Multi-agent Optimization Algorithm Research Articles

Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

Integrating the stochastic multiproject scheduling and material ordering problems for offshore projects: multiagent optimization methodology

Purpose The purpose of this study is to develop an integrated model for the stochastic multiproject scheduling and material ordering problems, where some of the prominent features of offshore projects and their environmental-degrading effects have been embraced as well. The durations of activities are uncertain in this model. The developed formulation is tri-objective that seeks to minimize the expected time, total cost and CO2 emission of all projects.Design/methodology/approach A new version of the multiobjective multiagent optimization (MOMAO) algorithm has been proposed to solve the amalgamated model. To empower the MOMAO, various procedures of this algorithm have been modified based on the multiattribute utility theory (MAUT) technique. Along with the MOMAO, this study has employed four other meta-heuristic methodologies to solve the model as well.Findings The outputs of the MOMAO have been put to test against four other optimizers in terms of convergence, diversity, uniformity and computation times. The results of the Mean Ideal Distance (MID) metric have revealed that the MOMAO has strongly prevailed its rival optimizers. In terms of diversity of the acquired solutions, the MOMAO has ranked the first among all employed optimizers since this algorithm has offered the best solutions in 56.66 and 63.33% of the test problems regarding the diversification metric and hyper-volume metrics. Regarding the uniformity of results, which is measured through the spacing metric (SP), the MOMAO has presented the best SP values in more than 96% of the test problems. The MOMAO has needed more computation times in comparison to its rivals.Practical implications A real case study comprising two concurrent offshore projects has been offered. The proposed formulation and the MOMAO have been implemented for this case study, and their effectiveness has been appraised.Originality/value Very few studies have focused on presenting an integrated formulation for the stochastic multiproject scheduling and material ordering problems. The model embraces some of the characteristics of the offshore projects which have not been adequately studied in the literature. Limited capacities of the offshore platforms and cargo vessels have been embedded in the proposed model. The offshore platforms have spatial limitations in storing the required materials. The vessels are also capacitated and they also have limited shipment capacities. Some of the required materials need to be transported from the base to the offshore platform via a fleet of cargo vessels. The workforces and equipment can become idle on the offshore platform due to material shortage. Various offshore-related costs have been integrated as a minimization objective function in the model. The cargo vessels release CO2 detrimental emissions to the environment which are sought to be minimized in the developed formulation. To the best of the authors' knowledge, the MOMAO has not been sufficiently employed as a solution methodology for the stochastic multiproject scheduling and material ordering problems.

Scheduling operations in a large hospital by multiple agents

The scheduling of operations in a large hospital is performed jointly by several groups of people, each with its own objective and constraints. It is a two-phase process, starting with the allocation of operating rooms to wards, and followed by the scheduling of operations in each operating room of the hospital on each day. The final schedule must satisfy all inter-ward hard constraints, such as the allocation of anesthetists, nurses, and equipment to operations that are taking place in parallel, and ideally, it should also address soft constraints such as taking the urgency and complexity of operations into consideration.This study contributes to the ongoing effort of adapting multi-agent optimization models and algorithms to real-world applications by modeling the problems in both phases as distributed constraint optimization problems (DCOPs), with different properties. The first phase includes partially cooperative ward-representing agents, allocating operating rooms for daily usage among themselves. In the second phase, ward-representing agents interact with agents representing constraining elements, in order to generate daily operation schedules for each operating room, thus forming a unique bipartite constraint graph. On one side are the ward representatives, while on the other are the agents representing the constraining resources. Each agent has a non-trivial local problem to solve, and its solution serves as the proposed assignment in the distributed algorithm.The study begins by discussing the properties required of the algorithms needed to solve the two phases. It then proposes adjustments to existing distributed partially cooperative algorithms and local search algorithms to solve these problems, and compares the results of different variants of these algorithms. The results obtained for both phases emphasize that successful collaboration is predicated on two requirements: that agents hold consistent information regarding their peers’ states and that the degree of exploration undertaken by the algorithm is restricted in order to produce high-quality solutions.

Decentralized online convex optimization with compressed communications

Due to the iterative information exchange between agents, decentralized multi-agent optimization algorithms often incur large communication overhead, which is not affordable in many practical systems with scarce resources. To address this communication bottleneck, we compress the exchanged information between neighboring agents to solve decentralized online convex optimization problem, where each agent has a time-varying local loss function and the goal is to minimize the accumulated global loss by choosing actions sequentially. We develop a decentralized online gradient descent algorithm based on compressed communications, where the compression operators can reduce the amount of data to be sent significantly. Error-compensation technique is utilized to mitigate the error accumulation caused by the communication compression. We further analyze the performance of the proposed algorithm. It is shown that the regret is bounded from above by O(T) (T is the time horizon), which is the same as (in order sense) the regret bound for vanilla decentralized online gradient descent with perfect communication. Thus, the proposed algorithm is capable of reducing the communication overhead remarkably without much degradation of the optimization performance. This is further corroborated by numerical experiments, where compressed communication reduces the number of transmitted bits by an order of magnitude without compromising the optimization performance.

A multi-agent optimization algorithm and its application to training multilayer perceptron models

A multi-agent optimization algorithm and its application to training multilayer perceptron models

Application of a Novel Multi-Agent Optimization Algorithm Based on PID Controllers in Stochastic Control Problems

The article considers the problem of finding the optimal on average control of the trajectories of continuous stochastic systems with incomplete feedback. This class of problems includes control problems in which the initial states are described by a given distribution law; random effects on the control object are taken into account; and it is also assumed that information is available only about some coordinates of the state vector. As special cases, the problems of determining the optimal open-loop control and control with complete feedback in the presence of information about all state vector coordinates are considered. A method for parameterization of the control law based on expansions in various systems of basis functions is described. The problem of parametric optimization obtained is solved using a new metaheuristic multi-agent algorithm based on the use of extended PID (Proportional-Integral-Derivative) controllers to control the movement of agents. Solutions of three model examples of control of nonlinear continuous stochastic systems with interval constraints on the amount of control for all possible cases of state vector awareness are presented.

Multi-agent optimal control algorithm nonlinear switching systems on the example of electric rolling stock

The article deals with the problem of optimizing the control of the switching system on the example of electric rolling stock (ERS) of railways. The processes in such a system have two levels of description: at the lower level, describing the physical features of its operation, in each mode it is represented by differential or difference equations, and at the upper level – a discrete-logical process of switching modes. A generalized formulation of the problem is proposed, which is typical for many types of multimode dynamic objects, in particular, ERS railway. It involves the search for an optimal management strategy as a solution to the problem of structural-parametric synthesis. A multi-agent optimization algorithm for its solution is proposed, which searches for the global extremum of the functional defined on the set of permissible trajectories of the object. Computational experiments with the reference model of the control object have shown that the use of the developed algorithm makes it possible to improve the quality of control compared to the one used earlier, which is expressed in the potential savings of electricity for train traction by about 2%.

Reduction of magnetic field level in residential old buildings from overhead power lines by means of active screening

Aim. Reduction of the magnetic field induction to the level of modern sanitary standards by means of active screening in residential old buildings which are located near existing typical overhead power lines are considered. Active shielding of the magnetic field inside a single-storey and multi-storey building is considered. During the design the number, configurations, spatial arrangement of the shielding windings, as well as the currents in the shielding windings were determined. Methodology. The design problem for the system of active shielding reduced to solving the minimax vector optimization problem. The vector of objective function in this minimax problem is calculated based on Biot-Savart's law. The solution of this problem is based on multi-agent optimization algorithms. Results. The results of theoretical and experimental studies of the systems of active shielding of the magnetic field generated by various overhead power lines inside a single and multi-storey building are presented. Originality. The possibility of reducing the induction of the initial magnetic field inside the shielded space to the level of sanitary standards is shown. Practical value. From the point of view of the practical implementation for a reasonable choice of the number and spatial arrangement of shielding windings of systems for active shielding of the magnetic field generated by various overhead power lines inside residential buildings of different storey’s are given.

A multi-objective multi-agent optimization algorithm for the multi-skill resource-constrained project scheduling problem with transfer times

This paper addresses the Multi-Skill Resource-Constrained Project Scheduling Problem with Transfer Times (MSRCPSP-TT). A new model has been developed that incorporates the presence of transfer times within the multi-skill RCPSP. The proposed model aims to minimize project’s duration and cost, concurrently. The MSRCPSP-TT is an NP-hard problem; therefore, a Multi-Objective Multi-Agent Optimization Algorithm (MOMAOA) is proposed to acquire feasible schedules. In the proposed algorithm, each agent represents a feasible solution that works with other agents in a grouped environment. The agents evolve due to their social, autonomous, and self-learning behaviors. Moreover, the adjustment of environment helps the evolution of agents as well. Since the MSRCPSP-TT is a multi-objective optimization problem, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used in different procedures of the MOMAOA. Another novelty of this paper is the application of TOPSIS in different procedures of the MOMAOA. These procedures are utilized for: (1) detecting the leader agent in each group, (2) detecting the global best leader agent, and (3) the global social behavior of the MOMAOA. The performance of the MOMAOA has been analyzed by solving several benchmark problems. The results of the MOMAOA have been validated through comparisons with three other meta-heuristics. The parameters of algorithms are determined by the Response Surface Methodology (RSM). The Kruskal–Wallis test is implemented to statistically analyze the efficiency of methods. Computational results reveal that the MOMAOA can beat the other three methods according to several testing metrics. Furthermore, the impact of transfer times on project’s duration and cost has been assessed. The investigations indicate that resource transfer times have significant impact on both objectives of the proposed model.

Performance evaluation and analysis of distributed multi-agent optimization algorithms with sparsified directed communication

There has been significant interest in distributed optimization algorithms, motivated by applications in Big Data analytics, smart grid, vehicle networks, etc. While there have been extensive theory and theoretical advances, a proportionally small body of scientific literature focuses on numerical evaluation of the proposed methods in actual practical, parallel programming environments. This paper considers a general algorithmic framework of first and second order methods with sparsified communications and computations across worker nodes. The considered framework subsumes several existing methods. In addition, a novel method that utilizes unidirectional sparsified communications is introduced and theoretical convergence analysis is also provided. Namely, we prove R-linear convergence in the expected norm. A thorough empirical evaluation of the methods using Message Passing Interface (MPI) on a High Performance Computing (HPC) cluster is carried out and several useful insights and guidelines on the performance of algorithms and inherent communication-computational trade-offs in a realistic setting are derived.

Hierarchical Multi-Agent Optimization for Resource Allocation in Cloud Computing

In cloud computing, an important concern is to allocate the available resources of service nodes to the requested tasks on demand and to make the objective function optimum, i.e., maximizing resource utilization, payoffs and available bandwidth. This paper proposes a hierarchical multi-agent optimization (HMAO) algorithm in order to maximize the resource utilization and make the bandwidth cost minimum for cloud computing. The proposed HMAO algorithm is a combination of the genetic algorithm (GA) and the multi-agent optimization (MAO) algorithm. With maximizing the resource utilization, an improved GA is implemented to find a set of service nodes that are used to deploy the requested tasks. A decentralized-based MAO algorithm is presented to minimize the bandwidth cost. We study the effect of key parameters of the HMAO algorithm by the Taguchi method and evaluate the performance results. When compared with genetic algorithm (GA) and fast elitist non-dominated sorting genetic (NSGA-II) algorithm, the simulation results demonstrate that the HMAO algorithm is more effective than the existing solutions to solve the problem of resource allocation with a large number of the requested tasks. Furthermore, we provide the performance comparison of the HMAO algorithm with the first-fit greedy approach in on-line resource allocation.

Distributed Zero-Order Algorithms for Nonconvex Multiagent Optimization

Distributed multi-agent optimization finds many applications in distributed learning, control, estimation, etc. Most existing algorithms assume knowledge of first-order information of the objective and have been analyzed for convex problems. However, there are situations where the objective is nonconvex, and one can only evaluate the function values at finitely many points. In this paper we consider derivative-free distributed algorithms for nonconvex multi-agent optimization, based on recent progress in zero-order optimization. We develop two algorithms for different settings, provide detailed analysis of their convergence behavior, and compare them with existing centralized zero-order algorithms and gradient-based distributed algorithms.

Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize

In this paper, we consider distributed convex optimization problems on multi-agent networks. We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution. Our approach can be applied to both synchronous and asynchronous communication protocols. Specifically, we propose the distributed subgradient with uncoordinated dynamic stepsizes (DS-UD) algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol. Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem. Moreover, the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works. Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.

Solving Routing Problem Using Improved Camel Herds Algorithm

This paper introduces a new adaptive, distributed routing algorithm based on the Improved Camel Herds Algorithm (CHA). It is an intelligent, multi-agent optimization algorithm that is inspired by the behavior of camels and how they search for food in their desert environment. We examine its ability to solve the routing problem in switched networks: finding the shortest path in the process of transferring data packets between networks. Many meta-heuristic algorithms have been previously proposed to address the routing problem, and this proposed approach is compared with three well-known algorithms (ACO, GA, PSO) on ten graphs (weighted, integer, and not negative) and datasets with various size of nodes (from 10 nodes to 297 nodes). Three performance criteria were used to evaluate the performance of the algorithms (mean relative error, standard deviation, and number of function evaluations). The results proved that the performance of the proposed algorithm is both promising and competitive with other algorithms.

Benchmark analysis of novel multi-agent optimization algorithm using linear regulators for agents motion control

The aim of this paper is to develop algorithm and software for a novel multi-agent constrained global optimization method. In multi-agent algorithms, the solution search area is populated with agents. Some transformations occur over them, which lead to a global extremum. It was proposed to take as a basis the use of linear regulators to control the movement of agents group. At each stage of the algorithm, a search is made by closed loop agents control with various types of criteria. Using criteria of various types, a more detailed study of the solution search area and finding a global extremum is provided. This is the main feature and novelty of the algorithm under consideration. The method efficiency is studied on a standard set of test functions of two variables with a complex structure of level lines using the software developed. Efficiency analysis is carried out for Schweffel function and multifunction from the benchmark set. During the study, statistical characteristics were calculated, according to which the most suitable parameters were selected. The results obtained indicate that the algorithm successfully copes with such problems and can be used, for example, for problems in the theory of optimal control of dynamic systems.

Fenchel Dual Gradient Methods for Distributed Convex Optimization Over Time-Varying Networks

To date, a large collection of distributed algorithms for convex multi-agent optimization have been reported, yet only few of them converge to an optimal solution at guaranteed rates when the topologies of the agent networks are time-varying. Motivated by this, we develop a family of distributed Fenchel dual gradient methods for solving strongly convex yet non-smooth multi-agent optimization problems with nonidentical local constraints over time-varying networks. The proposed algorithms are constructed based on the application of weighted gradient methods to the Fenchel dual of the multiagent optimization problem. They are able to drive all the agents to dual optimality at an O(1/k) rate and to primal optimality at an O(1/√k) rate under a standard network connectivity condition. The competent convergence performance of the Fenchel dual gradient methods is demonstrated via numerical examples.

Using artificial intelligence to optimize intermodal networking of organizational agents within the digital economy

The problems of forming a digital economy supersystem have been analyzed by the authors using a key business model of sharing digital assets by organizational agents based on the convergence of telematic, computing and information services with the final output of a complex of managed digital objects to a new quality control based on the M2M principle integration. The integration of standardized network infrastructures allows the transformation of traditional linear-hierarchical chains of management transactions in a network of transactions of digital objects that perform intelligent interaction without human intervention through IP-like connections. The introduction of universal shells of any business process from the processing of primary data to processing in the deep region with the use of advanced multi-agent optimization algorithms of the next [after 3G] generation [based on 4G, 5G, etc.], implemented within the electronic micro-, meso-and macrocontent allows us to ensure the stability of the super system within the optimal values of the activities of controlled digital objects due to the increased possibilities of observation and control.

HIGH VOLTAGE POWER LINES MAGNETIC FIELD SYSTEM OF ACTIVE SHIELDING WITH COMPENSATION COIL DIFFERENT SPATIAL ARRANGEMENT

Aim. The synthesis of single-circuit system of active shielding of magnetic field, generated by group of high voltage power lines, with different spatial arrangement of shielding coil. Methodology. The synthesis is based on the decision of a multi-criteria stochastic game, in which the vector payoff is calculated on the basis of the Maxwell equations solutions in the quasi-stationary approximation. The game decision is based on the stochastic multiagent optimization algorithms by multiswarm particles. The initial parameters for the synthesis of active shielding system are the location of the high voltage power lines with respect to the shielding space, geometry and number of shielding coils, operating currents, as well as the size of the shielding space and normative value magnetic flux density, which should be achieved as a result of shielding. The objective of the synthesis of the active shielding system is to determine their number, configuration, spatial arrangement, wiring diagrams and shielding coils currents, setting algorithm of the control systems as well as the resulting of the magnetic flux density value at the points of the shielding space. Results. Three variant of single-circuit robust system of active shielding with different spatial arrangement of shielding coil synthesis results for reduction of a magnetic field generated by group of high voltage power lines is given. The possibility of a significant reduction in the level of magnetic flux density of the magnetic field source within and reducing the sensitivity of the system to uncertainty of the plant parameters is given. Originality. For the first time carried out the synthesis, theoretical and experimental research of the robust system of active shielding of magnetic field generated by group of high voltage power lines with different spatial arrangement of compensation coil. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of shielding coil of robust single-circuit system of active shielding of the magnetic field generated by the group of high voltage power lines is given.

Distributed Proximal Algorithms for Multiagent Optimization With Coupled Inequality Constraints

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set constraint and coupled inequality constraints whose information is only partially accessible to each agent. For this problem, a distributed proximal-based algorithm, called distributed proximal primal-dual (DPPD) algorithm, is proposed based on the celebrated centralized proximal point algorithm. It is shown that the proposed algorithm can lead to the global optimal solution with a general stepsize, which is diminishing and non-summable, but not necessarily square-summable, and the saddle-point running evaluation error vanishes proportionally to $O(1/\sqrt{k})$, where $k>0$ is the iteration number. Finally, a simulation example is presented to corroborate the effectiveness of the proposed algorithm.

A distributed Newton–Raphson-based coordination algorithm for multi-agent optimization with discrete-time communication

This paper proposes a novel distributed continuous-time Newton–Raphson algorithm for distributed convex optimization problem, where the components of the goal are obtainable at different agents. To accelerate convergence speed, we focus on introducing Newton descent idea in our algorithm and extending it in a distributed setting. It is proved that the proposed algorithm can converge to the global optimal point with exponential convergence rate under weight-balanced directed graphs. Motivated by practical considerations, an event-triggered broadcasting strategy is further developed for each agent. Therein, the implementation of communication is driven by the designed triggered condition monitored by agents. Consequently, the proposed continuous-time algorithm can be executed with discrete-time communication, thus being able to greatly save communication expenditure. Moreover, the strategy is proved to be free of Zeno behavior. Eventually, the simulation results illustrate the advantages of the proposed algorithm.