Mixed Discrete Optimization Problems Research Articles

Deep Reinforcement Learning Driven UAV-Assisted Edge Computing

Unmanned aerial vehicles (UAVs) are playing a critical role in provisioning instant connectivity and computational needs of Internet of Things Devices (IoTDs), especially in crisis and disaster management. In this work, we focus on optimizing trajectories of UAVs along which IoTDs are served with communication and computing resources in multiple time slots. The Quality of Experience (QoE) of an IoTD depends on its latency performance; we thus aim to maximize the average aggregate QoE of all IoTDs overall time slots. However, this is a nonconvex, nonlinear, and mixed discrete optimization problem, which is difficult to solve and obtain the optimal solution. We thus propose two deep reinforcement learning algorithms to solve this problem by considering UAV path planning, user assignment, bandwidth, and computing resource assignment. We compare the performance of our proposed algorithms through simulations with three baseline cases: 1) with fixed UAV locations; 2) without UAVs; and 3) the fixed UAV trajectories. We demonstrate that the deep reinforcement learning algorithms perform better than all baseline cases.

Mixed–discrete structural optimization using a rank-niche evolution strategy

In this study, the evolution strategy, which is one of the evolutionary algorithms, is modified to solve mixed–discrete optimization problems. Three approaches are proposed for handling discrete variables. The first approach is to treat discrete variables as continuous variables and replace the latter with discrete variables that are closest to the continuous variables. The second approach is to compress the difference between discrete variables so that discrete variables far away from the current value will have a higher probability of being selected. The third approach is to represent the discrete variables as integers. As a result, the difference between neighbouring discrete variables becomes equal. This also increases the probability of selection of discrete variables far away from the current value through the mutation operation. Five examples are tested representing single objective, multi-objective, unconstrained, constrained, pure discrete and mixed–discrete variable problems. From the results obtained from the test problems it is evident that the enhanced rank-niche evolution strategy algorithm yields better solutions than other methods for most of the test problems.

A Fuzzy Dynamic Programming Approach for the Mixed-Discrete Optimization of Mechanical Systems

Many engineering optimization problems can be considered as multistage decision-making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms cannot deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The method can also be extended to solve general mixed-discrete fuzzy nonlinear programming problems if their corresponding crisp problems can be solved using dynamic programming approaches. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss and the reliability-based optimization of a gearbox. To the authors’ knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.

A Unified Gradient Flow Approach to Constrained Nonlinear Optimization Problems

This paper presents a unified gradient flow approach to nonlinear constrained optimization problems. This method is based on a continuous gradient flow reformulation of constrained optimization problems and on a two level time discretization of the gradient flow equation with a splitting parameter t. The convergence of the scheme is analyzed and it is shown that the scheme becomes first order when t ∈ [0, 1] and second order when t e 1 and the time discretization step length is sufficiently large. Numerical experiments for continuous, discrete and mixed discrete optimization problems were performed, and the numerical results show that the approach is effective for solving these problems.

Optimum Design of Actively Controlled Structures Using Genetic Algorithms

Optimal placement of actuators in actively controlled structures is a mixed-discrete optimization problem; it has the characteristics of nonlinear, non-continuous, and so on. For this type of optimization problem, traditional optimization methods based on mathematical programming may not be effective. In this paper, the complexity, discreteness and non-linearity of the optimal design problems of actuator placement are investigated. An optimal control algorithm and active tendon controllers are applied to control the response of a 16-storey building under earthquake loads. A mathematical model of optimal actuator configuration is established. Based on the special optimization problem of actuator configuration in an actively controlled structure, a modified genetic algorithm is presented and applied to solve the problems. A design procedure/method is presented for this kind of optimization problem, and the suitability of this method for the optimization problem is investigated. The numerical calculation and analysis are carried out for the building controlled by active tendon control mechanisms, and the results are discussed and analyzed in detail.

Fuzzy and improved penalty approaches for multiobjective mixed-discrete optimization in structural systems

Three fuzzy models are employed to combine with an improved imposed-on penalty approach for attacking a nonlinear multiobjective in the mixed-discrete optimization problem. The model can generate a unique compromise solution with the maximum design satisfaction. A systematic study of the proposed penalty method is presented, including the forms of penalty function and the values of each parameter. A default value of the parameter and an optimization algorithm are presented in the paper. One can easily program and reach the solution by any nonlinear programming method. Several structural design systems serve as the illustrative examples. The presented strategy is suggested as appropriate for solving a generalized mixed-discrete optimization problem.

Genetic algorithms for solving mixed-discrete optimization problems

This paper presents the applications of genetic algorithms to nonlinear constrained mixed-discrete optimization problems that occur in engineering design. Genetic algorithms are heuristic combinatorial optimization strategies. Several strategies are adopted to enhance the search efficiency and reduce the computational cost. The effectiveness, robustness, and fast convergence of modified genetic algorithms are demonstrated through the results of several examples. Moreover, genetic algorithms are more capable of locating the global optimum.