This paper presents a reference framework for the configuration process. The reference framework is established through an extensive review of existing literature, and as such consolidates an extensive theoretical base. The review of literature shows a broadening of the understanding of the configuration task. The definition of the configuration task is somewhat ambiguous because different research groups define configuration tasks differently. This paper proposes a reference framework for configuration that permits a more precise understanding of a configuration task, a definition of the basic concepts in product configuration, and a total configuration system view that describes how operators come together to perform the configuration task in the configuration process. We will define the product, the product model, the configuration task, and the configuration system, and put the whole thing into perspective with the theory of technical systems, where we describe the configuration process and the different abstraction level of configurations. We will also use our resulting framework to describe sales configuration, technical configuration, and reconfiguration. We do this to synthesize previous work, to clarify and make coherent definitions of relevant terms, to extent the definition of product configuration to include “softer” products like information and service, and finally, to give a comparative framework to analyze work done in the field of product configuration. The total configuration system, together with the definition of key concepts, comprises a strong reference framework when working with, developing, and analyzing configuration systems.

A novel swarm intelligence approach for combinatorial optimization is proposed, which we call probability increment based swarm optimization (PIBSO). The population evolution mechanism of PIBSO is depicted. Each state in search space has a probability to be chosen. The rule of increasing the probabilities of states is established. Incremental factor is proposed to update probability of a state, and its value is determined by the fitness of the state. It lets the states with better fitness have higher probabilities. Usual roulette wheel selection is employed to select states. Population evolution is impelled by roulette wheel selection and state probability updating. The most distinctive feature of PIBSO is because roulette wheel selection and probability updating produce a trade-off between global and local search; when PIBSO is applied to solve the printed circuit board assembly optimization problem (PCBAOP), it performs superiorly over existing genetic algorithm and adaptive particle swarm optimization on length of tour and CPU running time, respectively. The reason for having such advantages is analyzed in detail. The success of PCBAOP application verifies the effectiveness and efficiency of PIBSO and shows that it is a good method for combinatorial optimization in engineering.

We present a two-parameter family $(G_{m,k})_{m, k \in \mathbb{N}_{\geq 2}}$, of finite, non-abelian random groups and propose that, for each fixed k, as m → ∞ the commuting graph of Gm,k is almost surely connected and of diameter k. We present heuristic arguments in favour of this conjecture, following the lines of classical arguments for the Erdős–Rényi random graph. As well as being of independent interest, our groups would, if our conjecture is true, provide a large family of counterexamples to the conjecture of Iranmanesh and Jafarzadeh that the commuting graph of a finite group, if connected, must have a bounded diameter. Simulations of our model yielded explicit examples of groups whose commuting graphs have all diameters from 2 up to 10.

Beginning with a deterministic distributed feedback control for nonholonomic vehicle formations, we develop a stochastic optimal control approach for agents to enhance their non-optimal controls with additive correction terms based on the Hamilton–Jacobi–Bellman equation, making them optimal and robust to uncertainties. In order to avoid discretization of the high-dimensional cost-to-go function, we exploit the stochasticity of the distributed nature of the problem to develop an equivalent Kalman smoothing problem in a continuous state space using a path integral representation. Our approach is illustrated by numerical examples in which agents achieve a formation with their neighbors using only local observations.

Consider the setting of sparse graphs on N vertices, where the vertices have distinct “names”, which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as c N log N for some model-dependent rate constant c. The mathematical content of this paper is the (often easy) calculation of c for a variety of models, in particular for various standard random graph models adapted to this setting. Our broader purpose is to publicize this particular setting as a natural setting for future theoretical study of data compression for graphs, and (more speculatively) for discussion of unorganized versus organized complexity.

Many research works on the control of nonholonomic wheeled mobile robots (WMRs) do not consider the actuator saturation problem and the absence of velocity sensors in practice. The actuator saturation deteriorates the tracking performance of the controller, and the use of velocity sensors increases the cost and weight of WMR systems. This paper simultaneously addresses these problems by designing a saturated output feedback controller for uncertain nonholonomic WMRs. First, a second-order input–output model of nonholonomic WMRs is developed by defining a suitable set of output equations. Then a saturated adaptive robust tracking controller is proposed without velocity measurements. For this purpose, a nonlinear saturated observer is used to estimate robot velocities. The risk of actuator saturation is effectively reduced by utilizing saturation functions in the design of the observer–controller scheme. Semi-global uniform ultimate boundedness of error signals is guarantied by the Lyapunov stability analyses. Finally, simulation results are provided to show the effectiveness of the proposed controller. Compared with one recent work of the author, a comparative study is also presented to illustrate that the proposed saturated controller is more effective when WMR actuators are subjected to saturation.