Mixed Binary Nonlinear Programming Problem Research Articles

Task offloading strategy and scheduling optimization for internet of vehicles based on deep reinforcement learning

Driven by the construction of smart cities, networks and communication technologies are gradually infiltrating into the Internet of Things (IoT) applications in urban infrastructure, such as automatic driving. In the Internet of Vehicles (IoV) environment, intelligent vehicles will generate a lot of data. However, the limited computing power of in-vehicle terminals cannot meet the demand. To solve this problem, we first simulate the task offloading model of vehicle terminal in Mobile Edge Computing (MEC) environment. Secondly, according to the model, we design and implement a MEC server collaboration scheme considering both delay and energy consumption. Thirdly, based on the optimization theory, the system optimization solution is formulated with the goal of minimizing system cost. Because the problem to be resolved is a mixed binary nonlinear programming problem, we model the problem as a Markov Decision Process (MDP). The original resource allocation decision is turned into a Reinforcement Learning (RL) problem. In order to achieve the optimal solution, the Deep Reinforcement Learning (DRL) method is used. Finally, we propose a Deep Deterministic Policy Gradient (DDPG) algorithm to deal with task offloading and scheduling optimization in high-dimensional continuous action space, and the experience replay mechanism is used to accelerate the convergence and enhance the stability of the network. The simulation results show that our scheme has good performance optimization in terms of convergence, system delay, average task energy consumption and system cost. For example, compared with the comparison algorithm, the system cost performance has improved by 9.12% under different task sizes, which indicates that our scheme is more suitable for highly dynamic Internet of Vehicles environment.

Whale Swarm Reinforcement Learning Based Dynamic Cooperation Clustering Method for Cell-Free Massive MIMO Systems

Dynamic cooperation clustering (DCC) becomes a main enabler for cell-free massive MIMO systems since it can improve the energy efficiency and reduce the complexity of signal processing significantly. However, DCC formation for all served users simultaneously is a very complicated mixed binary nonlinear programming problem, a single agent has limited capability to search the optimal schemes. In this paper, we propose a whale swarm reinforcement learning (WSRL) based DCC method. Exploiting multiple searching agent imitated by a group of whales, whale swarm optimization (WOA) algorithm searches the optimal DCC scheme simultaneously and learn the searching experience from each other. Moreover, the reinforcement learning is integrated to select the most efficient hunting action for each whale, which can accelerate the convergence and avoid the local trap. Simulation results demonstrate that the proposed method has better searching ability and higher convergence speed than the existing works.

Energy Efficiency Maximization in the Uplink Delta-OMA Networks

Delta-orthogonal multiple access (D-OMA) has been recently investigated as a potential technique to enhance the spectral efficiency in the sixth-generation (6G) networks. D-OMA enables partial overlapping of the adjacent sub-channels that are assigned to different clusters of users served by non-orthogonal multiple access (NOMA), at the expense of additional interference. In this paper, we analyze the performance of D-OMA in the uplink and develop a multi-objective optimization framework to maximize the uplink energy efficiency (EE) in a multi-access point (AP) network enabled by D-OMA. Specifically, we optimize the sub-channel and transmit power allocations of the users as well as the overlapping percentage of the spectrum between the adjacent sub-channels. The formulated problem is a mixed binary non-linear programming problem. Therefore, to address the challenge we first transform the problem into a single-objective problem using Tchebycheff method. Then, we apply the monotonic optimization (MO) to explore the hidden monotonicity of the objective function and constraints, and reformulate the problem into a standard MO in canonical form. The reformulated problem is then solved by applying the outer polyblock approximation method. Our numerical results show that D-OMA outperforms the conventional non-orthogonal multiple access (NOMA) and orthogonal frequency division multiple access (OFDMA) when the adjacent sub-channel overlap and scheduling are optimized jointly.

Joint Computation Offloading and Radio Resource Allocations in Small-Cell Wireless Cellular Networks

Mobile computation offloading (MCO) is a technique that can help reduce energy consumption of mobile devices (MDs) by offloading their tasks to more powerful devices for execution. In MCO, the offloading decision for a task depends on availability of both communication and computation resource. In small cell cellular networks, cloudlet servers are usually co-located with the small base stations (SBSs). As a result, offloading decisions of the MDs are coupled with SBS associations, while strong overlapping coverage between the SBSs can result in complicated interference conditions in wireless transmissions that affect the offloading performance. In this paper, offloading decisions and SBS associations are jointly optimized with transmission power and channel assignments in a small cell cellular network. The objective is to minimize the total energy consumption of all MDs, subject to task’s latency constraints. The problem is first formulated as a mixed binary nonlinear programming problem, then transformed and solved using the general bender decomposition (GBD). A heuristic solution is proposed that recursively allows more MDs to make offloading decisions based on the current transmission conditions. Compared to using GBD, this solution results in much lower worst-case complexity, while achieving good energy performance for a wide range of system parameters.

On numerical methods for singular optimal control problems: An application to an AUV problem

We discuss and compare numerical methods to solve singular optimal control problems by the direct method. Our discussion is illustrated by an Autonomous Underwater Vehicle (AUV) problem with state constraints. For this problem, we test four different approaches to solve numerically our problem via the direct method. After discretizing the optimal control problem we solve the resulting optimization problem with (ⅰ) A Mathematical Programming Language ($ \text{AMPL} $), (ⅱ) the Imperial College London Optimal Control Software ($ \text{ICLOCS} $), (ⅲ) the Gauss Pseudospectral Optimization Software ($ \text{GPOPS} $) as well as with (ⅳ) a new algorithm based on mixed-binary non-linear programming reported in [7]. This algorithm consists on converting the optimal control problem to a Mixed Binary Optimal Control (MBOC) problem which is then transcribed to a mixed binary non-linear programming problem ($ \text{MBNLP} $) problem using Legendre-Radau pseudospectral method. Our case study shows that, in contrast with the first three approaches we test (all relying on $ \text{IPOPT} $ or other numerical optimization software packages like $ \text{KNITRO} $), the $ \text{MBOC} $ approach detects the structure of the AUV's problem without a priori information of optimal control and computes the switching times accurately.

Global blending optimization of laminated composites with discrete material candidate selection and thickness variation

A method capable of simultaneous topology and thickness optimization of laminated composites has previously been published by one of the authors. Mass constrained compliance minimization subject to certain manufacturing constraints was solved on basis of interpolation schemes with penalization. In order to obtain large patchwise material candidate continuity while also accommodating variable laminate thickness, a bi-linear stiffness parameterization was introduced, causing a non-convex problem. In this present work, we introduce an alternative problem formulation that holds identical capabilities but is, however, convex in the original mixed binary nested form. Convexity is the foremost important property of optimization problems, and the proposed method can guarantee the global or near-global optimal solution; unlike most topology optimization methods. The material selection is limited to a distinct choice among predefined numbers of candidates. The laminate thickness is variable but the number of plies must be integer. We solve the convex mixed binary non-linear programming problem by an outer approximation cutting-plane method augmented with a few heuristics to accelerate the convergence rate. The capabilities of the method and the effect of active versus inactive manufacturing constraints are demonstrated on several numerical examples of limited size, involving at most 320 binary variables. Most examples are solved to guaranteed global optimality and may constitute benchmark examples for popular topology optimization methods and heuristics based on solving sequences of non-convex problems. The results will among others demonstrate that the difficulty of the posed problem is highly dependent upon the composition of the constitutive properties of the material candidates.

Investigating the commonality attributes for scaling product families using comprehensive product platform planning (CP3)

A product family with a platform paradigm is expected to increase the flexibility of the manufacturing process to market changes, and to take away market share from competitors that develop one product at a time. The recently developed Comprehensive Product Platform Planning (CP3) method (i) presents a generalized model, (ii) allows the formation of product sub-families, and (iii) provides simultaneous identification and quantification of platform/scaling design variables. The CP3 model is founded on a generalized commonality matrix that represents the platform planning process as a mixed-binary nonlinear programming (MBNLP) problem. This MBNLP problem is high-dimensional and multimodal, owing to the commonality constraint. In this paper, the complex MBNLP model is reduced to a tractable MINLP problem without resorting to limiting approximations; along the reduction process, redundancies in the original commonality matrix are also favorably addressed. To promote a better understanding of the importance of a reduced MINLP, this paper also provides a uniquely comprehensive formulation of the number of possible platform combinations (or commonality combinations). In addition, a new commonality index (CI) is developed to simultaneously account for the inter-product commonalities (based on design variable sharing) and the overlap between groups of products sharing different platform variables. To maximize the performance of the product family and the commonality index yielded by the new CP3 model, we apply an advanced mixed-discrete Particle Swarm Optimization algorithm. The potential of the new CP3 framework is illustrated through its application to design scalable families of electric motors. Maximizing the new CI produced families with more commonality among similar sets of motor variants (compared to maximizing the conventional CI), which can be a beneficial platform attribute for a wide range of product families.

A Joint Resource Allocation Scheme for Relay Enhanced Multi-cell Orthogonal Frequency Division Multiple Networks

This paper formulates resource allocation for decode-and-forward (DF) relay assisted multi-cell orthogonal frequency division multiple (OFDM) networks as an optimization problem taking into account of inter-cell interference and users fairness. To maximize the transmit rate of system we propose a joint interference coordination, subcarrier and power allocation algorithm. To reduce the complexity, this semi-distributed algorithm divides the primal optimization into three sub-optimization problems, which transforms the mixed binary nonlinear programming problem (BNLP) into standard convex optimization problems. The first layer optimization problem is used to get the optimal subcarrier distribution index. The second is to solve the problem that how to allocate power optimally in a certain subcarrier distribution order. Based on the concept of equivalent channel gain (ECG) we transform the max-min function into standard closed expression. Subsequently, with the aid of dual decomposition, water-filling theorem and iterative power allocation algorithm the optimal solution of the original problem can be got with acceptable complexity. The third sub-problem considers dynamic co-channel interference caused by adjacent cells and redistributes resources to achieve the goal of maximizing system throughput. Finally, simulation results are provided to corroborate the proposed algorithm.

Congestion management considering hydro–thermal combined operation in a pool based electricity market

This paper proposes a novel congestion management strategy for a pool based electricity market considering combined operation of hydro and thermal generator companies. The proposed congestion management problem is formulated as mixed binary nonlinear programming problem to minimize the cost of re-dispatching the hydro and thermal generator companies to alleviate congestion subject to operational, line overloading and water availability constraints. A piecewise-linearized unit performance curve is used in this formulation, which takes into account its non-concave nature. The effectiveness of the proposed technique is demonstrated by solving the modified IEEE 57-bus and IEEE 118-bus systems for congestion management under line outages.

A Constructive Heuristic Algorithm for Distribution System Planning

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.