Smart grid topology designs

This paper addresses supports for evolving design demands of electricity low voltage networks in urban areas. Innovations in how electricity is generated and supplied are required to support transformation of energy systems in response to climate change. We describe a MIP model to support grid upgrade decisions in the context of an energy community in an existing urban setting. We evaluate the MIP model on an adaption of an IEEE radial network benchmark instance augmented with geographic data. We present interesting computational results which suggest additional arcs to be added. Our results highlight potential research opportunities for the network optimisation community to facilitate the desired energy systems transformation challenge.publishe

A hybrid heuristic for a stochastic production-inventory-routing problem

We consider a stochastic single item production-inventory-routing problem with a single producer and multiple clients. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented where the production and routing decisions are taken before the scenario is known, and the quantities to deliver to the clients and the inventory levels are adjustable to the scenario. Valid inequalities are introduced and a hybrid heuristic that combines ideas from the sample average approximation method and from relax-and-fix approaches is proposed. Preliminary tests based on randomly generated instances are reported showing that the hybrid heuristic performs better than the classical sample approximation algorithm for hard instances.publishe

A computational comparison of compact MILP formulations for the zero forcing number

Consider a graph where some of its vertices are colored. A colored vertex with a single uncolored neighbor forces that neighbor to become colored. A zero forcing set is a set of colored vertices that forces all vertices to become colored. The zero forcing number is the size of a minimum forcing set. Finding the minimum forcing set of a graph is NP-hard. We give a new compact mixed integer linear programming formulation (MILP) for this problem, and analyse this formulation and establish relation to an existing compact formulation and to two variants. In order to solve large size instances we propose a sequential search algorithm which can also be used as a heuristic to derive upper bounds for the zero forcing number. A computational study using Xpress (a MILP solver) is conducted to test the performances of the discussed compact formulations and the sequential search algorithm. We report results on cubic, Watts-Strogatz and randomly generated graphs with 10, 20 and 30 vertices.publishe

Lagrangian duality for robust problems with decomposable functions: the case of a robust inventory problem

We consider a class of min-max robust problems in which the functions that need to be “robustified” can be decomposed as the sum of arbitrary functions. This class of problems includes many practical problems, such as the lot-sizing problem under demand uncertainty. By considering a Lagrangian relaxation of the uncertainty set, we derive a tractable approximation, called the dual Lagrangian approach, that we relate with both the classical dualization approximation approach and an exact approach. Moreover, we show that the dual Lagrangian approach coincides with the affine decision rule approximation approach. The dual Lagrangian approach is applied to a lot-sizing problem, in which demands are assumed to be uncertain and to belong to the uncertainty set with a budget constraint for each time period. Using the insights provided by the interpretation of the Lagrangian multipliers as penalties in the proposed approach, two heuristic strategies, a new guided iterated local search heuristic, and a subgradient optimization method are designed to solve more complex lot-sizing problems in which additional practical aspects, such as setup costs, are considered. Computational results show the efficiency of the proposed heuristics that provide a good compromise between the quality of the robust solutions and the running time required in their computation.publishe

Comparing techniques for modelling uncertainty in a maritime inventory routing problem

Uncertainty is inherent in many planning situations. One example is in maritime transportation, where weather conditions and port occupancy are typically characterized by high levels of uncertainty. This paper considers a maritime inventory routing problem where travel times are uncertain. Taking into account possible delays in the travel times is of main importance to avoid inventory surplus or shortages at the storages located at ports. Several techniques to deal with uncertainty, namely deterministic models with inventory buffers; robust optimization; stochastic programming and models incorporating conditional value-at-risk measures, are considered. The different techniques are tested for their ability to deal with uncertain travel times for a single product maritime inventory routing problem with constant production and consumption rates, a fleet of heterogeneous vessels and multiple ports. At the ports, the product is either produced or consumed and stored in storages with limited capacity. We assume two-stages of decisions, where the routing, the visit order of the ports and the quantities to load/unload are first-stage decisions (fixed before the uncertainty is revealed), while the visit time and the inventory levels at ports are second-stage decisions (adjusted to the observed travel times). Several solution approaches resulting from the proposed techniques are considered. A computational comparison of the resulting solution approaches is performed to compare the routing costs, the amount of inventory bounds deviation, the total quantities loaded and unloaded, and the running times. This computational experiment is reported for a set of maritime instances having up to six ports and five ships.publishe

Compact mixed integer linear programming models to the Minimum Weighted Tree Reconstruction problem

The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in several areas, namely, the inference of phylogenetic trees, the modeling of traffic networks and the analysis of internet infrastructures. In this paper, we investigate the MWTR problem and we present two compact mixed-integer linear programming models to solve the problem. Computational results using two different sets of instances, one from the phylogenetic area and another from the telecommunications area, show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes

A decomposition approach for the p-median problem on disconnected graphs

The p-median problem seeks for the location of p facilities on the vertices (customers) of a graph to minimize the sum of transportation costs for satisfying the demands of the customers from the facilities. In many real applications of the p-median problem the underlying graph is disconnected. That is the case of p-median problem defined over split administrative regions or regions geographically apart (e.g. archipelagos), and the case of problems coming from industry such as the optimal diversity management problem. In such cases the problem can be decomposed into smaller p-median problems which are solved in each component k for different feasible values of pk, and the global solution is obtained by finding the best combination of pk medians. This approach has the advantage that it permits to solve larger instances since only the sizes of the connected components are important and not the size of the whole graph. However, since the optimal number of facilities to select from each component is not known, it is necessary to solve p-median problems for every feasible number of facilities on each component. In this paper we give a decomposition algorithm that uses a procedure to reduce the number of subproblems to solve. Computational tests on real instances of the optimal diversity management problem and on simulated instances are reported showing that the reduction of subproblems is significant, and that optimal solutions were found within reasonable time

The Effect of 5-HT1A Receptor Agonists on the Entopeduncular Nucleus is Modified in 6-Hydroxydopamine-Lesioned Rats

Background and Purpose l-DOPA prolonged treatment leads to disabling motor complications as dyskinesia that could be decreased by drugs acting on 5-HT1A receptors. Since the internal segment of the globus pallidus, homologous to the entopeduncular nucleus in rodents, seems to be involved in the etiopathology of l-DOPA-induced dyskinesia, we investigated whether the entopeduncular nucleus is modulated by the 5-HT1A receptor partial and full agonists, buspirone, and 8-hydroxy-2-(di-n-propylamino)-tetralin (8-OH-DPAT) in control and 6-hydroxydopamine (6-OHDA)-lesioned rats with or without long-term l-DOPA treatment. Experimental Approach Extracellular single-unit electrocorticogram and local field potential recordings under anaesthesia, immunostaining assays and optogenetic manipulation coupled to electrophysiological recordings were performed. Key Results Systemic buspirone reduced the entopeduncular nucleus firing rate in the sham animals and burst activity in the 6-OHDA-lesioned rats (with or without l-DOPA treatment), while local administration reduced entopeduncular nucleus activity in all the groups, regardless of DA integrity. Systemic 8-OH-DPAT also induced inhibitory effects only in the sham animals. Effects triggered by buspirone and 8-OH-DPAT were reversed by the 5-HT1A receptor antagonist, WAY-100635. Neither buspirone nor 8-OH-DPAT modified the low-frequency oscillatory activity in the entopeduncular nucleus or its synchronization with the motor cortex. Buspirone did not alter the response induced by subthalamic nucleus opto-stimulation in the entopeduncular nucleus. Conclusion and Implications Systemic 5-HT1A receptor activation elicits different effects on the electrophysiological properties of the entopeduncular nucleus depending on the integrity of the nigrostriatal pathway and it does not alter the relationship between subthalamic nucleus and entopeduncular nucleus neuron activity.Euskal Herriko Unibertsitatea, Grant/Award Number: GIU19/092; Basque Government, Grant/Award Numbers: PIBA 2019-38, T747-13; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: SAF2016-77758-R AEI/FEDER, U

6-Hydroxydopamine lesion and levodopa treatment modif y the effect of buspirone in the substantia nigra pars reticulata

Background and Purpose l-DOPA-induced dyskinesia (LID) is considered a major complication in the treatment of Parkinson's disease (PD). Buspirone (5-HT(1A)partial agonist) have shown promising results in the treatment of PD and LID, however no 5-HT-based treatment has been approved in PD. The present study was aimed to investigate how thesubstantia nigra pars reticulata(SNr) is affected by buspirone and whether it is a good target to study 5-HT antidyskinetic treatments. Experimental Approach Buspirone was studied usingin vivosingle-unit, electrocorticogram, local field potential recordings along with microdialysis and immunohistochemistry in naive/sham, 6-hydroxydopamine (6-OHDA)-lesioned or 6-OHDA-lesioned andl-DOPA-treated (6-OHDA/l-DOPA) rats. Key Results Local buspirone inhibited SNr neuron activity in all groups. However, systemic buspirone reduced burst activity in 6-OHDA-lesioned rats (with or withoutl-DOPA treatment), whereas 8-OH-DPAT, a full 5-HT(1A)agonist induced larger inhibitory effects in sham animals. Neither buspirone nor 8-OH-DPAT markedly modified the low-frequency oscillatory activity in the SNr or synchronization within the SNr with the cortex. In addition, local perfusion of buspirone increased GABA and glutamate release in the SNr of naive and 6-OHDA-lesioned rats but no effect in 6-OHDA/l-DOPA rats. In the 6-OHDA/l-DOPA group, increased 5-HT transporter and decreased 5-HT(1A)receptor expression was found. Conclusions and Implications The effects of buspirone in SNr are influenced by dopamine loss andl-DOPA treatment. The present results suggest that the regulation of burst activity of the SNr induced by DA loss may be a good target to test new drugs for the treatment of PD and LID.Eusko Jaurlaritza, Grant/Award Numbers: IT747-13, T747-13; Ministerio de Economia y Competitividad, Grant/Award Number: SAF2016-77758-

Genetic algorithm for the topological design of survivable optical transport networks

We develop a genetic algorithm for the topological design of survivable optical transport networks with minimum capital expenditure. Using the developed genetic algorithm we can obtain near-optimal topologies in a short time. The quality of the obtained solutions is assessed using an integer linear programming model. Two initial population generators, two selection methods, two crossover operators, and two population sizes are analyzed. Computational results obtained using real telecommunications networks show that by using an initial population that resembles real optical transport networks a good convergence is achieved