Solving the bi-objective capacitated p -median problem with multilevel capacities using compromise programming and VNS

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.A bi‐objective optimisation using a compromise programming (CP) approach is proposed for the capacitated p‐median problem (CPMP) in the presence of the fixed cost of opening facility and several possible capacities that can be used by potential facilities. As the sum of distances between customers and their facilities and the total fixed cost for opening facilities are important aspects, the model is proposed to deal with those conflicting objectives. We develop a mathematical model using integer linear programming (ILP) to determine the optimal location of open facilities with their optimal capacity. Two approaches are designed to deal with the bi‐objective CPMP, namely CP with an exact method and with a variable neighbourhood search (VNS) based matheuristic. New sets of generated instances are used to evaluate the performance of the proposed approaches. The computational experiments show that the proposed approaches produce interesting results

A simulation-based optimisation for the stochastic green capacitated p-median problem

Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem. Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature. Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations). Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulationPeer Reviewe

Models and Matheuristics for Large-Scale Combinatorial Optimization Problems

Combinatorial optimization deals with efficiently determining an optimal (or at least a good) decision among a finite set of alternatives. In business administration, such combinatorial optimization problems arise in, e.g., portfolio selection, project management, data analysis, and logistics. These optimization problems have in common that the set of alternatives becomes very large as the problem size increases, and therefore an exhaustive search of all alternatives may require a prohibitively long computation time. Moreover, due to their combinatorial nature no closed-form solutions to these problems exist. In practice, a common approach to tackle combinatorial optimization problems is to formulate them as mathematical models and to solve them using a mathematical programming solver (cf., e.g., Bixby et al. 1999, Achterberg et al. 2020). For small-scale problem instances, the mathematical models comprise a manageable number of variables and constraints such that mathematical programming solvers are able to devise optimal solutions within a reasonable computation time. For large-scale problem instances, the number of variables and constraints becomes very large which extends the computation time required to find an optimal solution considerably. Therefore, despite the continuously improving performance of mathematical programming solvers and computing hardware, the availability of mathematical models that are efficient in terms of the number of variables and constraints used is of crucial importance. Another frequently used approach to address combinatorial optimization problems are matheuristics. Matheuristics decompose the considered optimization problem into subproblems, which are then formulated as mathematical models and solved with the help of a mathematical programming solver. Matheuristics are particularly suitable for situations where it is required to find a good, but not necessarily an optimal solution within a short computation time, since the speed of the solution process can be controlled by choosing an appropriate size of the subproblems. This thesis consists of three papers on large-scale combinatorial optimization problems. We consider a portfolio optimization problem in finance, a scheduling problem in project management, and a clustering problem in data analysis. For these problems, we present novel mathematical models that require a relatively small number of variables and constraints, and we develop matheuristics that are based on novel problem-decomposition strategies. In extensive computational experiments, the proposed models and matheuristics performed favorably compared to state-of-the-art models and solution approaches from the literature. In the first paper, we consider the problem of determining a portfolio for an enhanced index-tracking fund. Enhanced index-tracking funds aim to replicate the returns of a particular financial stock-market index as closely as possible while outperforming that index by a small positive excess return. Additionally, we consider various real-life constraints that may be imposed by investors, stock exchanges, or investment guidelines. Since enhanced index-tracking funds are particularly attractive to investors if the index comprises a large number of stocks and thus is well diversified, it is of particular interest to tackle large-scale problem instances. For this problem, we present two matheuristics that consist of a novel construction matheuristic, and two different improvement matheuristics that are based on the concepts of local branching (cf. Fischetti and Lodi 2003) and iterated greedy heuristics (cf., e.g., Ruiz and Stützle 2007). Moreover, both matheuristics are based on a novel mathematical model for which we provide insights that allow to remove numerous redundant variables and constraints. We tested both matheuristics in a computational experiment on problem instances that are based on large stock-market indices with up to 9,427 constituents. It turns out that our matheuristics yield better portfolios than benchmark approaches in terms of out-of-sample risk-return characteristics. In the second paper, we consider the problem of scheduling a set of precedence-related project activities, each of which requiring some time and scarce resources during their execution. For each activity, alternative execution modes are given, which differ in the duration and the resource requirements of the activity. Sought is a start time and an execution mode for each activity, such that all precedence relationships are respected, the required amount of each resource does not exceed its prescribed capacity, and the project makespan is minimized. For this problem, we present two novel mathematical models, in which the number of variables remains constant when the range of the activities' durations and thus also the planning horizon is increased. Moreover, we enhance the performance of the proposed mathematical models by eliminating some symmetric solutions from the search space and by adding some redundant sequencing constraints for activities that cannot be processed in parallel. In a computational experiment based on instances consisting of activities with durations ranging from one up to 260 time units, the proposed models consistently outperformed all reference models from the literature. In the third paper, we consider the problem of grouping similar objects into clusters, where the similarity between a pair of objects is determined by a distance measure based on some features of the objects. In addition, we consider constraints that impose a maximum capacity for the clusters, since the size of the clusters is often restricted in practical clustering applications. Furthermore, practical clustering applications are often characterized by a very large number of objects to be clustered. For this reason, we present a matheuristic based on novel problem-decomposition strategies that are specifically designed for large-scale problem instances. The proposed matheuristic comprises two phases. In the first phase, we decompose the considered problem into a series of generalized assignment problems, and in the second phase, we decompose the problem into subproblems that comprise groups of clusters only. In a computational experiment, we tested the proposed matheuristic on problem instances with up to 498,378 objects. The proposed matheuristic consistently outperformed the state-of-the-art approach on medium- and large-scale instances, while matching the performance for small-scale instances. Although we considered three specific optimization problems in this thesis, the proposed models and matheuristics can be adapted to related optimization problems with only minor modifications. Examples for such related optimization problems are the UCITS-constrained index-tracking problem (cf, e.g., Strub and Trautmann 2019), which consists of determining the portfolio of an investment fund that must comply with regulatory restrictions imposed by the European Union, the multi-site resource-constrained project scheduling problem (cf., e.g., Laurent et al. 2017), which comprises the scheduling of a set of project activities that can be executed at alternative sites, or constrained clustering problems with must-link and cannot-link constraints (cf., e.g., González-Almagro et al. 2020)

A Multi-objective Harmony Search Algorithm for Optimal Energy and Environmental Refurbishment at District Level Scale

Nowadays municipalities are facing an increasing commitment regarding the energy and environmental performance of cities and districts. The multiple factors that characterize a district scenario, such as: refurbishment strategies’ selection, combination of passive, active and control measures, the surface to be refurbished and the generation systems to be substituted will highly influence the final impacts of the refurbishment solution. In order to answer this increasing demand and consider all above-mentioned district factors, municipalities need optimisation methods supporting the decision making process at district level scale when defining cost-effective refurbishment scenarios. Furthermore, the optimisation process should enable the evaluation of feasible solutions at district scale taking into account that each district and building has specific boundaries and barriers. Considering these needs, this paper presents a multi-objective approach allowing a simultaneous environmental and economic assessment of refurbishment scenarios at district scale. With the aim at demonstrating the effectiveness of the proposed approach, a real scenario of Gros district in the city of Donostia-San Sebastian (North of Spain) is presented. After analysing the baseline scenario in terms of energy performance, environmental and economic impacts, the multi-objective Harmony Search algorithm has been employed to assess the goal of reducing the environmental impacts in terms of Global Warming Potential (GWP) and minimizing the investment cost obtaining the best ranking of economic and environmental refurbishment scenarios for the Gros district.OptEEmAL project, Grant Agreement Number 68067

Automatic Domain Decomposition in Finite Element Method – A Comparative Study

In this paper, an automatic data clustering approach is presented using some concepts of the graph theory. Some Cluster Validity Index (CVI) is mentioned, and DB Index is defined as the objective function of meta-heuristic algorithms. Six Finite Element meshes are decomposed containing two- and three- dimensional types that comprise simple and complex meshes. Six meta-heuristic algorithms are utilized to determine the optimal number of clusters and minimize the decomposition problem. Finally, corresponding statistical results are compared

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

Iterative restricted space search : a solving approach based on hybridization

Face à la complexité qui caractérise les problèmes d'optimisation de grande taille l'exploration complète de l'espace des solutions devient rapidement un objectif inaccessible. En effet, à mesure que la taille des problèmes augmente, des méthodes de solution de plus en plus sophistiquées sont exigées afin d'assurer un certain niveau d 'efficacité. Ceci a amené une grande partie de la communauté scientifique vers le développement d'outils spécifiques pour la résolution de problèmes de grande taille tels que les méthodes hybrides. Cependant, malgré les efforts consentis dans le développement d'approches hybrides, la majorité des travaux se sont concentrés sur l'adaptation de deux ou plusieurs méthodes spécifiques, en compensant les points faibles des unes par les points forts des autres ou bien en les adaptant afin de collaborer ensemble. Au meilleur de notre connaissance, aucun travail à date n'à été effectué pour développer un cadre conceptuel pour la résolution efficace de problèmes d'optimisation de grande taille, qui soit à la fois flexible, basé sur l'échange d'information et indépendant des méthodes qui le composent. L'objectif de cette thèse est d'explorer cette avenue de recherche en proposant un cadre conceptuel pour les méthodes hybrides, intitulé la recherche itérative de l'espace restreint, ±Iterative Restricted Space Search (IRSS)>>, dont, la principale idée est la définition et l'exploration successives de régions restreintes de l'espace de solutions. Ces régions, qui contiennent de bonnes solutions et qui sont assez petites pour être complètement explorées, sont appelées espaces restreints "Restricted Spaces (RS)". Ainsi, l'IRSS est une approche de solution générique, basée sur l'interaction de deux phases algorithmiques ayant des objectifs complémentaires. La première phase consiste à identifier une région restreinte intéressante et la deuxième phase consiste à l'explorer. Le schéma hybride de l'approche de solution permet d'alterner entre les deux phases pour un nombre fixe d'itérations ou jusqu'à l'atteinte d'une certaine limite de temps. Les concepts clés associées au développement de ce cadre conceptuel et leur validation seront introduits et validés graduellement dans cette thèse. Ils sont présentés de manière à permettre au lecteur de comprendre les problèmes que nous avons rencontrés en cours de développement et comment les solutions ont été conçues et implémentées. À cette fin, la thèse a été divisée en quatre parties. La première est consacrée à la synthèse de l'état de l'art dans le domaine de recherche sur les méthodes hybrides. Elle présente les principales approches hybrides développées et leurs applications. Une brève description des approches utilisant le concept de restriction d'espace est aussi présentée dans cette partie. La deuxième partie présente les concepts clés de ce cadre conceptuel. Il s'agit du processus d'identification des régions restreintes et des deux phases de recherche. Ces concepts sont mis en oeuvre dans un schéma hybride heuristique et méthode exacte. L'approche a été appliquée à un problème d'ordonnancement avec deux niveaux de décision, relié au contexte des pâtes et papier: "Pulp Production Scheduling Problem". La troisième partie a permit d'approfondir les concepts développés et ajuster les limitations identifiées dans la deuxième partie, en proposant une recherche itérative appliquée pour l'exploration de RS de grande taille et une structure en arbre binaire pour l'exploration de plusieurs RS. Cette structure a l'avantage d'éviter l'exploration d 'un espace déjà exploré précédemment tout en assurant une diversification naturelle à la méthode. Cette extension de la méthode a été testée sur un problème de localisation et d'allocation en utilisant un schéma d'hybridation heuristique-exact de manière itérative. La quatrième partie généralise les concepts préalablement développés et conçoit un cadre général qui est flexible, indépendant des méthodes utilisées et basé sur un échange d'informations entre les phases. Ce cadre a l'avantage d'être général et pourrait être appliqué à une large gamme de problèmes

A Novel Grouping Harmony Search Algorithm for Clustering Problems

The problem of partitioning a data set into disjoint groups or clusters of related items plays a key role in data analytics, in particular when the information retrieval becomes crucial for further data analysis. In this context, clustering approaches aim at obtaining a good parti- tion of the data based on multiple criteria. One of the most challenging aspects of clustering techniques is the inference of the optimal number of clusters. In this regard, a number of clustering methods from the literature assume that the number of clusters is known a priori and sub- sequently assign instances to clusters based on distance, density or any other criterion. This paper proposes to override any prior assumption on the number of clusters or groups in the data at hand by hybridizing the grouping encoding strategy and the Harmony Search (HS) algorithm. The resulting hybrid approach optimally infers the number of clusters by means of the tailored design of the HS operators, which estimates this important structural clustering parameter as an implicit byproduct of the instance-to-cluster mapping performed by the algorithm. Apart from inferring the optimal number of clusters, simulation results ver- ify that the proposed scheme achieves a better performance than other na ̈ıve clustering techniques in synthetic scenarios and widely known data repositories