Nonlinear Discrete Optimization Research Articles

Finite-Alphabet Precoding for Massive MU-MIMO With Low-Resolution DACs

Massive multiuser multiple-input multiple-output (MU-MIMO) systems are expected to be the core technology in fifth-generation wireless systems because they significantly improve spectral efficiency. However, the requirement for a large number of radio frequency (RF) chains results in high hardware costs and power consumption, which obstruct the commercial deployment of massive MIMO systems. A potential solution is to use low-resolution digital-to-analog converters (DAC)/analog-to-digital converters for each antenna and RF chain. However, using low-resolution DACs at the transmit side directly limits the degree of freedom of output signals and thus poses a challenge to the precoding design. In this study, we develop efficient and universal algorithms for a downlink massive MU-MIMO system with finite-alphabet precodings. Our algorithms are developed based on the alternating direction method of multipliers (ADMM) framework. The original ADMM does not converge in a nonlinear discrete optimization problem. The primary cause of this problem is that the alternating (update) directions in ADMM on one side are biased, and those on the other side are unbiased. By making the two updates consistent in an unbiased manner, we develop two algorithms called iterative discrete estimation (IDE) and IDE2: IDE demonstrates excellent performance and IDE2 possesses a significantly low computational complexity. Compared with state-of-the-art techniques, the proposed precoding algorithms present significant advantages in performance and computational complexity.

Discrete time-variant nonlinear optimization and system solving via integral-type error function and twice ZND formula with noises suppressed

In this paper, by using integral-type error function and twice zeroing neural-dynamics (or termed, Zhang neural-dynamics, ZND) formula, continuous-time advanced zeroing neural-dynamics (CT-AZND) model is proposed for solving the continuous time-variant nonlinear optimization problem. Furthermore, a discrete-time advanced zeroing neural-dynamics (DT-AZND) model is first proposed, analyzed, and investigated for solving the discrete time-variant nonlinear optimization (DTVNO) problem. Theoretical analyses show that the proposed DT-AZND model is convergent, and its steady-state residual error has an \(O(g^3)\) pattern with g denoting the sampling gap. In addition, in the presence of various kinds of noises, the proposed DT-AZND model possesses advantaged performance. In detail, the proposed DT-AZND model converges toward the time-variant theoretical solution of the DTVNO problem with \(O(g^3)\) residual error in the presence of an arbitrary constant noise and has excellent ability to suppress linear-form time-variant noise and bounded random noise. Illustrative numerical experiments further substantiate the efficacy and advantage of the proposed DT-AZND model for solving the DTVNO problem.

Research of Enterprise Storage Ecosystem Based on Storage Theory and Nonlinear Discrete Optimization

Warehousing and transferring strategies are an important part of business operations. The issue of optimal warehousing and transferring strategy is studied in this paper. Wal-Mart in Wuhan serves as an example to establish a (s, S) random storage strategy model, a Markov chain model, and a nonlinear discrete programming model, aiming at maximizing the profit per cycle of every branch and further maximizing the company’s total profit per cycle. Among them, the random storage strategy model establishes a security zone of inventory for every branch, that is, it can meet consumers’ demand without spending too much storage costs. The Markov chain model is used to get the probability of losing sales opportunities in every branch. The nonlinear discrete programming model takes into account the horizontal transferring among branches, which further maximizes the company’s overall profit expectations. The three models above can be used to formulate inventory strategies, assess risks, and provide advice for every branch in order to form a complete storage ecosystem and provide constructive suggestions for the company’s operations.

Discrete Nonlinear Optimization by State-Space Decompositions

This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2849 . This paper was accepted by Yinyu Ye, optimization.

Cohort intelligence algorithm for discrete and mixed variable engineering problems

In this study, the performance of an emerging socio inspired metaheuristic optimization technique referred to as Cohort Intelligence (CI) algorithm is evaluated on discrete and mixed variable nonlinear constrained optimization problems. The investigated problems are mainly adopted from discrete structural optimization and mixed variable mechanical engineering design domains. For handling the discrete solution variables, a round off integer sampling approach is proposed. Furthermore, in order to deal with the nonlinear constraints, a penalty function method is incorporated. The obtained results are promising and computationally more efficient when compared to the other existing optimization techniques including a Multi Random Start Local Search algorithm. The associated advantages and disadvantages of CI algorithm are also discussed evaluating the effect of its two parameters namely the number of candidates, and sampling space reduction factor.

Discrete-Phase Constant Envelope Precoding for Massive MIMO Systems

We consider downlink of a multiuser massive multiple-input multiple-output (MIMO) system and focus on reducing the hardware costs by using a single common power amplifier and separate phase shifters (PSs) for antenna front-ends. In the previous literature, the use of analog PSs in this setup has been considered. Here, we study the use of practical digital PSs, which only support a limited set of discrete phases. Considering the sum of interference powers as a metric, we formulate the corresponding nonlinear discrete optimization problem and solve for the phases to be used during transmission. We devise a low-complexity algorithm, which employs a trellis structure providing suboptimal, but efficient and effective solutions. We demonstrate via examples that the proposed solutions have comparable performance to conventional analog PS-based algorithms. Furthermore, we prove that by utilizing discrete-phase constant envelope precoding, the interference can be made arbitrarily small by increasing the number of antennas. Therefore, the asymptotic gains promised by massive MIMO systems are preserved. We also obtain closed-form expressions for the rate loss due to errors in the phase and amplitude of the PSs, for both low and high SNR regimes.

Community detection in social networks with node attributes based on multi-objective biogeography based optimization

Detecting communities in complex networks is one of the most important issues considered when analyzing these kinds of networks. A majority of studies in the field of community detection tend to detect communities through analyzing linkages of the networks. What this paper aims to achieve is to reach to a trade-off between similarity of nodes' attributes and density of connections in finding communities of social networks with node attributes. Since the community detection problem can be modeled as a seriously non-linear discrete optimization problem, we have hereby proposed a multi-objective discrete Biogeography Based Optimization (BBO) algorithm to find communities in social networks with node attributes. This algorithm uses the Pareto-based approach for community detection. Also, we introduced a new metric, SimAtt, to measure the similarity of node attributes in a community of a network and used it along with Modularity, which considers the linkage structure of a network to detect communities, as the two objective functions of the proposed method to be maximized. In the proposed method, a two phase sorting strategy is introduced which uses the non-dominated sorting and Crowding-distance to sort the generated solution of a population in each iteration. Moreover, this paper introduces a method for mutation probability approximation and uses a chaotic mechanism to dynamically tune the mutation probability in each iteration. Additionally, two novel strategies are introduced for mutation in unweighted and weighted networks. Since the final output of the proposed method is a set of non-dominated (Pareto-optimal) solutions, a metric named alpha_SAM is proposed to determine the best compromise solution among these non-dominated ones. Quantitative evaluations based on extensive experiments on 14 real-life data sets reveals that the method presented in this study achieves favorable results which are quite superior to other relevant algorithms in the literature.

A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

The problem of allocating different types of vehicles for transporting a set of products from a manufacturer to its depots/cross docks, in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles, with a variable transportation cost and a fixed cost in which a discount mechanism is applied on the fixed part of the transportation costs. It is assumed that the number of available vehicles is limited for some types. A mathematical programming model in the form of the discrete nonlinear optimization model is proposed. A hybrid dynamic programming algorithm is developed for finding the optimal solution. To increase the computational efficiency of the solution algorithm, several concepts and routines, such as the imbedded state routine, surrogate constraint concept, and bounding schemes, are incorporated in the dynamic programming algorithm. A real world case problem is selected and solved by the proposed solution algorithm, and the optimal solution is obtained.

Stability of discrete time recurrent neural networks and nonlinear optimization problems

We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems produce rather weak results. The method mentioned above is proved to be more powerful. It involves a multi-step procedure with maximization of special nonconvex functions over polytopes on every step. We derive conditions which guarantee an existence of at most one point of local maximum for such functions over every hyperplane. This nontrivial result is valid for wide range of neuron transfer functions.

Mixed-Integer Nonlinear Programming Model for Nonlinear Discrete Optimization of Project Schedules under Restricted Costs

AbstractThis paper presents the mixed-integer nonlinear programming (MINLP) model for nonlinear discrete optimization of project schedules under restricted costs. The proposed model includes cost-objective function, generalized precedence relationship constraints, project duration restraints, logical conditions, and cost restrictions. The MINLP model allows inclusion of a wide variety of nonlinear expressions and provides the exact optimal output data for construction project management, such as a Gantt chart, histogram, and S-curve of total project cost. The novelty of the contribution is that the planner is now enabled to perform the exact optimal scheduling of project activities simultaneously with scheduling of nonlinearly restricted total project cost at each discrete working time unit. At this point, the restrictions can be set on increments and cumulative values of total project cost. A set of application examples is shown in this paper to demonstrate the advantages of the proposed model.

Optimal Use of Existing Distribution Feeders to Accommodate Transportation Electrification

An analytical method that can be used to study the optimal topology and maximum capacity of the existing distribution network to accommodate electric vehicle (EV) charging demands is presented in this paper. In order to facilitate a large number of EV integrations, the feeder reconfiguration problem is formulated as a discrete nonlinear optimization problem that finds optimal feeders' tie switch locations and their on/off schedule to minimize operation costs and comply with the system operation constraints. A novel stochastic dynamic programming technique is adopted to solve the problem that includes various uncertainties associated with feeder baseline and EV charging loads. Simulation results obtained from an 84-bus feeder test system have indicated that for a case with 20% EV penetration to a 70% capacity utilization feeder area, a 10.78% reduction of operation cost and a 14.4% decrease in maximum feeder utilization can be obtained by distribution feeder reconfiguration.

Considering uncertainty in the fuel cell and capacitor allocation problem using a novel self adaptive modification approach

Optimal Fuel Cell (FC) allocation and Shunt Capacitor Placement (SCP) are two significant and precious strategies that can improve the system performance greatly. In order to make use of these two useful strategies efficiently, they should be investigated in one single framework simultaneously. Thi s paper aims to solve the optimal allocation and sizing of FC and SCP problems for reducing the total system costs. In order to make the analysis practical, the uncertainties of the active and reactive loads are modeled using the probabilistic load flow based on point estimate method (PEM). In this way, each random variable is replaced by its appropriate probability density function to capture the uncertainty effects in the analysis. The problem investigated is a kind of discrete nonlinear and non-convex optimization problem that requires a powerful optimizer to escape from the several local optima. In this regard, this work suggests a new optimization method based on Krill Herd (KH) algorithm to solve the problem deeply. A new self-adaptive modification method is also proposed to improve the total search ability of the algorithm. The feasibility and satisfying performance of the proposed method is examined on the IEEE 69-bus test system.

Gait Generation for the Compass-Type Biped Robot on General Irregular Grounds Via a New Blending Method of Discrete Mechanics and Nonlinear optimization

This paper develops a unified gait generation method based on discrete mechanics and nonlinear optimization technique for the compass-type biped robot on general irregular grounds. First, we derive the models of continuous-time/discrete-time compass-type biped robot (DCBR/CCBR). Next, a discrete gait generation problem on an irregular ground for the DCBR as a finite-dimensional nonlinear optimal control problem is formulated, and a solving method of it with the sequential quadratic programming is presented. Then, a transformation method of a discrete-time input into a continuous-time one is shown. Finally, some numerical simulations are illustrated to verify the effectiveness of our new approach. As a result, it is confirmed that the new method can generate stable gaits for the CCBR on various irregular grounds.

Managing Underperformance Risk in Project Portfolio Selection

We consider a project selection problem where each project has an uncertain return with partially characterized probability distribution. The decision maker selects a feasible subset of projects so that the risk of the portfolio return not meeting a specified target is minimized. To model and evaluate this risk, we propose and justify a general performance measure, the underperformance riskiness index (URI). We define a special case of the URI, the entropic underperformance riskiness index (EURI), for the project selection problem. We minimize the EURI of the project portfolio, which is the reciprocal of the absolute risk aversion (ARA) of an ambiguity-averse individual with constant ARA who is indifferent between the target return with certainty and the uncertain portfolio return. The EURI extends the riskiness index of Aumann and Serrano (2008) by incorporating the target and distributional ambiguity, and controls the underperformance probability (UP) for any target level. Our model includes correlation and interaction effects such as synergies. Since the model is a discrete nonlinear optimization problem, we derive the optimal solution using Benders decomposition techniques. We show that computationally efficient solution of the model is possible. Furthermore, the project portfolios generated by minimizing the underperformance risk are more than competitive in achieving the target with those found by benchmark approaches, including maximization of expected return, minimization of UP, mean-variance analysis, and maximization of Roy’s safety-first ratio (1952). When there is only a single constraint for the budget, we describe a heuristic which routinely provides project portfolios with near-optimal underperformance risk.

An optimization model to agroindustrial sector in antioquia (Colombia, South America)

This paper develops a proposal of a general optimization model for the flower industry, which is defined by using discrete simulation and nonlinear optimization, whose mathematical models have been solved by using ProModel simulation tools and Gams optimization. It defines the operations that constitute the production and marketing of the sector, statistically validated data taken directly from each operation through field work, the discrete simulation model of the operations and the linear optimization model of the entire industry chain are raised. The model is solved with the tools described above and presents the results validated in a case study.

Circular Obstacle Avoidance Control of the Compass-Type Biped Robot Based on a Blending Method of Discrete Mechanics and Nonlinear Optimization

This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the circular obstacle is derived. Next, an optimal control problem for the discrete compass-type robot is formulated and a solving method of the problem by the sequential quadratic programming is presented in order to calculate a discrete control input. Then, a transformation method that converts a discrete control input into a continuous zero-order hold input via discrete Lagrange-d’ Alembert principle is explained. From the results of numerical simulations, it turns out that obstacle avoidance control for the continuous compass-type robot can be achieved by the proposed method.

Reliability constrained generation expansion planning by a modified shuffled frog leaping algorithm

Abstract This paper introduces a modified shuffled frog leaping algorithm (MSFLA) to solve reliability constrained generation expansion planning (GEP) problem. GEP, as a crucial issue in power systems, is a highly constrained non-linear discrete dynamic optimization problem. To solve this complicated problem by MSFLA, a new frog leaping rule, associated with a new strategy for frog distribution into memeplexes, is proposed to improve the local exploration and performance of the SFLA. Furthermore, integer encoding, mapping procedure and penalty factor approach are implemented to improve the efficiency of the proposed methodology. To show the effectiveness of the method, it is applied to a test system for two planning horizon of 12 and 24 years. For the sake of methodology validation, an ordinary SFLA as well as a Genetic Algorithm (GA) are both applied to solve the same problem. Simulation results show the advantages of the proposed MSFLA over the SFLA and GA.

Predictive Dispatch Across Time of Hybrid Isolated Power Systems

The paper proposes a methodology for the optimal dispatch of energy sources in hybrid and isolated energy systems. The proposed approach is based on the formulation and solution of a nonlinear discrete optimization problem aimed at optimizing input and output time trajectories for a set of combined generating and storage technologies. Loads and interruptible loads are among controlled variables, and are modeled according to their interruption costs. The approach is general enough to be applied to any hybrid system configuration and was developed having in mind the complex hybrid system architectures comprising several competing storage technologies (battery, pumping, and hydrogen). Test results are aimed at showing the feasibility of the proposed methodology, comparing optimal trajectories to suboptimal system behavior given by load-following strategies.

Optimal reconfiguration and capacitor placement for power loss reduction of distribution system using improved binary particle swarm optimization

Optimal reconfiguration and capacitor placement are used to reduce power losses and keep the voltage within its allowable interval in power distribution systems considering voltage, current, and radial condition constraints. It is needed to solve two nonlinear discrete optimization problems simultaneously, so an intelligent algorithm is used to reach an optimum solution for network power losses. An effective method and a new optimization algorithm using “improved binary PSO” is presented and discussed to minimize power losses in distribution network by simultaneous networking of reconfiguration and capacitor placement. The proposed model uses binary strings which represent the state of the network switches and capacitors. The algorithm is applied and tested on 16- and 33-bus IEEE test systems to find the optimum configuration of the network with regard to power losses. Five different cases are considered and the effectiveness of the proposed technique is also demonstrated with improvements in power loss reduction compared to other previously researched methods, through MATLAB under steady-state conditions.

Soccer league competition algorithm: A novel meta-heuristic algorithm for optimal design of water distribution networks

Water distribution networks are one of the most important elements in the urban infrastructure system and require huge investment for construction. Optimal design of water systems is classified as a large combinatorial discrete non-linear optimization problem. The main concern associated with optimization of water distribution networks is related to the nonlinearity of discharge-head loss equation, availability of the discrete nature of pipe sizes, and constraints, such as conservation of mass and energy equations. This paper introduces an efficient technique, entitled Soccer League Competition (SLC) algorithm, which yields optimal solutions for design of water distribution networks. Fundamental theories of the method are inspired from soccer leagues and based on the competitions among teams and players. Like other meta-heuristic methods, the proposed technique starts with an initial population. Population individuals (players) are in two types: fixed players and substitutes that all together form some teams. The competition among teams to take the possession of the top ranked positions in the league table and the internal competitions between players in each team for personal improvements are used for simulation purpose and convergence of the population individuals to the global optimum. Results of applying the proposed algorithm in three benchmark pipe networks show that SLC converges to the global optimum more reliably and rapidly in comparison with other meta-heuristic methods.