in reasonable time.

Engineering Applications of Artificial Intelligence, 2017

This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method ... more This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method for solving multi-objective problems. Most of the multi-objective optimization algorithms use different search techniques inspired by different optimization techniques such as genetic algorithms, differential evolutions, particle swarm optimization, cuckoo search etc., but search techniques of recently developed metaheuristics have hardly been investigated. Non-dominated moth-flame optimization algorithm (NS-MFO) is based on the search technique of moth-flame optimization algorithm (MFO) algorithm and utilizes the elitist non-dominated sorting and crowding distance approach for obtaining different non domination levels and to preserve the diversity among the optimal set of solutions respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems and multi-objective engineering design problems with distinctive features. It is shown in this paper that this method effectively generates the Pareto front and also, this method is easy to implement and algorithmically simple.

East Asian Journal on Applied Mathematics, 2016

A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Ne... more A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms, and the numerical results show the optimal or near optimal solution is obtained faster.

Soft Computing, 2016

The minimization of the molecular potential energy function is one of the most important real-lif... more The minimization of the molecular potential energy function is one of the most important real-life problems which can help to predict the 3D structure of the protein by knowing the steady (ground) state of the molecules of the protein. In this paper, we propose a new hybrid algorithm between the social spider algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by hybrid social spider optimization and genetic algorithm (HSSOGA). The HSSOGA comprises of three main steps. In the first step, we apply the social spider optimization algorithm to balance between the exploration and the exploitation processes in the proposed algorithm. In the second step, we use the dimensionality reduction process and the population partitioning process by dividing the population into subpopulations and applying the arithmetical crossover operator for each subpopulation order to increase the diversity of the search in the algorithm. In the last steps, we use the genetic mutation operator in the whole population to avoid the premature convergence and avoid trapping in local minima. The combination of three steps helps the proposed algorithm to solve the molecular potential energy function with different molecules size, especially when the problem dimension Communicated by V. Loia.

Applied Mathematics & Information Sciences, 2016

In this paper, we propose a new hybrid algorithm for solving global optimization problems, namely... more In this paper, we propose a new hybrid algorithm for solving global optimization problems, namely, integer programming and minimax problems. The main idea of the proposed algorithm, Direct Search Firefly Algorithm (DSFFA), is to combine the firefly algorithm with direct search methods such as pattern search and Nelder-Mead methods. In the proposed algorithm, we try to balance between the global exploration process and the local exploitation process. The firefly algorithm has a good ability to make a wide exploration process while the pattern search can increase the exploitation capability of the proposed algorithm. In the final stage of the proposed algorithm, we apply a final intensification process by applying the Nelder-Mead method on the best solution found so far, in order to accelerate the search instead of letting the algorithm running with more iterations without any improvement of the results. Moreover, we investigate the general performance of the DSFFA algorithm on 7 integer programming problems and 10 minimax problems, and compare it against 5 benchmark algorithms for solving integer programming problems and 4 benchmark algorithms for solving minimax problems. Furthermore, the experimental results indicate that DSFFA is a promising algorithm and outperforms the other algorithms in most cases.

SpringerPlus, 2016

Background Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed b... more Background Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed by Yang et al. (2007). CS (Garg 2015a, d) and other meta-heuristic algorithms such as ant colony optimization (ACO)

INFOR: Information Systems and Operational Research, 2015

In this article, we propose a new hybrid algorithm by combining the particle swarm optimization a... more In this article, we propose a new hybrid algorithm by combining the particle swarm optimization and genetic arithmetical crossover operator. We adjust the proposed algorithm in order to avoid the problem of stagnation and premature convergence of the population. Invoking the modified arithmetical crossover operator improves the exploration process of the proposed algorithm. We call the new proposed algorithm hybrid particle swarm optimization with a modified arithmetical crossover (HPSOAC). Also, we test HPSOAC on 26 functions (16 unconstrained optimization benchmark functions and 10 CEC05 special session functions). Furthermore, we compare the general performance of the proposed algorithm against 6 various particle swarm optimization algorithms. Moreover, we show the efficiency of the proposed algorithm and its ability to solve unconstrained optimization problems by giving several computational results.

Australian Journal of Mathematical Analysis and Applications

Computational Optimization, 1999

Given a continuous P 0-function F : R n → R n , we describe a method of constructing trajectories... more Given a continuous P 0-function F : R n → R n , we describe a method of constructing trajectories associated with the P 0-equation F (x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P 0-function lead to P 0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P 0-equations when the underlying function is P 0. To generate the trajectories, we perturb the given P 0-function F to a P-function F (x, ε); unique solutions of F (x, ε) = 0 as ε varies over an interval in (0, ∞) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.

2009 7th IEEE International Conference on Industrial Informatics, 2009

ABSTRACT The nonlinear complementarity problem (NCP) has been served as a general framework for l... more ABSTRACT The nonlinear complementarity problem (NCP) has been served as a general framework for linear, quadratic, and nonlinear programming, linear complementarity problem, and some equilibrium problems. Applications of the NCP can be found in many important fields such as economics, mathematical programming, operations research, engineering and mechanics. In this article, we consider smooth NCP on the basis of the square penalized Fischer-Burmeister function. We show under certain assumptions, any stationary point of the unconstrained minimization problem is already a solution of smooth NCP. Furthermore, a derivative-free descent algorithm is suggested and conditions for its convergence are given. Finally, some preliminary numerical results are presented.

Abstract and Applied Analysis, 2014

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeiste... more We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.