Search results for: multi-objective combinatorial optimization problem

Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Mandeep Kaur, Fatehgarh Sahib

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The purpose of economic load dispatch is to allocate the required load demand between the available generation units such that the cost of operation is minimized. It is an optimization problem to find the most economical schedule of the generating units while satisfying load demand and operational constraints. The multiobjective optimization problem in which the engineer’s goal is to maximize or minimize not a single objective function but several objective functions simultaneously. The purpose of multiobjective problems in the mathematical programming framework is to optimize the different objective functions. Many approaches and methods have been proposed in recent years to solve multiobjective optimization problems. Weighting method has been applied to convert multiobjective optimization problems into scalar optimization. MATLAB 7.10 has been used to write the code for the complete algorithm with the help of genetic algorithm (GA). The validity of the proposed method has been demonstrated on a three-unit power system.

Keywords: economic load dispatch, genetic algorithm, generating units, multiobjective optimization, weighting method

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Authors: M. Moradi Dalini, M. R. Talebi

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This research revolves around a technical method according to combines econometric and multiobjective programming to select and obtain optimal solutions to management problems. It is taken for a generation that; it is important to analyze which combination of values of the explanatory variables -in an econometric method- would point to the simultaneous achievement of the best values of the response variables. In this case, if a certain degree of conflict is viewed among the response variables, we suggest a multiobjective method in order to the results obtained from a regression analysis. In fact, with the use of a multiobjective method, we will have the best decision about the conflicting relationship between the response variables and the optimal solution. The combined multiobjective programming and econometrics benefit is an assessment of a balanced “optimal” situation among them because a find of information can hardly be extracted just by econometric techniques.

Keywords: econometrics, multiobjective optimization, management problem, optimization

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Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

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Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: particle swarm optimization, migration, variable neighborhood search, multiobjective optimization

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Konstantinos Metaxiotis, Konstantinos Liagkouras

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The objective of this study is to examine the performance of three well-known multiobjective evolutionary algorithms for solving optimization problems. The first algorithm is the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the second one is the Strength Pareto Evolutionary Algorithm 2 (SPEA-2), and the third one is the Multiobjective Evolutionary Algorithms based on decomposition (MOEA/D). The examined multiobjective algorithms are analyzed and tested on the ZDT set of test functions by three performance metrics. The results indicate that the NSGA-II performs better than the other two algorithms based on three performance metrics.

Keywords: MOEAs, multiobjective optimization, ZDT test functions, evolutionary algorithms

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Authors: Alexandre Barbosa de Almeida, Telma Woerle de Lima Soares

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Protein structure prediction is a challenging task in the bioinformatics field. The biological function of all proteins majorly relies on the shape of their three-dimensional conformational structure, but less than 1% of all known proteins in the world have their structure solved. This work proposes a deep learning model to address this problem, attempting to predict some aspects of the protein conformations. Throughout a process of multiobjective dominance, a recurrent neural network was trained to abstract the particular bias of each individual multiobjective algorithm, generating a heuristic that could be useful to predict some of the relevant aspects of the three-dimensional conformation process formation, known as protein folding.

Keywords: Ab initio heuristic modeling, multiobjective optimization, protein structure prediction, recurrent neural network

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Authors: J. Satya Eswari, Ch. Venkateswarlu

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The formulation of a commercial pharmaceutical product involves several composition factors and response characteristics. When the formulation requires to satisfy multiple response characteristics which are conflicting, an optimal solution requires the need for an efficient multiobjective optimization technique. In this work, a regression is combined with a non-dominated sorting differential evolution (NSDE) involving Naïve & Slow and ε constraint techniques to derive different multiobjective optimization strategies, which are then evaluated by means of a trapidil pharmaceutical formulation. The analysis of the results show the effectiveness of the strategy that combines the regression model and NSDE with the integration of both Naïve & Slow and ε constraint techniques for Pareto optimization of trapidil formulation. With this strategy, the optimal formulation at pH=6.8 is obtained with the decision variables of micro crystalline cellulose, hydroxypropyl methylcellulose and compression pressure. The corresponding response characteristics of rate constant and release order are also noted down. The comparison of these results with the experimental data and with those of other multiple regression model based multiobjective evolutionary optimization strategies signify the better performance for optimal trapidil formulation.

Keywords: pharmaceutical formulation, multiple regression model, response surface method, radial basis function network, differential evolution, multiobjective optimization

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Elham Kazemi

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Quadratic Assignment Problem (QAP) is one the combinatorial optimization problems about which research has been done in many companies for allocating some facilities to some locations. The issue of particular importance in this process is the costs of this allocation and the attempt in this problem is to minimize this group of costs. Since the QAP’s are from NP-hard problem, they cannot be solved by exact solution methods. Cuckoo Optimization Algorithm is a Meta-heuristicmethod which has higher capability to find the global optimal points. It is an algorithm which is basically raised to search a continuous space. The Quadratic Assignment Problem is the issue which can be solved in the discrete space, thus the standard arithmetic operators of Cuckoo Optimization Algorithm need to be redefined on the discrete space in order to apply the Cuckoo Optimization Algorithm on the discrete searching space. This paper represents the way of discretizing the Cuckoo optimization algorithm for solving the quadratic assignment problem.

Keywords: Quadratic Assignment Problem (QAP), Discrete Cuckoo Optimization Algorithm (DCOA), meta-heuristic algorithms, optimization algorithms

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Authors: Yassir AbdelRazig

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Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: ant colony, construction site layout, optimization, genetic algorithms

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Gia Sirbiladze

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Route planning problems are among the activities that have the highest impact on logistical planning, transportation, and distribution because of their effects on efficiency in resource management, service levels, and client satisfaction. In extreme conditions, the difficulty of vehicle movement between different customers causes the imprecision of time of movement and the uncertainty of the feasibility of movement. A feasibility level of vehicle movement on the closed route of the disaster-streaking zone is defined for the construction of an objective function. Experts’ evaluations of the uncertain parameters in q-rung ortho-pair fuzzy numbers (q-ROFNs) are presented. A fuzzy bi-objective combinatorial optimization problem of fuzzy vehicle routine problem (FVRP) is constructed based on the technique of possibility theory. The FVRP is reduced to the bi-criteria partitioning problem for the so-called “promising” routes which were selected from the all-admissible closed routes. The convenient selection of the “promising” routes allows us to solve the reduced problem in real-time computing. For the numerical solution of the bi-criteria partitioning problem, the -constraint approach is used. The main results' support software is designed. The constructed model is illustrated with a numerical example.

Keywords: q-rung ortho-pair fuzzy sets, facility location selection problem, multi-objective combinatorial optimization problem, partitioning problem

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Authors: P. Parthiban, Sonu Rajak, N. Kannan, R. Dhanalakshmi

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This paper deals with the Vehicle Routing Problem (VRP) with environmental considerations which is called Pollution Routing Problem (PRP). The objective is to minimize the operational and environmental costs. It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. In this context, we presented an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the PRP. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage a SOA is run on the resulting VRPTW solutions. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route in order to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm is able to provide good solutions.

Keywords: ant colony optimization, CO2 emissions, combinatorial optimization, speed optimization, vehicle routing

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Authors: Ernesto Linan, Linda Cruz, Lucero Becerra

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In this paper, a new hybridized algorithm based on Chemical Reaction Optimization and Simulated Annealing is proposed to solve the alignment sequence Problem. The Chemical Reaction Optimization is a population-based meta-heuristic algorithm based on the principles of a chemical reaction. Simulated Annealing is applied to solve a large number of combinatorial optimization problems of general-purpose. In this paper, we propose hybridization between Chemical Reaction Optimization algorithm and Simulated Annealing in order to solve the Sequence Alignment Problem. An initial population of molecules is defined at beginning of the proposed algorithm, where each molecule represents a sequence alignment problem. In order to simulate inter-molecule collisions, the process of Chemical Reaction is placed inside the Metropolis Cycle at certain values of temperature. Inside this cycle, change of molecules is done due to collisions; some molecules are accepted by applying Boltzmann probability. The results with the hybrid scheme are better than the results obtained separately.

Keywords: chemical reaction optimization, sequence alignment problem, simulated annealing algorithm, metaheuristics

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Jalal Abdulkareem Sultan, Abdulhakeem Luqman Hasan

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With the development of health care systems competition, hospitals face more and more pressures. Meanwhile, resource allocation has a vital effect on achieving competitive advantages in hospitals. Selecting the appropriate number of beds is one of the most important sections in hospital management. However, in real situation, bed allocation selection is a multiple objective problem about different items with vagueness and randomness of the data. It is very complex. Hence, research about bed allocation problem is relatively scarce under considering multiple departments, nursing hours, and stochastic information about arrival and service of patients. In this paper, we develop a fuzzy multiobjective bed allocation model for overcoming uncertainty and multiple departments. Fuzzy objectives and weights are simultaneously applied to help the managers to select the suitable beds about different departments. The proposed model is solved by using Artificial Bee Colony (ABC), which is a very effective algorithm. The paper describes an application of the model, dealing with a public hospital in Iraq. The results related that fuzzy multi-objective model was presented suitable framework for bed allocation and optimum use.

Keywords: bed allocation problem, fuzzy logic, artificial bee colony, multi-objective optimization

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Authors: Wuthichai Wongthatsanekorn, Nuntana Matheekrieangkrai

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This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: bee colony optimization, ready mixed concrete problem, ruck scheduling, multiple construction sites

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Authors: Li Dan, Zhao Junsuo, Zhang Wenjun

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Aiming at the shortcomings of the Quantum Genetic Algorithm such as the multimodal function optimization problems easily falling into the local optimum, and vulnerable to premature convergence due to no closely relationship between individuals, the paper presents an Improved Many Worlds Quantum Genetic Algorithm (IMWQGA). The paper using the concept of Many Worlds; using the derivative way of parallel worlds’ parallel evolution; putting forward the thought which updating the population according to the main body; adopting the transition methods such as parallel transition, backtracking, travel forth. In addition, the algorithm in the paper also proposes the quantum training operator and the combinatorial optimization operator as new operators of quantum genetic algorithm.

Keywords: quantum genetic algorithm, many worlds, quantum training operator, combinatorial optimization operator

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid particle swarm optimization algorithm is proposed for the multi-objective flexible job shop scheduling problem that is very important and hard combinatorial problem. The Pareto approach is used for solving the multi-objective problem. Several new local search heuristics are integrated into an algorithm based on the critical block concept to enhance the performance of the algorithm. The algorithm is compared with the recently published multi-objective algorithms based on benchmarks selected from the literature. Several metrics are used for quantifying performance and comparison of the achieved solutions. The algorithms are also compared based on the Weighting summation of objectives approach. The proposed algorithm can find the Pareto solutions more efficiently than the compared algorithms in less computational time.

Keywords: swarm-based optimization, local search, Pareto optimality, flexible job shop scheduling, multi-objective optimization

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Authors: Feijoo E. Colomine Duran, Carlos E. Peñaloza Corredor

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There modeling component selection financial investment (Portfolio) a variety of problems that can be addressed with optimization techniques under evolutionary schemes. For his feature, the problem of selection of investment components of a dichotomous relationship between two elements that are opposed: The Portfolio Performance and Risk presented by choosing it. This relationship was modeled by Markowitz through a media problem (Performance) - variance (risk), ie must Maximize Performance and Minimize Risk. This research included the study and implementation of multi-objective evolutionary techniques to solve these problems, taking as experimental framework financial market equities Colombia Stock Exchange between 2009-2015. Comparisons three multiobjective evolutionary algorithms, namely the Nondominated Sorting Genetic Algorithm II (NSGA-II), the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Indicator-Based Selection in Multiobjective Search (IBEA) were performed using two measures well known performance: The Hypervolume indicator and R_2 indicator, also it became a nonparametric statistical analysis and the Wilcoxon rank-sum test. The comparative analysis also includes an evaluation of the financial efficiency of the investment portfolio chosen by the implementation of various algorithms through the Sharpe ratio. It is shown that the portfolio provided by the implementation of the algorithms mentioned above is very well located between the different stock indices provided by the Colombia Stock Exchange.

Keywords: finance, optimization, portfolio, Markowitz, evolutionary algorithms

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Authors: Badr M. Alshammari, T. Guesmi

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In recent years, the combined economic and emission power dispatch is one of the main problems of electrical power system. It aims to schedule the power generation of generators in order to minimize cost production and emission of harmful gases caused by fossil-fueled thermal units such as CO, CO₂, NO_x, and SO₂. To solve this complicated multi-objective problem, an improved version of the particle swarm optimization technique that includes non-dominated sorting concept has been proposed. Valve point loading effects and system losses have been considered. The three-unit and ten-unit benchmark systems have been used to show the effectiveness of the suggested optimization technique for solving this kind of nonconvex problem. The simulation results have been compared with those obtained using genetic algorithm based method. Comparison results show that the proposed approach can provide a higher quality solution with better performance.

Keywords: power dispatch, valve point loading effects, multiobjective optimization, Pareto solutions

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Authors: Guilherme Baldo Carlos

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The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Aleksandar Jovanovic, Katarina Kukic, Ana Uzelac, Dusan Teodorovic

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Wisdom of the Crowd (WoC) is a decentralized method that uses the collective intelligence of humans. Individual guesses may be far from the target, but when considered as a group, they converge on optimal solutions for a given problem. We will utilize WoC to address the challenge of controlling traffic lights within intersections from the streets of Kragujevac, Serbia. The problem at hand falls within the category of NP-hard problems. We will employ an algorithm that leverages the swarm intelligence of bees: Bee Colony Optimization (BCO). Data regarding traffic signal timing at a single intersection will be gathered from citizens through a survey. Results obtained in that manner will be compared to the BCO results for different traffic scenarios. We will use Vissim traffic simulation software as a tool to compare the performance of bees’ and humans’ collective intelligence.

Keywords: wisdom of the crowd, traffic signal control, combinatorial optimization, bee colony optimization

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Authors: Imen Boudali, Marwa Ragmoun

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The Vehicle Routing Problem with Hard Time Windows (VRPHTW) is a basic distribution management problem that models many real-world problems. The objective of the problem is to deliver a set of customers with known demands on minimum-cost vehicle routes while satisfying vehicle capacity and hard time windows for customers. In this paper, we propose to deal with our optimization problem by using a new hybrid stochastic algorithm based on two metaheuristics: Chemical Reaction Optimization (CRO) and Greedy Randomized Adaptive Search Procedure (GRASP). The first method is inspired by the natural process of chemical reactions enabling the transformation of unstable substances with excessive energy to stable ones. During this process, the molecules interact with each other through a series of elementary reactions to reach minimum energy for their existence. This property is embedded in CRO to solve the VRPHTW. In order to enhance the population diversity throughout the search process, we integrated the GRASP in our method. Simulation results on the base of Solomon’s benchmark instances show the very satisfactory performances of the proposed approach.

Keywords: Benchmark Problems, Combinatorial Optimization, Vehicle Routing Problem with Hard Time Windows, Meta-heuristics, Hybridization, GRASP, CRO

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Mukhtiar Singh, Sumeet Nagar

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Vehicle routing problem (VRP) is a combinatorial optimization and nonlinear programming problem aiming to optimize decisions regarding given set of routes for a fleet of vehicles in order to provide cost-effective and efficient delivery of both services and goods to the intended customers. This paper proposes the application of integrated particle swarm optimization (PSO) and genetic optimization algorithm (GA) to address the Vehicle routing problem in sugarcane industry in India. Suger industry is very prominent agro-based industry in India due to its impacts on rural livelihood and estimated to be employing around 5 lakhs workers directly in sugar mills. Due to various inadequacies, inefficiencies and inappropriateness associated with the current vehicle routing model it costs huge money loss to the industry which needs to be addressed in proper context. The proposed algorithm utilizes the crossover operation that originally appears in genetic algorithm (GA) to improve its flexibility and manipulation more readily and avoid being trapped in local optimum, and simultaneously for improving the convergence speed of the algorithm, level set theory is also added to it. We employ the hybrid approach to an example of VRP and compare its result with those generated by PSO, GA, and parallel PSO algorithms. The experimental comparison results indicate that the performance of hybrid algorithm is superior to others, and it will become an effective approach for solving discrete combinatory problems.

Keywords: fuzzy logic, genetic algorithm, particle swarm optimization, vehicle routing problem

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Authors: Boumesbah Asma, Chergui Mohamed El-amine

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Since it has been shown that the multi-objective minimum spanning tree problem (MOST) is NP-hard even with two criteria, we propose in this study a hybrid NSGA-II algorithm with an exact mutation operator, which is only used with low probability, to find an approximation to the Pareto front of the problem. In a connected graph G, a spanning tree T of G being a connected and cycle-free graph, if k edges of G\T are added to T, we obtain a partial graph H of G inducing a reduced size multi-objective spanning tree problem compared to the initial one. With a weak probability for the mutation operator, an exact method for solving the reduced MOST problem considering the graph H is then used to give birth to several mutated solutions from a spanning tree T. Then, the selection operator of NSGA-II is activated to obtain the Pareto front approximation. Finally, an adaptation of the VNS metaheuristic is called for further improvements on this front. It allows finding good individuals to counterbalance the diversification and the intensification during the optimization search process. Experimental comparison studies with an exact method show promising results and indicate that the proposed algorithm is efficient.

Keywords: minimum spanning tree, multiple objective linear optimization, combinatorial optimization, non-sorting genetic algorithm, variable neighborhood search

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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