Mixed Binary Nonlinear Programming 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.

A Ubiquitous Clinic Recommendation System Using the Modified Mixed-Binary Nonlinear Programming-Feedforward Neural Network Approach

Most of the existing ubiquitous clinic recommendation (UCR) systems adopt linear mechanisms to aggregate the attribute-level performances of a clinic to evaluate the overall performance. However, such linear mechanisms may not be able to explain the choices of all patients. To solve this problem, the modified mixed binary nonlinear programming (MMBNLP)–feedforward neural network (FNN) approach is proposed in this study. In the proposed methodology, first, the existing MBNLP model is modified to improve the successful recommendation rate using a linear recommendation mechanism. Subsequently, an FNN is constructed to fit the relationship between the attribute-level performances of a clinic and its overall performance, thereby providing possible ways to further enhance the recommendation performance. The results of a regional experiment showed that the MMBNLP–FNN approach improved the successful recommendation rate by 30%.

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.

Component rearrangement and system replacement for a system with stochastic degradation processes

Consider a system of multiple functionally-interchangeable components. These components degrade following non-homogeneous stochastic processes that are related to different workloads, usage rates, or operating environment. The unbalanced degradation levels of components affect the overall performance of the system. This paper studies a preventive maintenance policy based on component rearrangement, and the goal is to prolong the useful time of a system before its replacement or overhaul. In this model, the optimal component rearrangement is planned to execute at optimal time. The stochastic degradation models and reliability functions that incorporate the component rearrangement are built. Then a mixed binary nonlinear programming model is established to optimize the component rearrangement plan, rearrangement time, and system replacement time. The models are derived for each of the Wiener process, gamma process, and inverse Gaussian process, which are three most widely used stochastic degradation processes. The specified models are derived for k-out-of-n:F, series–parallel, and parallel–series systems. Furthermore, a hybrid approach is proposed that integrates permutation-based heuristic global search for solving a combinatorial subproblem and nonlinear optimization method for solving constrained continuous subproblems. The analytical results and numerical experiments demonstrate the efficiency of the models and solution approach and provide the insights of the component-rearrangement based maintenance policy.

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.

Optimum reassignment of degrading components for non-repairable systems

The components in a system can degrade differently, due to the operational loads or environmental conditions, or both, in their positions being different. Therefore, reassignment of the functionally exchangeable components to the positions at appropriate time can increase system reliability and extend system lifetime. In this article, a new component reassignment problem is proposed, and a mixed binary nonlinear programming model is built to determine the optimal reassignment time and optimal reassignment of degrading components with the objective of maximizing system lifetime. The model integrates continuous optimization and combinatorial optimization, and provides a framework for optimizing the component reassignment decisions for various degradation models and system structures. Furthermore, the optimization model and analytical results are derived for k-out-of-n systems of linearly degrading components or exponentially degrading components. The analytical results reduce the complexity of solving the optimization model and are used to design an efficient solution method. Finally, numerical examples in a power supply system demonstrate applications of the optimization model and further provide managerial insights for the component reassignment problem of degrading components.

Interval fuzzy number-based approach for modeling an uncertain fuzzy yield learning process

An interval fuzzy number-based approach was proposed in this study to model an uncertain yield learning process. The study aimed to overcome the limitations of present methods, wherein the lower and upper bounds of the yield are generally determined by few extreme cases, thus resulting in an unacceptable widening of the yield range. In the proposed interval fuzzy number-based approach, the range of yield was divided into two sections, namely inner and outer sections, which corresponded with the lower and upper membership functions of a fuzzy yield forecast based on interval fuzzy numbers, respectively. To fulfill different managerial objectives, in this approach, all actual values are included in the outer section, whereas most of these values fall within the inner section. To derive the values of parameters in a fuzzy yield learning model based on interval fuzzy numbers, a mixed binary nonlinear programming model was proposed and optimized. The interval fuzzy number-based approach was applied to two real-time cases for evaluating its effectiveness. According to experimental results, the performance of the proposed method was superior to that of several existing methods, particularly in terms of forecasting precision for the average range. Forecasting accuracy obtained using the interval fuzzy number-based approach was satisfactory.

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.

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

ABSTRACTThis paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then, by utilising the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the optimal control and to compute the approximating solution. The main advantages of the present method are that: (1) without a priori information, the structure of optimal control is detected; (2) it produces good results even using a small number of collocation points; (3) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples.

Parallel Multiagent Coordination Optimization Algorithm: Implementation, Evaluation, and Applications

In this paper, a parallel computing implementation of a multiagent coordination optimization (MCO) algorithm is introduced using $\mathtt {parfor}$ , a built-in MATLAB function. As a novel variation of particle swarm optimization (PSO), the MCO algorithm has demonstrated significant performance improvement, in terms of both accuracy and efficiency, in solving real-time optimization problems when compared with PSO. However, the ability to handle large-scale optimization problems or use more particles in the algorithm is limited by the sequential implementation of the original MCO algorithm. A numerical evaluation of the parallel MCO algorithm was conducted using the supercomputers in the High Performance Computing Center at Texas Tech University. Based on the results of this evaluation, it was determined that the performance of the parallel MCO is not only superior to that of PSO but is highly efficient as it reduces the computational time. The parallel binary MCO (BMCO) algorithm is presented here as well. By combining the parallel MCO with parallel BMCO algorithms, a new parallel mixed-binary nonlinear programming MCO solver is proposed. Finally, a load balancing coordination problem, a multiagent formation control problem, and a power system vulnerability analysis problem are solved using the corresponding parallel MCO algorithm.

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.

An improved decomposition-based heuristic to design a water distribution network for an irrigation system

In this paper the authors address a pressurized water distribution network design problem for irrigation purposes. Two mixed binary nonlinear programming models are proposed for this NP-hard problem. Furthermore, a heuristic algorithm is presented for the problem, which considers a decomposition sequential scheme, based on linearization of the second model, coupled with constructive and local search procedures designed to achieve improved feasible solutions. To evaluate the robustness of the method we tested it on several instances generated from a real application. The best solutions obtained are finally compared with solutions provided by standard software. These computational experiments enable the authors to conclude that the decomposition sequential heuristic is a good approach to this difficult real problem.

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.