Variable Neighborhood Search

Given an undirected graph with edge weights, the MAX-CUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. It is a well-known NP-hard problem with applications in several fields, including VLSI design and statistical physics. In this paper, a greedy randomized adaptive search procedure (GRASP), a variable neighborhood search (VNS), and a path-relinking (PR) intensification heuristic for MAX-CUT are proposed and tested. New hybrid heuristics that combine GRASP, VNS, and PR are also proposed and tested. Computational results indicate that these randomized heuristics find near-optimal solutions. On a set of standard test problems, new best known solutions were produced for many of the instances.

In this work we present a new hybrid approach for solving the clustering problem for geographic data, which is known to be NP-hard. Two metaheuristics that have proven efficiency in combinatory optimization problems have been chosen for the comparison: Simulated Annealing (SA) and Variable Neighborhood Search (VNS). The proposed model is based on the partitioning around the medoids and on P-median. Previous test runs have shown satisfactory results (in terms of quality and time) for instances of 469 geographic objects, but when instances of greater size are used then variability in the results has been detected. In an effort to achieve better results for the clustering problem, we have incorporated a hybridization of simulated annealing and variable neighborhood search to the geographic clustering problem. We have considered different sizes in the tests runs for distinct groups observing that the solutions obtained with the hybrid approach, named SA-VNS hybrid, overcome SA and VNS when they have been implemented individually. Finally, with the aim of evaluating the benefits of the meta-heuristic proposed, we have measured the internal connection of the obtained clusters by means of the Dunn Index. The results obtained show that the hybrid SA-VNS performs better than SA and VNS with respect to the compactness feature.

In the last few years, the application of decision making to logistic problems has become crucial for public and private organizations. Efficient decisions clearly contribute to improve operational aspects such as cost reduction or service improvement. The particular case of waste collection service considered in this paper involves a set of economic, labor and environmental issues that translate into difficult operational problems. They pose a challenge to nowadays optimization technologies since they have multiple constraints and multiple objectives that may be in conflict. We therefore need to resort to multiobjective approaches to model and solve this problem, providing efficient solutions in short computational times. In particular, we consider four different objectives to model the waste collection problem: travel cost, route length balance, route time balance, and number of routes. We propose an iterated greedy algorithm coupled with a variable neighborhood search to minimize an achievement function to determine a good approximation to the Pareto front. The performance of our method is empirically analyzed on a set of instances (both generated and real), and compared with the well-known NSGA-II and SPEA2 methods. The comparison favors our proposal.

This paper addresses a problem faced by maintenance service providers: performing maintenance activities at the right time on geographically distributed machines subjected to random failures. This problem requires determining for each technician the sequence of maintenance operations to perform to minimize the total expected costs while ensuring a high level of machine availability. To date, research in this area has dealt with routing and maintenance schedules separately. This study aims to determine the optimal maintenance and routing plan simultaneously. A new bi-objective mathematical model that integrates both routing and maintenance considerations is proposed for time-based preventive maintenance. The first objective is to minimize the travel cost related to technicians' routing. The second objective can either minimize the total preventive and corrective maintenance cost or the failure cost. New general variable neighborhood search (GVNS) and variable neighborhood descent (VND) algorithms based on the Pareto dominance concept are proposed and performed over newly generated instances. The efficiency of our approach is demonstrated through several experiments. Compared to the commercial solver and existing multi-objective VND and GVNS, these new algorithms obtain highly competitive results on both mono-objective and bi-objective variants.

This paper addresses a problem faced by maintenance service providers: performing maintenance activities at the right time on geographically distributed machines subjected to random failures. This problem requires determining for each technician the sequence of maintenance operations to perform to minimize the total expected costs while ensuring a high level of machine availability. To date, research in this area has dealt with routing and maintenance schedules separately. This study aims to determine the optimal maintenance and routing plan simultaneously. A new bi-objective mathematical model that integrates both routing and maintenance considerations is proposed for time-based preventive maintenance. The first objective is to minimize the travel cost related to technicians’ routing. The second objective can either minimize the total preventive and corrective maintenance cost or the failure cost. New general variable neighborhood search (GVNS) and variable neighborhood descent (VN...

The minimum-sum-of-squared error clustering (MSSC) is one of the most intuitive and popular clustering algorithms. In this paper, we first show that MSSC can be equivalently cast as a concave minimization problem. To find the global solution of MSSC, we construct a procedure to move from a fractional solution of the relaxed minimization problem to an integer solution with improved objective value. Then we adapt Tuy's convexity cut method, a powerful algorithm for global concave optimization, to find a global optimum to MSSC. Promising numerical examples are reported.

This paper proposes a number of forward VNS and reverse VNS algorithms for job-shop scheduling problem. The forward VNS algorithms are the variable neighborhood search algorithms applied to the original problem (i.e., the problem instance with the original precedence constraints). The reverse VNS algorithms are the variable neighborhood search algorithms applied to the reversed problem (i.e., the problem instance with the reversed precedence constraints). This paper also proposes a multi-VNS algorithm which assigns an identical initial solution-representing permutation to the selected VNS algorithms, runs these VNS algorithms, and then uses the best solution among the final solutions of all selected VNS algorithms as its final result. The aim of the multi-VNS algorithm is to utilize each single initial solution-representing permutation most efficiently and thus receive its best result in return.

Traditionally, practical clique algorithms have been compared based on their performance on various random graphs. We propose a new testing methodology which permits testing to be completed in a fraction of the time required by previous methods. In addition, the range of testing can be extended to include problems that could not be attempted in the past because of being too time consuming. We accomplish this by applying the approach that makes dynamic programming a very e ective algorithmic technique: we use tabulated estimates for the time required to solve subproblems rather than timing each exactly. Our computational experiments validate this approach. The next step is to use this workbench to develop fast new algorithms for the maximum clique problem. A mixed algorithm is an algorithm which applies di erent strategies for the subproblems that arise. Using the dynamic programming approach again for timing, we mechanize the process of developing table driven algorithms which apply the best possible strategy to each subproblem. We demonstrate the utility of this approach by creating new algorithms for random graphs with varying densities. Our resulting clique algorithms are extremely simple, yet signi cantly faster than the best approach found in the literature to date.

The vehicle routing problem (VRP) is one of the challenging problems in optimization and can be described as combinatorial optimization and NP-hard problem. Researchers have used many artificial intelligence techniques in order to try to solve this problem. Among these techniques, metaheuristic algorithms that can perform random search are the most promising because they can be used to find the right solution in the shortest possible time. Therefore, in this paper, the Harris hawks optimization (HHO) algorithm was used to attempt to solve the VRP. The algorithm was applied to 10 scenarios and the experimental results revealed that the HHO had a strong ability to check for and find the best route as compared to other metaheuristic algorithms, namely, simulated annealing and artificial bee colony optimization. The comparison was based on three criteria: minimum objective function obtained, minimum number of iterations required and satisfaction of capacity constraints. In all scenarios...

Trained Reward-based Action Classification Engine (TRACE) is a general process for capturing operator outcome data during metaheuristic search, training classifiers to predict whether an operator will yield an improved solution, and deploying those models to guide neighborhood selection during future search runs. This study introduces TRACE-VNS, a modular extension of General Variable Neighborhood Search (GVNS) applied to the Capacitated Vehicle Routing Problem (CVRP), where neighborhood selection is driven by these offline-trained models. Classifiers are trained on features extracted from GVNS traces, including action history, graph metrics, temporal state, and Upper Confidence Bound (UCB) indicators. Twelve classifiers, including tree ensembles, neural networks, and kernel-based models, are benchmarked using the Precision-Recall Area Under the Curve (PR-AUC) to evaluate predictive quality. Empirical results show that TRACE-VNS improves convergence speed and final solution quality over conventional GVNS across 84 CVRP instances. A detailed feature importance analysis identifies strong contributors, offering insights into the effective selection of operators. TRACE requires no runtime exploration or feedback loops and can generalize to other metaheuristics through minimal structural adaptation.

The ease and affordability offered by the cloud computing has attracted large number of customers towards it. Cloud service providers offer its services, to the cloud customers, usually in form of Virtual Machines (VMs). With the growth in the number of customers, cloud data centers encounter overwhelming number of VM requests. These requests need to be mapped on the real cloud hardware and therefore, VM placement has been an important research area in the cloud research community. Virtual machine placement, being an NP hard problem, is modelled as an optimization problem with the objective to optimize resource wastage. Dragonfly Algorithm (DA), a nature inspired technique, originates from static and dynamic swarming behavior of dragonfly and is well suited to solve VM placement problem. Therefore, in the proposed work, a modified dragonfly algorithm is applied for VM placement for better resource utilization at cloud data centers. The performance of the proposed model is analyzed through simulation and comparative study. Observations, obtained from the experiments, exhibit the superiority of the proposed model in solving VM placement problem. Binary dragonfly algorithm (BDA) • Virtual machine (VM) • Cloud data center (CDC) • Cloud service provider (CSP) • NP-hard problem • Resource utilization • Information technology (IT) * Deo Prakash Vidyarthi

Logistics and transportation issues have been receiving increasing attention during the last decades and their requirements have gradually changed, making it necessary to take into account new situations and conditions. The Double Traveling Salesman Problem with Multiple Stacks (DTSPMS) is a pickup and delivery problem in which some additional precedence and loading constraints are imposed on the vehicle to be used. In this paper we approach the problem using intermediate infeasible solutions to diversify the search process and we develop some fixing procedures and infeasibility measures to deal with this kind of solutions and take advantage of their potential.

The joint optimization of routing and loading operations is crucial to fully optimize the overall planning process in logistics, and as a result routing problems with side constraints are becoming more and more important during the last years. This paper approaches the design of optimal routes for pickup and delivery operations considering in addition some capacity and loading constraints on the vehicles to be used. It is focused on exploiting new ideas to deal with real life situations in which the customers are not uniformly distributed on the pickup or delivery regions of the problem. An adapted and effective heuristic based on a Variable Neighborhood Search framework using improved neighborhood structures is proposed and discussed. The algorithm is applied to several new sets of instances with special structures to better represent real life situations, providing computational results to evaluate its performance.

) have been proposed to work over different combinatorial problems. However, both MPPMX and ABC neither suffered from a very high computational time neither poor performance. Therefore, this work proposes a novel multiparent order crossover (MPOX) for solving several combinatorial optimization problems with reasonable amount of time. The MPOX extends the two-parent order crossover by modifying the recombination operator to recombine more than two parents and generates a new offspring. MPOX at first selects the crossover points and divides the parents into n substrings based on these points (where n is the number of parents). Then, MPOX copies a predefined number of elements from each parent into the offspring based on their order while checking the feasibility of the offspring. The performance of MPOX is tested on the traveling salesman problems and berth allocation problems, which are widely studied in the literature. Experimental results demonstrated that the MPOX significantly improves the OX in both problem domains and outperforms both ABC and MPPMX over the travelling salesman problem and the berth allocation problem with less computational time. These results indicate the effectiveness of MPOX over OX, ABC and MPPMX, and its capability for solving both problems.

In this paper, we consider a capacitated single-level dynamic lot-sizing problem with sequence-dependent setup costs and times that includes product substitution options. The model is motivated from a real-world production planning problem of a manufacturer of plastic sheets used as an interlayer in car windshields. We develop a mixed-integer programming (MIP) formulation of the problem and devise MIP-based Relax&Fix and Fix&Optimize heuristics. Unlike existing literature, we combine Fix&Optimize with a time decomposition. Also, we develop a specialized substitute decomposition and devise a computation budget allocation scheme for ensuring a uniform, efficient usage of computation time by decompositions and their subproblems. Computational experiments were performed on generated instances whose structure follows that of the considered practical application and which have rather tight production capacities. We found that a Fix&Optimize algorithm with an overlapping time decomposition yielded the best solutions. It outperformed the state-of-the-art approach Relax&Fix and all other tested algorithm variants on the considered class of instances, and returned feasible solutions with neither overtime nor backlogging for all instances. It returned solutions that were on average only 5% worse than those returned by a standard MIP solver after 4 hours and 19% better than those of Relax&Fix.

This paper introduces a parallel iterated tabu search heuristic for solving four different routing problems: the classical vehicle routing problem (VRP), the periodic VRP, the multi-depot VRP, and the site-dependent VRP. In addition, it is applicable to the time-window constrained variant of these problems. Using the iterated local search framework, the heuristic combines tabu search with a simple perturbation mechanism to ensure a broad exploration of the search space. We also describe a parallel implementation of the heuristic to take advantage of multiple-core processors. Extensive computational results show that the proposed heuristic outperforms tabu search alone and is competitive with recent heuristics designed for each particular problem.

This paper introduces a parallel iterated tabu search heuristic for solving four different routing problems: the classical vehicle routing problem (VRP), the periodic VRP, the multi-depot VRP, and the site-dependent VRP. In addition, it is applicable to the time-window constrained variant of these problems. Using the iterated local search framework, the heuristic combines tabu search with a simple perturbation mechanism to ensure a broad exploration of the search space. We also describe a parallel implementation of the heuristic to take advantage of multiple-core processors. Extensive computational results show that the proposed heuristic outperforms tabu search alone and is competitive with recent heuristics designed for each particular problem.

Human factor is one of the important elements in manufacturing world, despite their important role in improvement the production flow, they have been neglected while scheduling for many decades. In this paper the researchers taken the human factor throughout their job performance weightage into consideration while using job shop scheduling (JSS) for a factory of glass industry, in order to improving the workers' flexibility. In other hand, the researchers suggested a new sequence of workers' weightage by using Taguchi method, which present the best flexibility that workers can have, while decreasing the total time that the factory need to complete the whole production flow.

Resumo: Este artigo discute a implementação e avaliação de uma heurística baseada em Busca Tabu para otimizar uma rede de cadeia de suprimentos. Para tanto, o modelo single-source proposto por foi implementado. O problema foi resolvido por uma adaptação do método de , substituindo centros de distribuição (CDs) e arcos a fim de encontrar o menor custo para uma rede de cadeia de suprimentos. Foram resolvidas as 22 instâncias propostas por e os resultados indicam que, para esses cenários, o método aplicado teve um bom desempenho computacional, obtendo resultados com uma redução de 81,03% no tempo médio de processamento. Contudo, houve um aumento de 4,98% no custo médio das soluções obtido pelo método heurístico quando comparado com os resultados ótimos. Por fim, o problema foi resolvido para outras quatro instâncias com características reais, comprovando a eficiência da heurística para problemas de grande escala, visto que todas as soluções foram obtidas em menos de 2 minutos de processamento.

The fragment assembly problem consists in the building of the DNA sequence from several hundreds (or even, thousands) of fragments obtained by biologists in the laboratory. This is an important task in any genome project, since the accuracy of the rest of the phases depends of the result of this stage. In addition, real instances are very large and therefore, the efficiency is also a very important issue in the design of fragment assemblers. In this paper, we propose two Variable Neighborhood Search variants for solving the DNA fragment assembly problem. These algorithms are specifically adapted for the problem being the difference between them the optimization orientation (fitness function). One of them maximizes the Parsons's fitness function (which only considers the overlapping among the fragments) and the other estimates the variation in the number of contigs during a local search movement, in order to minimize the number of contigs. The results show that doesn't exist a direct relation between these functions (even in several cases opposite values are generated) although for the tested instances, both variants allow to find similar and very good results but the second option reduces significatively the consumed-time.

A particle swarm optimizer (PSO) loosely based on the phenomena of crystallization and a chaos factor which follows the complimentary error function is described. The method features three phases: diffusion, directed motion, and nucleation. During the diffusion phase random walk is the only contributor to particle motion. As the algorithm progresses the contribution from chaos decreases and movement toward global best locations is pursued until convergence has occurred. The algorithm was found to be more robust to local minima in multimodal test functions than a standard PSO algorithm and is designed for problems which feature experimental precision.

This study intends to develop the Emergency Medical Service Support System (EMSS) by incorporating Emergency Medical Service (EMS) data and trauma registry data recorded by the Khon Kaen Regional Hospital with the aid of GIS. Landmark, street networks and intersection's name incorporated into the developed digital map of Khon Kaen provide a means to help the dispatcher to identify and confirm the location of any accident sites from the receiving emergency calls. Consequently, from a well-prepared database system, using GIS capabilities can provide the appropriate route, the travel direction and information. Additionally, the accident severity derived from systematic medical data can be spatially monitored in the developed map. Using their spatial proprieties, the black spot locations are automatically identified as well. Finally, to assist those who are not familiar with the GIS software, a customized graphical interface is provided in this developed EMSS for the accessibility o...

As minhas conquistas, nem só por mim me são direito. Existem pessoas fundamentais, sem as quais eu não teria finalizado a minha jornada para me tornar um Mestre em Matemática. Devo agradecer primeiramente aos meus pais, José Fernandes e Francisca Dayse, que mesmo com toda a dificultade decorrente de ter um filho longe de casa, ficaram muito felizes, me apoiaram e me incentivaram a todo momento, do início ao fim desse mestrado. Quando me via em meio a solidão e confusões mentais, eles não me deixavam parar. Mesmo quado eu pensei que tudo estava indo por água abaixo, eles me diziam para tentar. Por isso e muito mais, sou eternamente grato à eles. Também sou grato à meu orientador, carinhosamente conhecido no IMECC como professor Chico. O que dizer de uma pessoa, que mesmo sem cobrar explicações sobre suas dificuldades -sejam financeiras, emocionais ou familiares -, nunca lhe virou as costas quando você o procurou pedindo ajuda? Assim foi o meu orientador, professor Francisco de Assis Magalhães, o qual passei a admirar não só profissionalmente, mas também, como pessoa. Um dia espero ter condições de recebê-lo para passar uns dias com sua família em minha cidade. Sou realmente muito grato por sua paciência e ajuda. Alguns amigos importantes saberão que têm toda minha gratidão. Agradeço pelas conversas, pelo tempo passado juntos, pelos conselhos e incentivos. Por nos reunirmos para almoçar ou jantar e pelos momentos divertidos. Viver em Campinas teria sido ainda mais complicado sem eles. Por fim, sou grato ao CNPq, pela colaboração de dois anos com a bolsa de mestrado. O Problema do Caixeiro Viajante tem sido objeto de estudo desde o início do século XIX, mantendo-se como um amplo ramo de pesquisa até hoje, tendo em vista o forte impacto do transporte no comércio mundial. Essa dissertação contém algumas variações desse problema, bem como técnicas para obtenção de sua solução. Como destaque, é apresentado o Problema do Caixeiro Viajante com Coleta de Prêmios e Janelas de Tempo, no qual a função objetivo relaciona custos, penalidades por clientes não atendidos e prêmios por clientes atendidos, os quais devem ser visitados dentro de suas respectivas janelas de tempo. GENIUS é a principal heurística utilizada para obtenção de solução inicial do problema em destaque, e a meta-heurística VNS é responsável pelo refinamento da solução inicial. Para o algoritmo que implementamos, são apresentados vários resultados numéricos.

The vehicle routing problem with multiple trips (V RP MT ) is a variants of the standard (V RP ), where each vehicle can be used more than once during the working period. For this NP-Hard problem, we propose a variable neighborhood search Algorithm in which four neighborhood structure are designed to find the planning of trips. The algorithm was tested over a set of benchmark problems and the obtained solutions were compared with five previously proposed algorithms. Encouraging results are obtained.

In MDVCSP, we deal with two NP-hard problems in an integrated way: the multiple-depot vehicle scheduling problem (MDVSP) and the crew scheduling problem (CSP). For solving the MDVCSP, we define the vehicles' operational routine and the workdays of the crews of a public bus transport system with multiple depots. Given the difficulty of solving real-world instances of the MDVCSP using exact mathematical methods, we propose a matheuristic algorithm for solving it. This matheuristic algorithm combines two strategies into an iterated local search (ILS) based framework: a branch-and-bound algorithm for solving the MDVSP and a variable neighborhood descent (VND) based algorithm for treating the associated CSPs. We compared the proposed ILS-MDVCSP with five approaches in the literature that use the same benchmark test instances. We also solved a real-world problem of one of Brazil's largest cities. For this problem, we proposed a formulation based on a time-space network to address the MDVSP subproblem. The results obtained showed the effectiveness of ILS-MDVCSP, mainly to deal with real-world and large-scale problems. The algorithm was able to solve the largest instances from the literature, for which there was no reported solution. Regarding the run time, as the instances' size increases, our approach becomes substantially less costly than the others from the literature. For the Brazilian instances, the ILS-MDVCSP saved, on average, the use of 12 vehicles per day and reduced by up to 15% the daily operational time of the vehicles. INDEX TERMS Iterated local search, matheuristic, multiple-depot vehicle and crew scheduling, public transportation, time-space network, variable neighborhood descent.

Effective computational methods are important for practitioners and researchers working in strategic underground mine planning. We consider a class of problems that can be modeled as a variant of the resource-constrained project scheduling problem with optional activities (or jobs) and generalized precedence constraints; the objective maximizes net present value. We provide a computational review of math programming and constraint programming, describe and implement novel problem-size reductions, and develop linear programmingand constraint programming-based hybrid techniques to significantly expand the number of computationally tractable problem instances. We analyze the efficacy of the methods applied to instances both from the literature and derived from real-world mines. These practical, large-scale planning problems cannot even be processed using standard optimization approaches. However, our reduction and hybrid strategies allow us to solve them to within less than 5% of optim...

In this paper, we extend and integrate previously reported techniques for resource constrained scheduling to develop a CSP procedure for solving RCPSP/max, the resource constrained project scheduling problem with time windows (generalized precedence relations between start time of activities). RCPSP/max is a well-studied problem within the Operations Research community and the presence of a large set of benchmark problems provides a good opportunity for comparative performance analysis. Our base CSP scheduling model generalizes previous profile-based approaches to cumulative scheduling by focusing on global analysis of minimal conflicting sets rather than pairwise conflict analysis. This generalization increases the tendency for more effective conflict resolution. Since RCPSP/max is an optimization problem, other ideas from prior work are adapted to embed this base CSP model within a multi-pass, iterative sampling procedure. The overall procedure, called ISES (Iterative Sampling Earliest Solutions), is applied to the above mentioned set of benchmark problems. ISES is shown to perform quite well in comparison to current state-of-the-art procedures for RCPSP/max, particularly as search space size becomes limiting for systematic procedures.

In this paper a variable neighborhood search approach as a method for solving combinatory optimization problems is presented. A variable neighborhood search based algorithm for solving the problem concerning the university course timetable design has been developed. This algorithm is used to solve the real problem regarding the university course timetable design. It is compared with other algorithms that are tested on the same sets of input data. The object and the methodology of study are presented. The main objectives of the experiment are formulated. The conditions for conducting the experiment are specified. The results are analyzed and appropriate conclusions are made. The future trends of work in this field are presented.

In this paper a variable neighborhood search approach as a method for solving combinatory optimization problems is presented. A variable neighborhood search based algorithm for solving the problem concerning the university course timetable design has been developed. This algorithm is used to solve the real problem regarding the university course timetable design. It is compared with other algorithms that are tested on the same sets of input data. The object and the methodology of study are presented. The main objectives of the experiment are formulated. The conditions for conducting the experiment are specified. The results are analyzed and appropriate conclusions are made. The future trends of work in this field are presented.

One purpose of this article is to refute some commonly held ideas which consider that ongoing changes in work and employment are inevitable and they have positive consequences at the social and individual level. It is subjacent on approach considering that there is no single striking trend while there are alternatives deserving discussion.

One purpose of this article is to refute some commonly held ideas which consider that ongoing changes in work and employment are inevitable and they have positive consequences at the social and individual level. It is subjacent on approach considering that there is no single striking trend while there are alternatives deserving discussion. The paper starts with analysis on the

In this paper, we study home healthcare routing and scheduling problem where multiple hospitals serve patients. In the public hospitals in healthcare system of Türkiye, patients requiring home healthcare are assigned to the hospital that serves their place of residence. This can cause the workload of hospitals to become unbalanced in terms of the time needed for both traveling and operation. The aim of this paper is to generate routes with a balanced workload for hospitals, giving consideration to the time windows of patients and the working hours of health workers. Firstly, we construct a mathematical model which can solve toy and small-scale problems whilst taking into account the importance of a balanced workload. Then, a Tabu Search with a Variable Neighborhood Search (TS-VNS) algorithm is developed to solve large-scale problems. The performance of the TS-VNS algorithm is tested by comparing the results of the mathematical model with the generated test problems at a small scale....

The paper discusses a containers' drayage by trucks, which is motivated by a real-life application arising in the intermodal freight transportation. This problem considers not only classical assumptions of the intermodal transportation, but also introduces the availability of containers as a new concept. For this purpose, we first describe the industrial context and provide the mathematical optimization model which combines a set of known and new constraints. We then propose a solution approach based on variable neighborhood search algorithm combined with pairing and insertion heuristics, as well as with variable neighborhood descent and tabu search methods. Optimization has then been embedded into a simulation model which designs the rail/ road terminal. To be more specific, this optimization model can be used to evaluate several distribution policies, which results in a set of routing decisions and can adopt the best policy in a distribution network with competing rail and road transport services. Finally, we test the proposed model on real and generated instances characterizing several scenarios to highlight the performance and efficiency of our approach.

Computational protein design (CPD) aims to predict amino acid sequences that fold to specific structures and perform desired functions. CPD depends on a rotamer library, an energy function, and an algorithm to search the sequence/conformation space. Variable neighborhood search (VNS) with cost function networks is a powerful framework that can provide tight upper bounds on the global minimum energy. We propose a new CPD heuristic based on VNS in which a subset of the solution space (a "neighborhood") is explored, whose size is gradually increased with a dedicated probabilistic heuristic. The algorithm was tested on 99 protein designs with fixed backbones involving nine proteins from the SH2, SH3, and PDZ families. The number of mutating positions was 20, 30, or all of the amino acids, while the rest of the protein explored side-chain rotamers. VNS was more successful than Monte Carlo (MC), replica-exchange MC, and a heuristic steepest-descent energy minimization, providing solutions with equal or lower best energies in most cases. For complete protein redesign, it gave solutions that were 2.5 to 11.2 kcal/mol lower in energy than those obtained with the other approaches. VNS is implemented in the toulbar2 software. It could be very helpful for large and/or complex design problems.

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is one of the variants of the Vehicle Routing Problem (VRP), which is the problem of determining the optimal route from the depot to the consumer which is located spread out with different requests. In CVRPTW problem solving considers capacity and time constraints. Determining the optimal route can reduce costs and energy spent during the distribution process. The General Variable Neighborhood Search (GVNS) algorithm can be applied to the CVRPTW problem. The GVNS algorithm is an improvement on the VNS algorithm using RVND. The GVNS algorithm starts with finding the initial solution, continues with perturbation, and then the repair procedure is carried out. Perturbation and improvements to the GVNS algorithm are performed repeatedly according to the predetermined IterMax. The GVNS algorithm for CVRPTW will be implemented using the Borland Delphi 7.0 programming language. The product in the form of this application can be used more practically to solve CVRPTW problems using the GVNS algorithm.

Previously, we hypothesized that overfitting occurs in the brain networks of the patients with autism. In this study, we implement this idea in an artificial neural network (ANN). A set of tasks, named configural grouping tests, used by Mottron and colleagues in 2003, were picked out to be applied on a typical ANN which we designed. The visual stimuli were fed as the input; over time, the output error was monitored to evaluate the generalization capability of the network. The ANN training results of 6 letters were represented and the over-fitting was observed in all of them. In the learning process, before over-fitting (over learning) occurrence, testing error diagram decreases with decay in training error which indicates that ANN was trained well. This condition simulates the behavior of a healthy person. By continuing the learning process, testing error begins to increase and over-fitting occurs in the ANN, i.e. the generalization capability of the network decreases which simulate...

Analyzing microarray data could help discover significant cancer genes and their mutual interactions, which can be used to generate hypothesis for the identification and validation of genetic biomarkers. However, the commonly used statistical significance analysis can only provide information of individual genes, thus neglecting influence of the mutual interactions. Therefore, methods aiming at discovering combinational gene signatures are highly valuable. In this paper, an integrated approach of support vector machine (SVM) and variable neighborhood search (VNS) is introduced in searching the gene signatures for predicting histologic response of chemotherapy on osteosarcoma patients. Cross validation results show that this method outperforms other existing algorithms. Further validation with the test dataset shows that only one of the fourteen samples is misclassified. The high testing accuracy further suggests that the proposed method has capability of extracting the stable discriminative signatures from microarray data. Terms-support vector machine, variable neighborhood search, osteosarcoma, gene signatures. Microarray chip can simultaneously interrogate thousands of genes, which provides an extremely powerful tool for genomic studies of cancer. A few key genes (typically involving oncogenes and tumor suppressor genes), when mutated, will cause dysregulation of the transcription and translation of other genes through complicated signaling pathways to initiate oncogenesis, and ultimately leading to derangement of the cellular phenotype and the clinical manifestations of cancer. Analyzing microarray data could help discover some significant cancer genes and their mutual interactions, which can be used to generate hypothesis for the identification and validation of genetic biomarkers for diagnostic and therapeutic purposes . This approach has

The routes in the health industry will be optimized and the transport, storage and labor costs will be reduced with the implementation of the Vehicle Routing Problem (VRP), which can be applied to many areas of health industry, which has the time constraint as the major limitation. The Vehicle Routing Problem (VRP) is the process of creating appropriate routes to meet the needs of customers or service buyers at the fastest and lowest cost. In the study, it is aimed to provide a solution to the problem of transporting dialysis patients from their residence to dialysis units. In this regard, the total distance traveled in the transport of dialysis patients was minimized by using VRP solution methods. For the solution to the problem, a web-based visual software was developed using the kNN (k-nearest neighbor) algorithm, which is one of the intuitive solution algorithms. It was found that the routes created with the developed software are shorter than the current routes, that the cost of patient transportation is reduced, the map-supported route will guide the service driver, and that the labor force is saved and the quality of service is improved thanks to the faster transportation of the patients.

This study presents the design and integration of novel adaptive components within the Double-Adaptive General Variable Neighborhood Search (DA-GVNS) algorithm, aimed at improving its overall efficiency. These adaptations utilize iteration-based data to refine the search process, with enhancements such as an adaptive reordering mechanism in the refinement phase and a knowledge-guided approach to adjust the search strategy. Additionally, an adaptive mechanism for dynamically controlling the shaking intensity was introduced. The proposed knowledge-guided adaptations demonstrated superior performance over the original DA-GVNS framework, with the most effective scheme selected for further evaluation. Initially, the symmetric Traveling Salesman Problem (TSP) was used as a benchmark to quantify the impact of these mechanisms, showing significant improvements through rigorous statistical analysis. A comparative study was then conducted against six advanced heuristics from the literature. Finally, the most promising knowledge-guided GVNS (KG-GVNS) was tested against the original DA-GVNS on selected instances of the Quadratic Assignment Problem (QAP), where detailed statistical analysis highlighted its competitive advantage and robustness in addressing complex combinatorial optimization problems.

The Capacitated Team Orienteering Problem (CTOP) is a variant of the well-known Team Orienteering Problem where additional capacity limitation constraints are considered for each vehicle. Solving CTOP consists of organizing a set of routes that maximize the total profit collected from the served customers while taking into consideration the capacity and travel time limitation for each vehicle. In this paper, we propose a variable space search heuristic to solve CTOP. Our algorithm alternates between two search spaces: the giant tour and routes search spaces. We develop a hybrid heuristic as a framework for our algorithm composed of a combination between Greedy Randomized Adaptive Search Procedure and Evolutionary Local Search. Several local search techniques were developed in each search space to improve the quality of the solutions and the giant tours. A dedicated optimal split procedure and a concatenation technique are performed to ensure the link between the search spaces. This approach shows its high performance on the benchmark of CTOP, and proves its competitiveness in comparison to the other heuristic methods available in the literature as it yields to strict improvements with small computational time.

Je dédie ce modeste travail À la mémoire de mon grand-père Mohamed, À la mémoire de ma grand-mère Khadija, À la mémoire de mon oncle Taoufik, À la mémoire de mon ami et collègue Malek, À ma chère soeur Myriam et son époux Khaled, À mon cher frère Ahmed et son épouse Sarah, À mes petits neuveux Mohamed Yassine et Amine, À mes tantes Hedia,

A significant portion of the total cost of the intermodal transportation is generated from the inland transportation of containers. In this paper, we design a mixed integer linear programming (MILP) model for combining orders in the inland, haulage transportation of containers. The pickup and delivery process of both 20 and 40 foot containers from the terminals to the customer locations and vice versa are optimized using heterogeneous fleet consisting of both 20 ft and 40 ft trucks/chasses. Important operational constraints such as the time window at order receivers, the payload weight of containers and the regulation of the working hours are considered. Based on an assignment problem structure, this MILP solves efficiently to optimality for problems with up to 120 orders. To deal with larger instances, a decomposition and aggregation heuristic is designed. The basic idea of this approach is to decompose order locations geographically into fan-shaped subareas based on the angle of the order location to the port baseline, and solve the sub problems using the proposed MILP model. To balance the fleet size amongst all subgroups, column generation is used to iteratively adjust the number of allocated trucks according to the shadowprice of each truck type. Based on decomposed solutions, orders that are "fully" combined with others are removed and an aggregation phase follows to enable wider combination choices across subgroups. The decomposition and aggregation solution process is tested to be both efficient and cost-saving.

The k-means problem is one of the most popular models in cluster analysis that minimizes the sum of the squared distances from clustered objects to the sought cluster centers (centroids). The simplicity of its algorithmic implementation encourages researchers to apply it in a variety of engineering and scientific branches. Nevertheless, the problem is proven to be NP-hard which makes exact algorithms inapplicable for large scale problems, and the simplest and most popular algorithms result in very poor values of the squared distances sum. If a problem must be solved within a limited time with the maximum accuracy, which would be difficult to improve using known methods without increasing computational costs, the variable neighborhood search (VNS) algorithms, which search in randomized neighborhoods formed by the application of greedy agglomerative procedures, are competitive. In this article, we investigate the influence of the most important parameter of such neighborhoods on the c...

An algorithm known as Simulated Annealing (SA) for Random Traveling Salesman Problem (RTSP) is presented in this paper. The computational SA model constructed is based on the simulating process of slow cooling of molten metal to achieve the minimum function value in a minimization problem. Random Traveling Salesman Problem (RTSP) is a variant of TSP. All TSP dataset used here are constructed randomly. And then SA model is applied on all those data sets. Experimental results are discussed based on various characteristics like time, quality and accuracy.

This paper presents an original hybrid approach to solve the Capacitated Vehicle Routing Problem (CVRP). The approach combines a Probabilistic Algorithm with Constraint Programming (CP) and Lagrangian Relaxation (LR). After introducing the CVRP and reviewing the existing literature on the topic, the paper proposes an approach based on a probabilistic Variable Neighbourhood Search (VNS) algorithm. Given a CVRP instance, this algorithm uses a randomized version of the classical Clarke and Wright Savings constructive heuristic to generate a starting solution. This starting solution is then improved through a local search process which combines: (a) LR to optimise each individual route, and (b) CP to quickly verify the feasibility of new proposed solutions. The efficiency of our approach is analysed after testing some well-known CVRP benchmarks. Benefits of our hybrid approach over already existing approaches are also discussed. In particular, the potential flexibility of our methodology is highlighted.

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Specifically, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimisation model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimisation model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most efficient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.