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The Cognitive Radio Network, incorporating Device-to-Device communication and a heterogeneous network, has garnered significant attention due to its ability to address spectrum shortage issues and optimize the efficient utilization of spectrum resources. However, resource allocation considering stochastic behavior has not been considered in existing studies. In this paper, our work aimed to maximize the throughput of the overall network considering multiple users under the umbrella of the Cognitive radio network assisted by amplify and forward relay. The constraints are treated as chance constraints with a probability of satisfaction in them, which leads to a non-convex mixed integer nonlinear problem which is an NP-Hard problem. To solve this problem an exhaustive search solution for optimal results is required. However, the computational burden always increases with the user equipment. Therefore, to obtain an optimal solution with having low computational burden, the Outer Approximation Algorithm is utilized in this research. To evaluate the desired results, extensive simulations have been carried out. The effectiveness of the proposed algorithm is verified by results in terms of throughput maximization under the impact of chance constraint formulation in the cognitive radio networks. [ABSTRACT FROM AUTHOR]

We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a methodology for proving geometric convergence of the parameter sequence { θ n } n ⩾ 0 of such algorithms. We employ the ordinary differential equation (ODE) method, which relates a stochastic algorithm to its mean ODE, along with a Lyapunov-like function Ψ such that the geometric convergence of Ψ (θ n) implies – in the case of an optimization algorithm – the geometric convergence of the expected distance between the optimum and the search point generated by the algorithm. We provide two sufficient conditions for Ψ (θ n) to decrease at a geometric rate: Ψ should decrease "exponentially" along the solution to the mean ODE, and the deviation between the stochastic algorithm and the ODE solution (measured by Ψ) should be bounded by Ψ (θ n) times a constant. We also provide practical conditions under which the two sufficient conditions may be verified easily without knowing the solution of the mean ODE. Our results are any-time bounds on Ψ (θ n) , so we can deduce not only the asymptotic upper bound on the convergence rate, but also the first hitting time of the algorithm. The main results are applied to a comparison-based stochastic algorithm with a constant step-size for optimization on continuous domains. [ABSTRACT FROM AUTHOR]

The coordination among drones and ground vehicles for last-mile delivery has gained significant interest in recent years. In this paper, we study multiple drone delivery scheduling problem (MDSP) [1] for last-mile delivery, where we have a set of drones with an identical battery budget and a set of delivery locations; along with profit for delivery, cost, and delivery time intervals. The objective of the MDSP is to find conflict-free schedules for each drone such that the total profit gained is maximum subject to the battery constraint of the drones. This paper proposes an optimal pseudo-polynomial algorithm and a fully polynomial time approximation scheme (FPTAS) for the single drone delivery scheduling problem (SDSP). Also, we propose two approximation algorithms of factor 1 3 for the MDSP with some constraints on the number of drones. We formulate the problem for the heterogeneous case, where the drones have non-identical battery capacities, and propose a 1 6 ρ -approximation algorithm, where ρ is the ratio between the minimum and maximum battery capacity of the drones. • An optimal pseudo-polynomial algorithm and FPTAS for the single drone delivery scheduling problem is proposed. • Two approximation algorithms for the multiple drone delivery scheduling problem are proposed. • An approximation algorithm for the multiple heterogeneous drone delivery scheduling problem is proposed. • We analyzed the approximation factors of all the aforementioned proposed algorithms and time complexities. [ABSTRACT FROM AUTHOR]

The design of optimal business processes is practically important in many areas including: manufacturing, process mining, planning & scheduling, and parallel computing. Business processes are usually required to satisfy correctness and robustness properties. Block-structured models have certain advantages by ensuring basic correctness and robustness by design. The aim of this work is to provide an in-depth investigation of the problem of automated synthesis of optimal block-structured processes. Our results concern new theoretical insights into this rather new problem, as well as new exact and approximation algorithms for various problem variants. [ABSTRACT FROM AUTHOR]

We present two results on slime mold computations. In wet-lab experiments by Nakagaki et al. (2000) [1] the slime mold Physarum polycephalum demonstrated its ability to solve shortest path problems. Biologists proposed a mathematical model, a system of differential equations, for the slime's adaption process (Tero et al., 2007) [3]. It was shown that the process convergences to the shortest path (Bonifaci et al., 2012) [5] for all graphs. We show that the dynamics actually converges for a much wider class of problems, namely undirected linear programs with a non-negative cost vector. Combinatorial optimization researchers took the dynamics describing slime behavior as an inspiration for an optimization method and showed that its discretization can ε -approximately solve linear programs with positive cost vector (Straszak and Vishnoi, 2016) [14]. Their analysis requires a feasible starting point, a step size depending linearly on ε , and a number of steps with quartic dependence on opt / (ε Φ) , where Φ is the difference between the smallest cost of a non-optimal basic feasible solution and the optimal cost (opt). We give a refined analysis showing that the dynamics initialized with any strongly dominating point converges to the set of optimal solutions. Moreover, we strengthen the convergence rate bounds and prove that the step size is independent of ε , and the number of steps depends logarithmically on 1 / ε and quadratically on opt / Φ. [ABSTRACT FROM AUTHOR]

Abstract We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using " t -spanning" routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t -spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time. [ABSTRACT FROM AUTHOR]

Abstract One of the most prevalent methods for enhanced oil recovery in heavy oil reservoirs is thermal techniques. Fast-SAGD process is an advance method of enhance oil recovery in which offset wells are drilled for cyclic steam injection and production. This leads to increasing the production efficiency. Optimization of this process was performed using various techniques including genetic algorithm (GA), imperialist competitive algorithm (ICA), and particle swarm optimization (PSO). Combination of recovery factor and cumulative steam to oil ratio was introduced as the objective function. This study represents a novel supplementary technique implemented in optimization algorithms to increase its speed, significantly. In this technique, effective parameters were defined using sensitivity analysis. Then they were converted to discrete variables. To discretize the selected parameters, three different functions including logarithmic, square, and linear were applied using Minitab 18. Moreover, repetition inhibitory algorithm (RIA) was implemented in optimization algorithms for the first time to prevent recalculation of duplicate states in optimization for the next generation, and to speed-up the optimization process. The results of sensitivity analysis indicated that maximum and minimum effective parameters were attributed to Fast-SAGD production well height and soak time, respectively. Results indicated that among various optimization algorithms, GA worked 6% better in comparison to other optimization techniques and linear discretization function resulted in better optimized point in a shorter time. Results indicated that optimization process using discrete variables and repetition inhibitory algorithm led to the optimized point 6.33 times faster than discrete optimization procedure without RIA. This was 16.46 times faster in comparison to continuous optimization algorithm. Moreover using RIA led to termination of optimization algorithm 9.67 times faster than continuous mode. Highlights • ICA, GA, and PSO algorithms were applied for Fast SAGD optimization. GA represented a medium speed with most accurate results and ICA displayed a high speed performance. • Linear, logarithmic and square functions were applied for discretization of optimization parameters among which linear function was more satisfactory. • Implementing the repetition inhibitory algorithm in optimization process, proved the importance of this innovative method for increasing the speed of optimization process in reservoir simulation studies. [ABSTRACT FROM AUTHOR]

A new method is proposed for the steady-state optimization of biochemical systems described by Generalized Mass Action (GMA) models. In this method, a bi-level programming with a two-layer nested structure is established. In this bi-level problem, the upper-level objective is to maximize a flux or a metabolite concentration, and the lower-level objective is to minimize the total sum of metabolite concentrations of biochemical systems. The biological significance of the presented bi-level programming problem is to maximize the production rate or concentration of the desired product under a minimal metabolic cost to the biochemical system. To efficiently solve the above NP-hard, non-convex and nonlinear bi-level programming problem, we reformulate it into a single-level optimization problem by using appropriate transformation strategies. The proposed framework is applied to four case studies and has shown the tractability and effectiveness of the method. A comparison of our proposed method and other methods is also given. [ABSTRACT FROM AUTHOR]

This paper introduces a new algorithm named Elitist Stepped Distribution Algorithm (ESDA), which is inspired from the existing Cross Entropy Method (CEM) through the modification of elite sample based normal distribution used in CEM. Considering the natural behavior of normal distribution, ESDA is proposed to enhance the drawbacks of CEM through improving the efficiency in both exploration and exploitation processes when applying for complex function optimization problems. In ESDA, the elite sample percent defined in CEM is separated into two parts: (1) elite sample percent to calculate the mean value, and (2) elite sample percent to calculate standard deviation of normal distribution to construct an applicable balance between exploration and exploitation ability of the algorithm at a reasonable convergence speed. The elite sample percent parameter for the mean guides the algorithm to focus more on the better solutions and therefore improves the exploitation ability, whereas the elite sample percent parameter for the standard deviation controls the length of standard deviation to handle the exploration process more effectively. Performance of ESDA is investigated using unconstrained benchmark problems and compared with CEM, Simple Genetic Algorithm and Particle Swarm Optimization. The comparisons on unimodal and multi-modal functions confirm the efficiency of the algorithm in both exploration and exploitation process. In addition, the performance of ESDA is tested using constrained engineering problems commonly used in literature by comparing its performance with the other ones statistically. The results on engineering problems also prove that ESDA is perfectly applicable in real-world applications. [ABSTRACT FROM AUTHOR]

To meet the futuristic communications needs, a satellite–terrestrial integrated network (STIN) has been proposed and is a strong contender amongst emerging architectures. In our STIN model, we have considered a satellite-based base station (BS), dovetailed with a terrestrial N-tier heterogeneous network (HetNets). Our work considers jointly admission control of user equipment (UE), power allocation , fairness-based user association (UA), and fair spectrum resource allocation to UEs in STIN. With throughput maximization as an objective, considering such an environment, has not been investigated in the past. The formulated problem is a mixed integer non-linear programming (MINLP) problem that is Non-deterministic Polynomial-time Hard (NP-hard) and to achieve an optimal solution, it requires an exhaustive search. But, the computational load of exhaustive search increases exponentially as the number of UEs increases. Therefore, to obtain a near-optimal solution having low computational load an outer approximation algorithm (OAA) is proposed. To evaluate the proposed algorithm, extensive simulation work has been performed. The effectiveness of the proposed approach is verified by the results in terms of fairness in UA, fairness in resource block (RB) allocation, and throughput in the downlink (DL). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the symbiosis between a truck and multiple drones in a last-mile package delivery scenario, introducing the Scheduling Conflictual Deliveries Problem (SCDP). From the main depot, a truck takes care of transporting a fleet of drones that will be used to deliver packages to customers. The route of the truck is predefined. Each delivery is associated with the energy cost of a drone, a reward that characterizes the priority of the delivery, and an interval between two points of the truck's route: the point from which the drone departs (launch point) and the point at which the drone returns to the truck (rendezvous point). The objective of the SCDP is to find a scheduling for the drones that maximizes the overall reward subject to the drone's battery capacity while ensuring that the same drone performs deliveries whose delivery intervals do not intersect. After showing that SCDP is an NP-hard problem, we devise an Integer Linear Programming (ILP) formulation for it. Furthermore, we devise a pseudo-polynomial time optimal algorithm for the single drone case and additional approximation algorithms for both the single and multiple drones case. Finally, we thoroughly compare the performances of our presented algorithms on different synthetic datasets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel algorithm for the rigorous design of distillation columns that integrates a process simulator in a generalized disjunctive programming formulation. The optimal distillation column, or column sequence, is obtained by selecting, for each column section, among a set of column sections with different number of theoretical trays. The selection of thermodynamic models, properties estimation, etc. is all in the simulation environment. All the numerical issues related to the convergence of distillation columns (or column sections) are also maintained in the simulation environment. The model is formulated as a Generalized Disjunctive Programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation. Some examples involving from a single column to thermally coupled sequence or extractive distillation shows the performance of the new algorithm. [ABSTRACT FROM AUTHOR]

The Quantum Circuit Compilation Problem (QCCP) is challenging to the Artificial Intelligence community. It was already tackled with temporal planning, constraint programming, greedy heuristics and other techniques. In this paper, QCCP is formulated as a scheduling problem and solved by a genetic algorithm. We focus on QCCP for Quantum Approximation Optimization Algorithms (QAOA) applied to the MaxCut problem and consider Noisy Intermediate Scale Quantum (NISQ) hardware architectures. Based on the fact that these algorithms apply a set of basic quantum operations repeatedly over a number of rounds, we propose a genetic algorithm approach, termed Decomposition Based Genetic Algorithm (DBGA), that in each round extends the partial solutions obtained for the previous ones. DBGA is compared to the state of the art across a set of conventional instances. The results of the experimental study provided interesting insight in the problem structure and showed that DBGA is quite competitive with the state of the art. In particular, DBGA outperformed the best current method on the largest instances and provided new best solutions to most of them. [ABSTRACT FROM AUTHOR]

Abstract: We consider the data gathering problem in wireless ad-hoc networks where a data mule traverses a set of sensors, each with vital information on its surrounding, and collects their data. The mule goal is to collect as much information as possible thereby reducing the information uncertainty but in the same time avoid visiting some of the nodes to minimize its travel distance. We study the problem when the mule travels over a tree or a tour and propose a 3-approximation algorithm that minimizes both the information uncertainty and travel distance. We also show the applicability of our approach for solving data collection problems in varying domains such as temperature monitoring, surveillance systems and sensor placement. Simulation results show that the proposed solution converges to the optimal for varying set of topologies, such as grids, stars, linear and random networks. [Copyright &y& Elsevier]

Abstract: In the rectangle packing problem we are given a set of rectangles with positive profits and the goal is to pack a subset of into a unit size square bin so that the total profit of the rectangles that are packed is maximized. We present algorithms that for any value find a subset of rectangles of total profit at least , where is the profit of an optimum solution, and pack them (either without rotations or with rotations) into the augmented bin . This algorithm can be used to design asymptotic polynomial time approximation schemes (APTAS) for the strip packing problem without and with rotations. The additive constant in the approximation ratios of both algorithms is , thus improving on the additive term in the approximation ratios of the algorithm by Kenyon and Rémila (for the problem without rotations) and Jansen and van Stee (for the problem with rotations), both of which have a much larger additive constant , . [Copyright &y& Elsevier]

Target coverage and connectivity are two fundamental and critical issues in wireless sensor networks. The former is for providing sufficient monitoring quality where all points of interest in the network are covered by sensor nodes. The latter is for guaranteeing satisfactory communicating capability where all sensor nodes can connect to at least one sink via nodes (i.e., sensor nodes and relay nodes). Though considerable efforts have been devoted to optimize the placement of sensor nodes and relay nodes under connected target coverage constraint (i.e., guaranteeing both target coverage and connectivity), all of the existing works in this area address only networks with one static sink. In the meanwhile, although there are many works in literature considered the networks with dynamic sinks, none of them studies how to optimize the location of sensor and relay nodes. In this article, we focus on wireless sensor networks with dynamic sinks, which consist of multiple sinks and the sinks' positions may change periodically, and study how to place a minimum number of nodes for connected target coverage. Specifically, we decompose the problem into two sub-problems. The first one, named as target coverage problem, is to place sensor nodes for covering all targets. The second one, named as network connectivity problem, is for placing relay nodes to connect sensor nodes to the sinks. We first formulate the target coverage problem under an integer linear programming model and present an exact algorithm to determine the optimal solution. We then propose a constant-approximation algorithm based on partitioning and shifting scheme. For the network connectivity problem, we first prove its NP-hardness and then propose two approximation algorithms. The first one exploiting the minimum group Steiner tree to minimize the placed relay nodes, while the second one is a time-efficient algorithm based on clustering and spanning tree approaches. The experiment results show the superiority of our proposed algorithms in terms of both the number of the required nodes and the time complexity. [ABSTRACT FROM AUTHOR]