Separable convexification and DCA techniques for capacity and flow assignment problems

Capacity assignment in multiservice packet networks with soft maximum waiting time guarantees

A typical operating environment of a packet switching (store-and-forward) computer communication network is that it is shared by many users with different classes of packets. Packets may be classified in a very general fashion by types of users, messages, applications, transactions, response time requirements, packet parameters such as packet rate and length, and by network parameters such as source-destination and path length. A well-designed network must provide access and performance assurance to all packet classes. This paper presents a heuristic algorithm for designing such a communication network. The algorithm presented contains heuristic algorithms for discrete link capacity assignment, priority assignment, and flow assignment problems with an additional feature which allows one to alter network topology interactively. Sample results from applications of the overall network design are also given.

Survivable ATM mesh networks: Techniques and performance evaluation

Due to the emergence of Software Defined Networking (SDN) with the idea of centralized control over computer networks, the Capacity and Flow Assignment Problem (CFA) may be approached in a classical non-distributed fashion in real-life scenarios. The question arises whether a heuristical approach to this NP-complete problem is of any use in practice.

Protected working capacity envelope concept has been proposed to simplify network management and operation in survivable WDM networks. Dynamic lightpath provisioning within working capacity envelope is only required to perform shortest path routing algorithm. Based on PWCE concept, we propose an efficient approximation approach, called Lagrangean relaxation with binary exponential reduction heuristics (LBER), aimed, to resolve the routing and capacity assignment (RCA) problem in survivable WDM networks to protect any single link failure. The task is first formulated as a mixed integer non-linear optimization problem in which the bottleneck link blocking probability for call setup is to be minimized. By sequentially solving a series of Lagrangean relaxation problems, the range of uncertainty of target blocking probability is reduced by half between the solutions of two adjacent problems such that the near optimal solution can be obtained in short time. We conduct a performance study on the proposed algorithms under different parameter settings. We further draw comparisons between LBER and a minimum working hop heuristic approach via experiments over two well known benchmark networks. Numerical results demonstrate that LBER outperforms minimum working hop approach for networks with both uniform and non-uniform demand distributions.

The use of multiple objective genetic algorithm in self-healing network

To aim at the parameter design and investment optimization of hybrid active power filter, then the price, reactive power compensation method and filter effect are all considered, A new mixed algorithm of genetic theory and particle swarm optimization has been proposed in this paper. Based on these, multi-object mathematical model of capacity assignment is created and penalty function theory is applied, so multi-objective design is converted into single-objective design, the problem of capacity assignment is simple and flexible. Secondly, simulation analysis is used by PSCAD/EMTDC, simulation result demonstrates that cost performance of hybrid active power filter is elevated according to the method. Finally, experimental results and contrastive analysis are presented to confirm the above-mentioned claims.

This thesis treats different aspects of the class of Mixed-Integer Optimal Control Problems (MIOCPs). These are optimization problems that combine the difficulties of underlying dynamic processes with combinatorial decisions. Typically, these combinatorial decisions are realized as switching decisions between the system’s different operations modes. During the last decades, direct methods emerged as the state-of-the-art solvers for MIOCPs. The formulation of a valid, tight and dependable integral relaxation, i.e., the formulation of a model for fractional values, plays an important role for these direct solution methods. We give detailed insight into several relaxation approaches for MIOCPs and compare them with regard to their respective structures. In particular, these are the typical solution’s structures and properties as convexity, problem size and numerical behavior. From these structural properties, we deduce some required specifications of a solver. Additionally, the modeling and subsequent limitation of the switching process directly tackle the class-specific typical issue of chattering solutions. One of the relaxation methods for MIOCPs is the outer convexification, where the binary variables only enter affinely. For the approximation of this relaxation’s solution, we took up on the control approximation problem in integral sense derived by Sager as part of a decomposition approach for MIOCPs with affine binary controls. This problem describes the optimal approximation of fractional controls with binary controls such that the corresponding dynamic process is changed as little as possible. For the multi-dimensional problem, we developed a new heuristic, which for the first time gives a bound that only depends on the control grid and not anymore on the number of the system’s controls. For the generalization of the control approximation problem with additional constraints, we derived a tailored branch-and-bound algorithm, which is based on the properties of the Lagrangian relaxation of the one-dimensional problem. This algorithm beats state-of-the-art commercial solvers for Mixed-Integer Linear Programs (MILPs) for this special approximation problem by several orders of magnitude. Overall, we present several, partially new modeling approaches for MIOCPs together with the accompanying structural properties. On this basis, we develop new theories for the approximation of certain relaxed solutions. We discuss the efficient implementation of the resulting structure exploiting algorithms. This leads to a deeper and better understanding of MIOCPs. We show the practicability of the theoretical observations with the help of four prototypical problems. The presented methods and algorithms allow on their basis the direct development of decision support and analysis tools in practice.

We investigate the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of strategy deviation on team performance. As a working use case, we focus on a class of flow assignment problems in which each source node acts as a cooperating decision maker (DM) within a team that minimizes the team cost based on the team-optimal strategy. In practice, some selfish DMs may prioritize their own marginal cost and deviate from NE strategies, thus potentially degrading the overall performance. To quantify this deviation, we explore the deviation bound between the team-optimal solution and the NE in two specific scenarios: (i) when the team-optimal solution is unique and (ii) when multiple solutions do exist. This helps DMs analyze the factors influencing the deviation and adopting the NE strategy within a tolerable range. Furthermore, in the special case of a potential game model, we establish the consistency between the team-optimal solution and the NE. Once the consistency condition is satisfied, the strategy deviation does not alter the total cost, and DMs do not face a strategic trade-off. Finally, we validate our theoretical analysis through simulation trials.

This thesis proposes a new parallel computing network--a binary relation inference network. The network topology is set up to match conventional optimization procedures. The network transforms some optimization problems (shortest path, transitive closure, assignment, etc.) into network convergence problems and divides the work load evenly among all processors. Link weights are known. It can operate in synchronous discrete-time, asynchronous discrete-time, and continuous-time domains. Inference network algorithms are derived directly from problem formulation, and are effective for a large range of problem sizes. The inference network consists of interconnected components; each component is composed of a unit, a number of sites attached to the unit, and links from the unit to sites on other units. Each unit is a simple computational engine. The topology of the inference network matches naturally to many optimization problems, since its deduction sites produce candidates to compete for the optimum and its decision-making units select the optimum from the site values. Either directly or through a transformation mapping to a systolic structure, discrete inference network algorithms can be implemented on a commercially available parallel processing facility, such as the Connection Machine. Analog inference network can be built using integrated circuits which solve problems efficiently in the continuous-time domain. In this thesis, mathematical analysis and numerical simulation were conducted for the synchronous, asynchronous, and analog inference network. Various applications has been discussed. The inference network has shown to solve the all-pair shortest path problem efficiently in various updating schemes. The inference network algorithm for the transitive closure problem parts derived straightforwardly from the formulation of the problem and the topology of the inference network. Efficient continuous-time solution was obtained from a non-synchronized logical circuit. The convergence of the network for the shortest path or transitive closure problems was shown to be independent of the problem size. It was demonstrated that the inference network can solve the assignment problem in a way similar to the Hopfield net's solution to the traveling salesman problem. However, the former was shown to converge for all test cases with problem size up to 128. (Abstract shortened by UMI.)

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling and transshipment problems, where a set of jobs needs to be assigned to the available set of machines or personnel (resources), in a way that all jobs have assigned resources, and no two jobs share the same resource. In its nominal form, the resulting computational problem becomes the assignment problem. This paper deals with the Robust Assignment Problem (RAP) which models situations in which certain assignments are vulnerable and may become unavailable after the solution has been chosen. The goal is to choose a minimum-cost collection of assignments (edges in the corresponding bipartite graph) so that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all jobs. We develop algorithms and hardness results for RAP and establish several connections to well-known concepts from matching theory, robust optimization, LP-based techniques and combinations thereof.

This chapter is devoted to capacity assignment problems in two contexts: (i) long-term capacity planning where link capacities are upgraded, for example every 6 months to match a forecasted traffic growth, (ii) fast capacity allocation in wireless networks, where capacities are updated at a subsecond rate to adapt to varying network conditions by adjusting transmission power or access probabilities in medium access control. Several case studies are analyzed. In the long-term planning we provide a closed formula for the minimum congestion capacities with concave link costs; thanks to a previous problem convexification, the minimum cost planning under modular capacities and the joint routing and capacity optimization exploiting forecasts spanning multiple upgrade periods. In the fast capacity adjustment scope, we model with convex programs the persistence probability optimization in Aloha-like random access networks, the backoff window sizes in CSMA medium access controls, and the transmission power adjustment in cellular networks.

On presente un algorithme dual pour le probleme d'affectation. L'algorithme est guide par la signature d'un arbre fortement realisable et se termine avec un tel arbre. Il a une complexite temporelle O(n 3 ) pour les problemes denses et O(n 2 logn+nm) pour les graphes creux

In this paper, we propose a process for small to medium scale multi-assignment problems. In addition to biddings, agents can give motivations to explain their choices in order to help decision makers break ties in a founded way. A group decision support system, based on Logical Information Systems, allows decision makers to easily face both biddings and motivations. Furthermore, it guaranties that all the agents are treated equally. A successful case study about a small course assignment problem at a technical university is reported.

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).