Search results for: Integer programming

Authors: Saleem Z. Ramadan, Gürsel A. Süer

Abstract:

In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

Abstract:

The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal openshop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Keywords: Integer programming, open shop problem, optimal staffing.

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Authors: Michael Todinov, Eberechi Weli

Abstract:

The paper suggests for the first time the use of dynamic programming techniques for optimal risk reduction in the railway industry. It is shown that by using the concept ‘amount of removed risk by a risk reduction option’, the problem related to optimal allocation of a fixed budget to achieve a maximum risk reduction in the railway industry can be reduced to an optimisation problem from dynamic programming. For n risk reduction options and size of the available risk reduction budget B (expressed as integer number), the worst-case running time of the proposed algorithm is O (n x (B+1)), which makes the proposed method a very efficient tool for solving the optimal risk reduction problem in the railway industry. 

Keywords: Optimisation, railway risk reduction, budget constraints, dynamic programming.

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Authors: Mehdi Seifbarghy, Keyvan Roshan

Abstract:

Main goal of preventive healthcare problems are at decreasing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The levels of establishment and staffing costs along with summation of the travel and waiting time that clients spent are considered as objectives functions of the proposed nonlinear integer programming model. In this paper, we have proposed a bi-objective mathematical model for designing a network of preventive healthcare facilities so as to minimize aforementioned objectives, simultaneously. Moreover, each facility acts as M/M/1 queuing system. The number of facilities to be established, the location of each facility, and the level of technology for each facility to be chosen are provided as the main determinants of a healthcare facility network. Finally, to demonstrate performance of the proposed model, four multi-objective decision making techniques are presented to solve the model.

Keywords: Preventive healthcare problems, Non-linear integer programming models, Multi-objective decision making techniques

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Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

Abstract:

Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

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Authors: Oscar Javier Herrera Ochoa, Ivan Dario Romero Fonseca

Abstract:

This paper presents a design of a model for planning the distribution logistics operation. The significance of this work relies on the applicability of this fact to the analysis of small and medium enterprises (SMEs) of dry freight in Bogotá. Two stages constitute this implementation: the first one is the place where optimal planning is achieved through a hybrid model developed with mixed integer programming, which considers the transhipment operation based on a combined load allocation model as a classic transshipment model; the second one is the specific routing of that operation through the heuristics of Clark and Wright. As a result, an integral model is obtained to carry out the step by step planning of the distribution of dry freight for SMEs in Bogotá. In this manner, optimum assignments are established by utilizing transshipment centers with that purpose of determining the specific routing based on the shortest distance traveled.

Keywords: Transshipment model, mixed integer programming, saving algorithm, dry freight transportation.

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Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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Authors: Eugene Kindler

Abstract:

2007 is a jubilee year: in 1967, programming language SIMULA 67 was presented, which contained all aspects of what was later called object-oriented programming. The present paper contains a description of the development unto the objectoriented programming, the role of simulation in this development and other tools that appeared in SIMULA 67 and that are nowadays called super-object-oriented programming.

Keywords: Simulation, super-object-oriented programming, object-oriented programming, SIMULA.

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Authors: Y. Wu

Abstract:

Today-s business has inevitably been set in the global supply chain management environment. International transportation has never played such an important role in the global supply chain network, because movement of shipments from one country to another tends to be more frequent than ever before. This paper studies international transportation problems experienced by an international transportation company. Because of the limited fleet capacity, the transportation company has to hire additional trucks from two countries in advance. However, customer-s shipment information is uncertain, and decisions have to be made before accurate information can be obtained. This paper proposes a stochastic mixed 0-1 programming model to solve the international transportation problems under uncertain demand. A series of experiments demonstrate the effectiveness of the proposed stochastic model.

Keywords: Global supply chain management, international transportation, stochastic programming.

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Authors: Omid S. Fard, Akbar H. Borzabadi

Abstract:

In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of project scheduling and material ordering can provide more flexibility to the project scheduling problem, as the project execution costs can be enhanced. Hence, the issue has been taken into account in this paper. To do so, a mixed-integer mathematical model is developed which considers the aforementioned flexibility, in addition to the materials quantity discount and space availability restrictions. Moreover, the activities duration has been treated as decision variables. Finally, the efficiency of the proposed model is tested by different instances. Additionally, the influence of the aforementioned parameters is investigated on the model performance.

Keywords: Material ordering, project scheduling, quantity discount, space availability.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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Authors: M. Esmaeeli Shahrakht, A. Kazemi

Abstract:

Due to uncertainty of wind velocity, wind power generators don’t have deterministic output power. Utilizing wind power generation and thermal power plants together create new concerns for operation engineers of power systems. In this paper, a model is presented to implement the uncertainty of load and generated wind power which can be utilized in power system operation planning. Stochastic behavior of parameters is simulated by generating scenarios that can be solved by deterministic method. A mixed-integer linear programming method is used for solving deterministic generation scheduling problem. The proposed approach is applied to a 12-unit test system including 10 thermal units and 2 wind farms. The results show affectivity of piecewise linear model in unit commitment problems. Also using linear programming causes a considerable reduction in calculation times and guarantees convergence to the global optimum. Neglecting the uncertainty of wind velocity causes higher cost assessment of generation scheduling.

Keywords: Load uncertainty, linear programming, scenario generation, unit commitment, wind farm.

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Authors: Sakol Udomsiri, Masahiro Iwahashi

Abstract:

This paper presents comparative study on recent integer DCTs and a new method to construct a low sensitive structure of integer DCT for colored input signals. The method refers to sensitivity of multiplier coefficients to finite word length as an indicator of how word length truncation effects on quality of output signal. The sensitivity is also theoretically evaluated as a function of auto-correlation and covariance matrix of input signal. The structure of integer DCT algorithm is optimized by combination of lower sensitive lifting structure types of IRT. It is evaluated by the sensitivity of multiplier coefficients to finite word length expression in a function of covariance matrix of input signal. Effectiveness of the optimum combination of IRT in integer DCT algorithm is confirmed by quality improvement comparing with existing case. As a result, the optimum combination of IRT in each integer DCT algorithm evidently improves output signal quality and it is still compatible with the existing one.

Keywords: DCT, sensitivity, lossless, wordlength.

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Authors: M. S. Osman, A. A. Tharwat, I. A. El-Khodary, A. G. Chalabi

Abstract:

In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.

Keywords: Equity Markets, Future Scenarios, PortfolioSelection, Multiple Criteria Fuzzy Optimization

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Authors: Ivan Stanev, Maria Koleva

Abstract:

Common Platform for Automated Programming (CPAP) is defined in details. Two versions of CPAP are described: Cloud based (including set of components for classic programming, and set of components for combined programming); and Knowledge Based Automated Software Engineering (KBASE) based (including set of components for automated programming, and set of components for ontology programming). Four KBASE products (Module for Automated Programming of Robots, Intelligent Product Manual, Intelligent Document Display, and Intelligent Form Generator) are analyzed and CPAP contributions to automated programming are presented.

Keywords: Automated Programming, Cloud Computing, Knowledge Based Software Engineering, Service Oriented Architecture.

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Authors: Y. Long, L. Liu, K. V. Branin

Abstract:

One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.

Keywords: Discontinuous cost function, mixed integer programming, optimization, procurement, rebate.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: Jae Young Park, Seung Wook Lee, Jong Tae Kim

Abstract:

OpenMP is an API for parallel programming model of shared memory multiprocessors. Novice OpenMP programmers often produce the code that compiler cannot find human errors. It was investigated how compiler coped with the common mistakes that can occur in OpenMP code. The latest version(4.4.3) of GCC is used for this research. It was found that GCC compiled the codes without any errors or warnings. In this paper the programming aid tool is presented for OpenMP programs. It can check 12 common mistakes that novice programmer can commit during the programming of OpenMP. It was demonstrated that the programming aid tool can detect the various common mistakes that GCC failed to detect.

Keywords: Parallel programming, OpenMP, programming aid.

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Authors: Abdolsalam Ghaderi

Abstract:

In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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Authors: Yuan-Kang Shih, Shu-Li Chang, Shin-Shin Kao

Abstract:

Qk n has been shown as an alternative to the hypercube family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk n is a bipartite graph. In this paper, we will prove that given any pair of vertices, w and b, from different partite sets of Qk n, there exist 2n internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1 i=0 Pi covers all vertices of Qk n. The result is optimal since each vertex of Qk n has exactly 2n neighbors.

Keywords: container, Hamiltonian, k-ary n-cube, m*-connected.

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Authors: Z. Babic, I. Veza, A. Balic, M. Crnjac

Abstract:

The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Keywords: De Novo Programming, production plan, stone souvenirs, variable prices.

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Authors: Marin Mandić, Elis Sutlović, Tonći Modrić, Luka Stanić

Abstract:

With the restructuring and deregulation of the power system, storage owners, generation companies or private producers can offer their multiple services on various power markets and earn income in different types of markets, such as the day-ahead, real-time, ancillary services market, etc. During the COVID-19 pandemic, electricity prices, as well as ancillary services prices, increased significantly. The optimization of the energy storage operation was performed using a suitable model for simulating the operation of a pumped storage hydropower plant under market conditions. The objective function maximizes the income earned through energy arbitration, regulation-up, regulation-down and spinning reserve services. The optimization technique used for solving the objective function is mixed integer linear programming (MILP). In numerical examples, the pumped storage hydropower plant operation has been optimized considering the already achieved hourly electricity market prices from Nord Pool for the pre-pandemic (2019) and the pandemic (2020 and 2021) years. The impact of the electricity market prices during the COVID-19 pandemic on energy storage operation is shown through the analysis of income, operating hours, reserved capacity and consumed energy for each service. The results indicate the role of energy storage during a significant fluctuation in electricity and services prices.

Keywords: Electrical market prices, electricity market, energy storage optimization, mixed integer linear programming, MILP, optimization.

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Authors: M. Samaka

Abstract:

This paper presents the development of a software application for Off-line robot task programming and simulation. Such application is designed to assist in robot task planning and to direct manipulator motion on sensor based programmed motion. The concept of the designed programming application is to use the power of the knowledge base for task accumulation. In support of the programming means, an interactive graphical simulation for manipulator kinematics was also developed and integrated into the application as the complimentary factor to the robot programming media. The simulation provides the designer with useful, inexpensive, off-line tools for retain and testing robotics work cells and automated assembly lines for various industrial applications.

Keywords: Robot programming, task-level programming, robot languages, robot simulation, robotics software.

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Authors: Siliang Wang, Minghui Wang, Jun Hu

Abstract:

A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: Jean Berger, Nassirou Lo, Martin Noel

Abstract:

Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: Search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization.

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Authors: Phruksaphanrat B.

Abstract:

This research presents a fuzzy multi-objective model for a machine selection problem in a flexible manufacturing system of a tire company. Two main objectives are minimization of an average machine error and minimization of the total setup time. Conventionally, the working team uses trial and error in selecting a pressing machine for each task due to the complexity and constraints of the problem. So, both objectives may not satisfy. Moreover, trial and error takes a lot of time to get the final decision. Therefore, in this research preemptive fuzzy goal programming model is developed for solving this multi-objective problem. The proposed model can obtain the appropriate results that the Decision Making (DM) is satisfied for both objectives. Besides, alternative choice can be easily generated by varying the satisfaction level. Additionally, decision time can be reduced by using the model, which includes all constraints of the system to generate the solutions. A numerical example is also illustrated to show the effectiveness of the proposed model.

Keywords: Machine Selection, Preemptive Fuzzy Goal Programming, Mixed Integer Programming, Application of Tire Industry.

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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: M. Al-Jepoori, D. Bennett

Abstract:

Teaching Object-Oriented Programming (OOP) as part of a Computing-related university degree is a very difficult task; the road to ensuring that students are actually learning object oriented concepts is unclear, as students often find it difficult to understand the concept of objects and their behavior. This problem is especially obvious in advanced programming modules where Design Pattern and advanced programming features such as Multi-threading and animated GUI are introduced. Looking at the students’ performance at their final year on a university course, it was obvious that the level of students’ understanding of OOP varies to a high degree from one student to another. Students who aim at the production of Games do very well in the advanced programming module. However, the students’ assessment results of the last few years were relatively low; for example, in 2016-2017, the first quartile of marks were as low as 24.5 and the third quartile was 63.5. It is obvious that many students were not confident or competent enough in their programming skills. In this paper, the reasons behind poor performance in Advanced OOP modules are investigated, and a suggested practice for teaching OOP based on a complex case study is described and evaluated.

Keywords: Complex programming case study, design pattern, learning advanced programming, object oriented programming.

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