Integer Linear Formulation Research Articles

MOCA: Multiobjective Cell Association for Device-to-Device Communications

It is widely accepted that device-to-device (D2D) communication is envisaged to become the key enabler of direct localized communication between mobile nodes in future wireless networks. However, little attention has been paid to an important aspect that can potentially affect both the performance of D2D and cellular transmissions, which is that of the D2D cell association. In this paper, a multiobjective cell association (MOCA) optimization framework for orchestrating a large number of D2D links in a multicell network is introduced. To this end, and without loss of generality, a differentiated Fractional Frequency Reuse (FFR) scheme is considered as the interference-limiting method, especially for cell-edge users, and we assume the provision of different resource pools for D2D and cellular users, which can vary according to their location. Under this assumption, we develop a set of integer linear programming optimization formulations for D2D links, part of which fall within the coverage area of different neighboring base stations. The main purpose is to achieve improved network traffic balancing via an efficient cell association scheme. Furthermore, we provide an iterative randomized resource allocation algorithm ( i-RRA ), which roots its logic on the differentiated FFR model in order to increase the overall network throughput. A wide set of numerical investigations demonstrate the benefits offered by MOCA, as well as the throughput gains that can be achieved through i-RRA , compared to existing solutions.

After-sales services network design of a household appliances manufacturer

After-sales services have become high-margin businesses that account for larger portions of corporate profits. Delivering the after-sales services is challenging as after-sales services supply chains are significantly different than production–distribution supply chains. The literature provides little guidance on the use of quantitative methods for after-sales services network design. We present a mixed integer linear programming problem formulation to determine warehouse locations, assign repair vendors to facilities and choose mode of transportation while minimizing the total network cost. We transform the large-scale real-life problem of a household appliances manufacturer into a smaller scale to solve optimally in reasonable time. Through a scenario-based approach, we evaluate different configurations of a decentralized network with choices of transportation mode. We test the sensitivity of the solutions. The total cost decreases with additional choices of transportation mode and only slightly increases with the next-day delivery policy while the network solution may change significantly.

Stochastic optimization of energy hub operation with consideration of thermal energy market and demand response

Multi carrier energy systems or energy hubs has provided more flexibility for energy management systems. On the other hand, due to mutual impact of different energy carriers in energy hubs, energy management studies become more challengeable. The initial patterns of energy demands from grids point of view can be modified by optimal scheduling of energy hubs. In this work, optimal operation of multi carrier energy system has been studied in the presence of wind farm, electrical and thermal storage systems, electrical and thermal demand response programs, electricity market and thermal energy market. Stochastic programming is implemented for modeling the system uncertainties such as demands, market prices and wind speed. It is shown that adding new source of heat energy for providing demand of consumers with market mechanism changes the optimal operation point of multi carrier energy system. Presented mixed integer linear formulation for the problem has been solved by executing CPLEX solver of GAMS optimization software. Simulation results shows that hub’s operation cost reduces up to 4.8% by enabling the option of using thermal energy market for meeting heat demand.

Improved handling of uncertainty and robustness in set covering problems

Set Covering Problems are one of the classical combinatorial optimization problems and part of many different practical applications, e. g., the location of emergency service facilities. In many real-world problems the required statistical parameters are not precisely known and the obtained solutions may reveal a non-adequate performance. We introduce a robust formulation of the uncertain/probabilistic Set Covering Problem which combines the concepts of robust and probabilistic optimization by introducing ’Γ-robust α-covering’ constraints. This Robust Uncertain Set Covering Problem can be stated as a compact mixed-integer linear programming model. Additionally, two non-compact integer linear model formulations are developed. As the strength of these formulations is not known a priori, we analyze the performance of these formulations in an extensive computational study. A case study for the location of emergency service facilities highlights the benefits of our approach in comparison to a formulation neglecting these uncertainties.

Online Reconfiguration of Active Distribution Networks for Maximum Integration of Distributed Generation

This paper proposes the online reconfiguration of active distribution networks. The control of the active/reactive output power of distributed generation (DG) units combined with the control of remote controlled switches are employed in order to minimize DG curtailment, alleviate lines congestion, and mitigate voltage rise issues due to DG integration. Convex relaxations of the ac power flow equations and mixed integer linear disjunctive formulations are adopted to the optimization model in order to obtain fast and optimal solutions using standard branch and bound solvers. The computation burden of the optimization procedure is drastically reduced by exploiting the assessment of switching actions, which is performed using multiple load/generation scenarios. The effectiveness of the proposed optimization model is verified using different distribution test systems.

The rainbow spanning forest problem

Given an undirected and edge-colored graph G, a rainbow component of G is a subgraph of G having all the edges with different colors. The Rainbow Spanning Forest Problem consists of finding a spanning forest of G with the minimum number of rainbow components. The problem is known to be NP-hard on general graphs and on trees. In this paper, we present an integer linear mathematical formulation and a greedy algorithm to solve it. To further improve the results, we applied a multi-start scheme to the greedy algorithm. Computational results are reported on randomly generated instances.

Formulations for the orienteering problem with additional constraints

This paper addresses a variant of the Orienteering Problem taking into account mandatory visits and exclusionary constraints (conflicts among nodes). Five mixed integer linear formulations are adapted from the Traveling Salesman Problem literature in order to provide a robust formulation for this problem. The main difference among these formulations lies in the way they deal with the subtour elimination constraints. The performance of the proposed formulations is evaluated over a large set of instances. Computational results reveal that the model that avoids subtours by means of a single-commodity flow formulation allows to solve to optimality more instances than the other formulations, within a time limit of 1 h.

Drone Package Delivery: A Heuristic approach for UAVs path planning and tracking

In this paper we propose a new approach based on a heuristic search for UAVs path planning with terrestrial wireless network tracking. In a previous work we proposed and exact solution based on an integer linear formulation of the problem. Unfortunately, the exact resolution is limited by the computation complexity. In this case, we propose in this paper a new approach based on a heuristic search. More precisely, a heuristic adaptive scheme based on Dijkstra algorithm is proposed to yield a simple but effective and fast solution. In addition, the proposed solution can cover a large area and generate a set of optimum and near optimum pa ths according to the drone battery capacities. Finally, the simulation results show that the drone tracking is sustainable even in noisy wireless network environment.

Facility location decisions in supply chain design under uncertainty: a robust optimisation approach

This paper presents a robust optimisation model for facility location decisions in supply chain design. Robust optimisation belongs to a prominent domain for dealing with optimisation problems with data uncertainty. In this study, a robust optimisation model for a three echelon supply chain is developed. First, a deterministic mixed integer linear formulation for the supply chain design problem is described. Then, the uncertainties in the coefficients of the objective function, left and right hand side parameters are considered and a robust mixed integer linear model is developed. Finally, the deterministic model and its robust counterpart are compared in a numerical experiment.

On Application of Least-delay Variation Problem in Ethernet Networks Using SDN Concept

The goal of this paper is to present an application idea of SDN in Smart Grids, particularly, in the area of L2 multicast as defined by IEC 61850-9-2. Authors propose an Integer Linear Formulation (ILP) dealing with a Least-Delay-Variation multicast forwarding problem that has a potential to utilize Ethernet networks in a new way. The proposed ILP formulation is numerically evaluated on random graph topologies and results are compared to a shortest path tree approach that is traditionally a product of Spanning Tree Protocols. Results confirm the correctness of the ILP formulation and illustrate dependency of a solution quality on the selected graph models, especially, in a case of scale-free topologies.

Capacitated transit service network design with boundedly rational agents

This paper proposes a new alternative modeling framework to systemically account for boundedly rational decision rules of travelers in a dynamic transit service network with tight capacity constraints. Within a time-discretized space-time network, the time-dependent transit services are characterized by traveling arcs and waiting arcs with constant travel times. Instead of using traditional flow-based formulations, an agent-based integer linear formulation is proposed to represent boundedly rational decisions under strictly imposed capacity constraints, due to vehicle carrying capacity and station storage capacity. Focusing on a viable and limited sets of space-time path alternatives, the proposed single-level optimization model can be effectively decomposed to a time-dependent routing sub-problem for individual agents and a knapsack sub-problem for service arc selections through the Lagrangian decomposition. In addition, several practically important modeling issues are discussed, such as dynamic and personalized transit pricing, passenger inflow control as part of network restraint strategies, and penalty for early/late arrival. Finally, numerical experiments are performed to demonstrate the methodology and computational efficiency of our proposed model and algorithm.

Efficient video transmission in D2D assisted mobile cloud networks

The increasing popularity of smart mobile devices and the rise of online services has increased the requirements for efficient dissemination of social video contents. In this paper, we study the problem of distributing video from cloud server to users in partially connected cooperative D2D network using network coding. In such a scenario, the transmission conflicts occur from simultaneous transmissions of multiple devices, and the scheduling decision should be made not only on the encoded packets but also on the set of transmitting devices. We analyze the lower bound and give an integer linear formulation of the joint optimization problem over the set of transmitting devices and the packet combinations. We also propose a heuristic solution for this setup using a conflict graph and local graph at every device. Simulation results show that our coding scheme significantly reduces the number of transmission slots, which will increase the efficiency of video delivery.

An efficient cutting plane algorithm for the minimum weighted elementary directed cycle problem in planar digraphs

In this paper, we study the efficiency (both theoretically and computationally) of a class of valid inequalities for the minimum weighted elementary directed cycle problem (MWEDCP) in planar digraphs with negative weight elementary directed cycles. These valid inequalities are called cycle valid inequalities and are parametrized by an integer called inequality’s order. From a theoretical point of view, we prove that separating cycle valid inequalities of order 1 in planar digraph can be done in polynomial time. From a computational point of view, we present a cutting plane algorithm featuring the efficiency of a lifted form of the cycle valid inequalities of order 1. In addition to these lifted valid inequalities, our algorithm is also based on a mixed integer linear formulation of the MWEDCP. The computational results are carried out on randomly generated planar digraph instances of the MWEDCP. For all 29 instances considered, we obtain in average 26.47% gap improvement. Moreover, for some of our instances the strengthening process directly displays the optimal integer elementary directed cycle.

Environment Learning-Based Coverage Maximization With Connectivity Constraints in Mobile Sensor Networks

This paper takes into consideration the problems related to monitoring a phenomenon of interest in an unknown and open environment using multiple mobile sensor (MS) nodes. We propose an environment learning-based phenomenon monitoring system that iteratively learns about the environment and relocates MS nodes to optimal positions, where MS nodes can attain a high weighted sensing coverage and maintain network connectivity. In this paper, finding optimal positions for MS nodes is defined as the connectivity-constrained coverage maximization problem. An integer linear programming optimization formulation is proposed to find the solution. We also propose three heuristics algorithms to efficiently solve the connectivity-constrained coverage maximization problem. Simulation results show that the proposed algorithms outperform other approaches in terms of the weighted coverage efficiency and energy efficiency.

The Electric Traveling Salesman Problem with Time Windows

To minimize greenhouse gas emissions, the logistic field has seen an increasing usage of electric vehicles. The resulting distribution planning problems present new computational challenges.We address a problem, called Electric Traveling Salesman Problem with Time Windows. We propose a mixed integer linear formulation that can solve 20-customer instances in short computing times and a Three-Phase Heuristic algorithm based on General Variable Neighborhood Search and Dynamic Programming.Computational results show that the heuristic algorithm can find the optimal solution in most small-size instances within a tenth of a second and achieves goods solutions in instances with up to 200 customers.

A hybrid optimization algorithm for surgeries scheduling

This paper deals with the Operating Room (OR) planning problem at an operational planning level. The problem addressed consists of two interrelated sub-problems usually referred to as “advance scheduling” and “allocation scheduling”. In the first sub-problem, the decisions considered are the assignment of a surgery date and an OR block to a set of patients to be operated on over a given planning horizon. The second aims at determining the sequence of selected patients in each OR and day. We assume that the duration of surgeries are random variables with known probability distributions. For each sub-problem an integer linear stochastic formulation is given. A hybrid two-phase optimization algorithm which exploits the potentiality of neighborhood search techniques combined with Monte Carlo simulation is developed to solve the overall problem. The approach developed searches for a feasible and robust solution designed to balance the trade-off arising between the hospital and patient perspectives, i.e. maximizing the OR utilization and minimizing the number of patient cancellations. The contribution of this paper is twofold. The former, more methodological, is to provide an efficient algorithmic framework to solve the joint advance and allocation scheduling problem taking into account the inherent uncertainty of surgery durations. The latter, more practical, is to provide a tool to develop robust offline OR schedules which consider the trade-off between reducing surgery cancellations and postponements while maximizing the operating theater utilization. To evaluate the efficiency of the proposed algorithmic approach, in terms of quality of solutions and solution time, we provide a computational analysis on a set of instances based on real data.

Solving a load balancing problem with a multi-objective particle swarm optimisation approach: application to aircraft cargo transportation

To make air cargo carrier operations cost-effective, a challenging task consists on making profitable the stowage step of the transported freight. This can be accomplished by maximising the weight of the loaded cargo. Owing to the nature and the urgency of the carried cargo, a priority level can also constitute a relevant potential objective to be maximised. In this paper, we present a two level load balancing problem that consists in loading items into containers which are then stowed in cargo holds of an aircraft. Two objectives are maximised: the total weight and the total priority of loaded cargo. In order to minimise fuel consumption and satisfy stability requirements, a load balancing constraints are expressed in terms of the deviation between the gravity centre after loading and its ideal position. An integer linear programming-based formulation is presented for the problem at hand. The loading process performs a discrete multi-objective particle swarm optimisation approach. In order to show the effectiveness of our algorithm and due to the importance of satisfying the load balancing constraints, a practical case study is addressed. An experimental investigation of our approach shows that the proposed approach performs well.

Improved mixed integer linear programing formulations for roman domination problem

The Roman domination problem is considered. An improvement of two existing Integer Linear Programing (ILP) formulations is proposed and a comparison between the old and new ones is given. Correctness proofs show that improved linear programing formulations are equivalent to the existing ones regardless of the variables relaxation and usage of lesser number of constraints.

Dynamic preprocessing for the minmax regret robust shortest path problem with finite multi-scenarios

The minmax regret robust shortest path problem aims at finding a path that minimizes the maximum deviation from the shortest paths over all scenarios. It is assumed that different arc costs are associated with different scenarios. This paper introduces a technique to reduce the network, before a minmax regret robust shortest path algorithm is applied. The preprocessing method enhances others explored in previous research. The introduced method acts dynamically and allows to update the conditions to be checked as new network nodes that can be discarded are identified. Computational results on random and Karasan networks are reported, which compare the dynamic preprocessing algorithm and its former static version. Two robust shortest path algorithms as well as the resolution of a mixed integer linear formulation by a solver are tested with and without these preprocessing rules.

The multi-vehicle cumulative covering tour problem

This paper introduces the multi-vehicle cumulative covering tour problem whose motivation arises from humanitarian logistics. The objective is to determine a set of tours that must be followed by a fleet of vehicles in order to minimize the sum of arrival times (latency) at each visited location. There are three types of locations: mandatory, optional, and unreachable. Each mandatory location must be visited, and optional locations are visited in order to cover the unreachable locations. To guarantee the vehicle autonomy, the duration of each tour should not exceed a given time limit. A mixed integer linear formulation and a greedy randomized adaptive search procedure are proposed for this problem. The performance of the algorithm is assessed over a large set of instances adapted from the literature. Computational results confirm the efficiency of the proposed algorithm.