Search results for: Combinatorial Optimization Problem

Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Jagabondhu Hazra, Avinash Sinha

Abstract:

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: M. Mahdavi, H. Monsef, A. Bagheri

Abstract:

Discrete particle swarm optimization (DPSO) is a powerful stochastic evolutionary algorithm that is used to solve the large-scale, discrete and nonlinear optimization problems. However, it has been observed that standard DPSO algorithm has premature convergence when solving a complex optimization problem like transmission expansion planning (TEP). To resolve this problem an advanced discrete particle swarm optimization (ADPSO) is proposed in this paper. The simulation result shows that optimization of lines loading in transmission expansion planning with ADPSO is better than DPSO from precision view point.

Keywords: ADPSO, TEP problem, Lines loading optimization.

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Authors: Mohammed A. Alolfe, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

The proper design of RF pulses in magnetic resonance imaging (MRI) has a direct impact on the quality of acquired images, and is needed for many applications. Several techniques have been proposed to obtain the RF pulse envelope given the desired slice profile. Unfortunately, these techniques do not take into account the limitations of practical implementation such as limited amplitude resolution. Moreover, implementing constraints for special RF pulses on most techniques is not possible. In this work, we propose to develop an approach for designing optimal RF pulses under theoretically any constraints. The new technique will pose the RF pulse design problem as a combinatorial optimization problem and uses efficient techniques from this area such as genetic algorithms (GA) to solve this problem. In particular, an objective function will be proposed as the norm of the difference between the desired profile and the one obtained from solving the Bloch equations for the current RF pulse design values. The proposed approach will be verified using analytical solution based RF simulations and compared to previous methods such as Shinnar-Le Roux (SLR) method, and analysis, selected, and tested the options and parameters that control the Genetic Algorithm (GA) can significantly affect its performance to get the best improved results and compared to previous works in this field. The results show a significant improvement over conventional design techniques, select the best options and parameters for GA to get most improvement over the previous works, and suggest the practicality of using of the new technique for most important applications as slice selection for large flip angles, in the area of unconventional spatial encoding, and another clinical use.

Keywords: Selective excitation, magnetic resonance imaging, combinatorial optimization, pulse design.

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Authors: S. Balaji

Abstract:

An edge based local search algorithm, called ELS, is proposed for the maximum clique problem (MCP), a well-known combinatorial optimization problem. ELS is a two phased local search method effectively £nds the near optimal solutions for the MCP. A parameter ’support’ of vertices de£ned in the ELS greatly reduces the more number of random selections among vertices and also the number of iterations and running times. Computational results on BHOSLIB and DIMACS benchmark graphs indicate that ELS is capable of achieving state-of-the-art-performance for the maximum clique with reasonable average running times.

Keywords: Maximum clique, local search, heuristic, NP-complete.

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Authors: Kostas Metaxiotis

Abstract:

Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.

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Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.

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Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: Economic dispatch, optimization, quadratic programming, MATLAB.

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Authors: Parviz Fattahi

Abstract:

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it quit difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. In this paper, a Pareto approach to solve the multi objective flexible job shop scheduling problems is proposed. The objectives considered are to minimize the overall completion time (makespan) and total weighted tardiness (TWT). An effective simulated annealing algorithm based on the proposed approach is presented to solve multi objective flexible job shop scheduling problem. An external memory of non-dominated solutions is considered to save and update the non-dominated solutions during the solution process. Numerical examples are used to evaluate and study the performance of the proposed algorithm. The proposed algorithm can be applied easily in real factory conditions and for large size problems. It should thus be useful to both practitioners and researchers.

Keywords: Flexible job shop, Scheduling, Hierarchical approach, simulated annealing, tabu search, multi objective.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

Abstract:

Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: A. Vasan

Abstract:

Particle swarm optimization (PSO) technique is applied to design the water distribution pipeline network. A simulation-optimization model is formulated with the objective of minimizing cost and is applied to a benchmark water distribution system optimization problem. The benchmark problem taken for the application of PSO technique to optimize the pipe size of the water distribution network is New York City water supply system problem. The results from the analysis infer that PSO is a potential alternative optimization technique when compared to other heuristic techniques for optimal sizing of water distribution systems.

Keywords: Water distribution systems, Optimization, Particle swarm optimization, Swarm intelligence, New York water supply system.

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Authors: Rimmy Yadav, Avtar Singh

Abstract:

Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in finding excellent solution to finding shortest path during communication link failure.

Keywords: Ant colony optimization, link failure, prim’s algorithm.

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Authors: Y. Shpungin

Abstract:

Estimating the lifetime distribution of computer networks in which nodes and links exist in time and are bound for failure is very useful in various applications. This problem is known to be NP-hard. In this paper we present efficient combinatorial approaches to Monte Carlo estimation of network lifetime distribution. We also present some simulation results.

Keywords: Combinatorial spectrum, Monte Carlo, Networklifetime, Unreliable nodes and edges.

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Authors: Esmail Limouzade, Mahmood.Joorabian, Najaf Hedayat

Abstract:

This paper undertakes the problem of optimal capacitor placement in a distribution system. The problem is how to optimally determine the locations to install capacitors, the types and sizes of capacitors to he installed and, during each load level,the control settings of these capacitors in order that a desired objective function is minimized while the load constraints,network constraints and operational constraints (e.g. voltage profile) at different load levels are satisfied. The problem is formulated as a combinatorial optimization problem with a nondifferentiable objective function. Four solution mythologies based on algorithms (GA),tabu search (TS), and hybrid GA-SA algorithms are presented.The solution methodologies are preceded by a sensitivity analysis to select the candidate capacitor installation locations.

Keywords: Genetic Algorithm (GA) , capacitor placement, voltage profile, network losses, Simulated Annealing, distribution network.

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

Abstract:

In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: Binary cat swarm optimization, set covering problem, metaheuristic, binarization methods.

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Authors: Nader A. Al Theeb, Zaid Abu Manneh, Ibrahim Al-Qadi

Abstract:

Traveling salesman problem (TSP) is a combinatorial integer optimization problem that asks "What is the optimal route for a vehicle to traverse in order to deliver requests to a given set of customers?”. It is widely used by the package carrier companies’ distribution centers. The main goal of applying the TSP in courier organizations is to minimize the time that it takes for the courier in each trip to deliver or pick up the shipments during a day. In this article, an optimization model is constructed to create a new TSP variant to optimize the routing in a courier organization with a consideration of congestion in Amman, the capital of Jordan. Real data were collected by different methods and analyzed. Then, concert technology - CPLEX was used to solve the proposed model for some random generated data instances and for the real collected data. At the end, results have shown a great improvement in time compared with the current trip times, and an economic study was conducted afterwards to figure out the impact of using such models.

Keywords: Travel salesman problem, congestions, pick-up, integer programming, package carriers, service engineering.

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Authors: Huang, Wei-Hsiu Chang, Pei-Chann, Wang, Lien-Chun

Abstract:

The problems with high complexity had been the challenge in combinatorial problems. Due to the none-determined and polynomial characteristics, these problems usually face to unreasonable searching budget. Hence combinatorial optimizations attracted numerous researchers to develop better algorithms. In recent academic researches, most focus on developing to enhance the conventional evolutional algorithms and facilitate the local heuristics, such as VNS, 2-opt and 3-opt. Despite the performances of the introduction of the local strategies are significant, however, these improvement cannot improve the performance for solving the different problems. Therefore, this research proposes a meta-heuristic evolutional algorithm which can be applied to solve several types of problems. The performance validates BBEA has the ability to solve the problems even without the design of local strategies.

Keywords: Combinatorial problems, Artificial Chromosomes, Blocks Mining, Block Recombination

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Authors: R. Hashemi, M.H.Kargarnovin

Abstract:

This paper presents the identification of the impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and the genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness vs. the measurement noise and sensor location.

Keywords: Genetic Algorithm, Inverse problem, Optimization, Vibration.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. This paper presents a hybrid artificial immune system for the JSSP with the objective of minimizing makespan. The proposed approach combines the artificial immune system, which has a powerful global exploration capability, with the local search method, which can exploit the optimal antibody. The antibody coding scheme is based on the operation based representation. The decoding procedure limits the search space to the set of full active schedules. In each generation, a local search heuristic based on the neighborhood structure proposed by Nowicki and Smutnicki is applied to improve the solutions. The approach is tested on 43 benchmark problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Artificial immune system, Job shop scheduling problem, Local search, Metaheuristic algorithm

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Authors: Omar M. Sallabi, Younis El-Haddad

Abstract:

The Genetic Algorithm (GA) is one of the most important methods used to solve many combinatorial optimization problems. Therefore, many researchers have tried to improve the GA by using different methods and operations in order to find the optimal solution within reasonable time. This paper proposes an improved GA (IGA), where the new crossover operation, population reformulates operation, multi mutation operation, partial local optimal mutation operation, and rearrangement operation are used to solve the Traveling Salesman Problem. The proposed IGA was then compared with three GAs, which use different crossover operations and mutations. The results of this comparison show that the IGA can achieve better results for the solutions in a faster time.

Keywords: AI, Genetic algorithms, TSP.

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Authors: Jyoti Chaturvedi Gursaran

Abstract:

Nature conducts its action in a very private manner. To reveal these actions classical science has done a great effort. But classical science can experiment only with the things that can be seen with eyes. Beyond the scope of classical science quantum science works very well. It is based on some postulates like qubit, superposition of two states, entanglement, measurement and evolution of states that are briefly described in the present paper. One of the applications of quantum computing i.e. implementation of a novel quantum evolutionary algorithm(QEA) to automate the time tabling problem of Dayalbagh Educational Institute (Deemed University) is also presented in this paper. Making a good timetable is a scheduling problem. It is NP-hard, multi-constrained, complex and a combinatorial optimization problem. The solution of this problem cannot be obtained in polynomial time. The QEA uses genetic operators on the Q-bit as well as updating operator of quantum gate which is introduced as a variation operator to converge toward better solutions.

Keywords: Quantum computing, qubit, superposition, entanglement, measurement of states, evolution of states, Scheduling problem, hard and soft constraints, evolutionary algorithm, quantum evolutionary algorithm.

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Authors: Ben Mohamed Ahemed Mohamed, Yassine Adnan

Abstract:

The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins. This article treats the case of objects with a free orientation of 90Ôùª. We propose an approach of resolution combining optimization by colony of ants (ACO) and the heuristic method IMA to resolve this NP-Hard problem.

Keywords: Ant colony algorithm, bin-packing problem, heuristics methods.

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Authors: M. Ahmad, M. Gourgand, C. Caux

Abstract:

The Resource-Constrained Project Scheduling Problem (RCPSP) is concerned with single-item or small batch production where limited resources have to be allocated to dependent activities over time. Over the past few decades, a lot of work has been made with the use of optimal solution procedures for this basic problem type and its extensions. Brucker and Knust[1] discuss, how timetabling problems can be modeled as a RCPSP. Authors discuss high school timetabling and university course timetabling problem as an example. We have formulated two mathematical formulations of course timetabling problem in a new way which are the prototype of single-mode RCPSP. Our focus is to show, how course timetabling problem can be transformed into RCPSP. We solve this transformation model with genetic algorithm.

Keywords: Course Timetabling, Integer programming, Combinatorial optimizations

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Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: P. Suryakumari, P. Kantarao

Abstract:

Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: Frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem.

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Authors: Hakim Akeb, Mhand Hifi

Abstract:

In this paper, the use of beam search and look-ahead strategies for solving the strip packing problem (SPP) is investigated. Given a strip of fixed width W, unlimited length L, and a set of n circular pieces of known radii, the objective is to determine the minimum length of the initial strip that packs all the pieces. An augmented algorithm which combines beam search and a look-ahead strategies is proposed. The look-ahead is used in order to evaluate the nodes at each level of the tree search. The best nodes are then retained for branching. The computational investigation showed that the proposed augmented algorithm is able to improve the best known solutions of the literature on most instances used.

Keywords: Combinatorial optimization, cutting and packing, beam search, heuristic, look-ahead strategy.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

Abstract:

A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: T. R. Alencar, P. T. Leite

Abstract:

Several optimization algorithms specifically applied to the problem of Operation Planning of Hydrothermal Power Systems have been developed and are used. Although providing solutions to various problems encountered, these algorithms have some weaknesses, difficulties in convergence, simplification of the original formulation of the problem, or owing to the complexity of the objective function. Thus, this paper presents the development of a computational tool for solving optimization problem identified and to provide the User an easy handling. Adopted as intelligent optimization technique, Genetic Algorithms and programming language Java. First made the modeling of the chromosomes, then implemented the function assessment of the problem and the operators involved, and finally the drafting of the graphical interfaces for access to the User. The program has managed to relate a coherent performance in problem resolution without the need for simplification of the calculations together with the ease of manipulating the parameters of simulation and visualization of output results.

Keywords: Energy, Optimization, Hydrothermal Power Systemsand Genetic Algorithms

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