Hybrid Meta-heuristics with VNS and Exact Methods: Application to Large Unconditional and Conditional Vertex p-Centre Problems

Large-scale unconditional and conditional vertex p-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with p varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex p-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems

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

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

The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field

The localized normal-score ensemble Kalman filter (NS-EnKF) coupled with covariance inflation is used to characterize the spatial variability of a channelized bimodal hydraulic conductivity field, for which the only existing prior information about conductivity is its univariate marginal distribution. We demonstrate that we can retrieve the main patterns of the reference field by assimilating a sufficient number of piezometric observations using the NS-EnKF. The possibility of characterizing the conductivity spatial variability using only piezometric head data shows the importance of accounting for these data in inverse modeling.The first author acknowledges the financial support from the China Scholarship Council (CSC). Financial support to carry out this work was also received from the Spanish Ministry of Science and Innovation through project CGL2011-23295.Xu, T.; Gómez-Hernández, JJ.; Zhou, H.; Li, L. (2013). The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field. Advances in Water Resources. 54:100-118. https://doi.org/10.1016/j.advwatres.2013.01.006S1001185

Simultaneous identification of a contaminant source and hydraulic conductivity via the restart normal-score ensemble Kalman filter

[EN] Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known.Financial support to carry out this work was received from the Spanish Ministry of Economy and Competitiveness through project CGL2014-59841-P. The authors acknowledge the Associate Editor, and the anonymous reviewers for their thoughtful and constructive comments.Xu, T.; Gómez-Hernández, JJ. (2018). Simultaneous identification of a contaminant source and hydraulic conductivity via the restart normal-score ensemble Kalman filter. Advances in Water Resources. 112:106-123. https://doi.org/10.1016/j.advwatres.2017.12.011S10612311

The continuous single source location problem with capacity and zone-dependent fixed cost: Models and solution approaches

The continuous capacitated single-source multi-facility Weber problem with the presence of facility fixed cost is investigated. A new mathematical model which incorporates multi-level type capacity (or design) and facility fixed cost that is capacity-based and zone-dependent is introduced. As no data set exists for this new location problem, a new data set based on convex polygons using triangular shape is constructed. A generalised two stage heuristic scheme that combines the concept of aggregation, an exact method, and an enhanced Cooper’s alternate location-allocation method is put forward. A framework that embeds Variable Neighbourhood Search is also proposed. Computational experiments show that these matheuristics produce encouraging results for this class of location problems. The proposed approaches are also easily adapted to cater for a recently studied variant namely the single-source capacitated multi-facility Weber problem where they outperform those recently published solution method

Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities

In this paper, the multi-product facility location problem in a two-stage supply chain is investigated. In this problem, the locations of depots (distribution centres) need to be determined along with their corresponding capacities. Moreover, the product flows from the plants to depots and onto customers must also be optimised. Here, plants have a production limit whereas potential depots have several possible capacity levels to choose from, which are defined as multilevel capacities. Plants must serve customer demands via depots. Two integer linear programming (ILP) models are introduced to solve the problem in order to minimise the fixed costs of opening depots and transportation costs. In the first model, the depot capacity is based on the maximum number of each product that can be stored whereas in the second one, the capacity is determined by the size (volume) of the depot. For large problems, the models are very difficult to solve using an exact method. Therefore, a matheuristic approach based on an aggregation approach and an exact method (ILP) is proposed in order to solve such problems. The methods are assessed using randomly generated data sets and existing data sets taken from the literature. The solutions obtained from the computational study confirm the effectiveness of the proposed matheuristic approach which outperforms the exact method. In addition, a case study arising from the wind energy sector in the UK is presented

A novel cash-plus intervention to safeguard sexual reproductive health and HIV vulnerabilities in young women in Cape Town, South Africa

Background Cash plus interventions augment cash transfers with other empowering interventions to influence behaviours. This research assesses the Women of Worth (WoW) program and evaluates the effectiveness of a cash transfer (CT) of ZAR300 ($22USD22) conditional on attending 12-session customised empowerment interventions to improve SRH/HIV outcomes in young women (19-24yrs) in Cape Town, South Africa. Methods A multiphase, mixed-methods, experimental study targeting 10 000 Participants in two subdistricts was conducted. Participants were randomised 1:1 to receive the interventions with CT ("cash + care" or C+C) or without CT (“Care”). Phase 1a piloted the interventions, Phase 1b implemented an adapted intervention, and Phase 2 was an open label C+C only scale up demonstration phase. Logistic regression models were fitted with subject-specific random mixed effects, to estimate changes in self-reported HIV, behavioural and structural SRH risks from baseline to (a) end of WoW and (b) follow up (6-30months post-exposure) irrespective of WoW completion. Mixed research methods were used to optimise engagement, evaluate implementation fidelity and determine the pathways of effectiveness for the interventions. Results The Women of Worth empowerment programme was implemented with adequate fidelity however adaptative research methods were essential for ensuring a sustained programme. 8765 (87,7%) of the 9995 WoW initiators were evaluated with 904 (10,3%); 4212 (48,1%) and 3649 (41,6%) women in Phases 1a, 1b and 2 respectively. In Phase 1a & 1b, participants in the “C+C” group were 60 times (OR 60.37; 95%CI: 17.32; 210.50.