Initialization strategies to enhancing the performance of genetic algorithms for the p-median problem

Finding solutions to the p-median problem is an important research topic in location science. A number of meta-heuristic methods have been developed in the literature to find optimal or near optimal solutions to large-scale p-median problems within an acceptable computational time. Among these methods, the recent literature has demonstrated the effectiveness of genetic algorithms (GAs) and hybrid GAs. In this paper, we focus on the strategies of generating the initial population of a genetic algorithm and examine the impact of such strategies on the overall GA performance in terms of solution quality and computational time. Our initialization approach first produces a near optimal solution with low computational complexity, and then uses this solution as a seed to generate a set of solutions as the initial GA population, which is then used in an existing hybrid GA to test the performance of the proposed approach. Experiments based on the forty p-median problems in the OR Library are conducted. Results demonstrate that the proposed approach can significantly reduce computational time without compromising the quality of resulting solutions in almost all cases, and the excellence of the proposed approach increases with the problem scale. Furthermore, a geo-referenced dataset is also tested and the resulting solution maps visualize and validate the principle of the proposed approach.     

A Sequential Design Approach for Switching ℌ∞ LPV Control

This paper proposes a sequential design scheme for switching ℌ_∞ LPV (Linear Parameter-Varying) control, aiming to reduce the computational complexity of the associated optimization problem. Different from the traditional approach that simultaneously designs switching LPV controllers and solves a high-dimensional optimization problem, the proposed sequential design approach renders a bundle of low-dimensional optimization problems to be solved iteratively. Individual ℌ_∞ LPV controller for each subregion is synthesized by independent PLMIs (Parametric Linear Matrix Inequalities) to guarantee ℌ_∞ performance, and controller variables are interpolated on the overlapped subregions such that the ℌ_∞ performance is also guaranteed on the overlapped subregion. Numerical examples are used to demonstrate the effectiveness of this method to reduce the computational load in each design iteration and improved ℌ_∞ performance over the conventional simultaneous design method with well-tuned interpolation coefficient.

     

Optimal Duration of Endurance Performance on the Cycle Ergometer in Relation to Maximal Oxygen Intake

The problem was to determine the optimal duration of endurance performance on the bicycle ergometer using max [Vdot]o₂ as the criterion of validity. Max [Vdot]o₂ was measured in 50 male college students using the, step-increment method (the initial resistance was 2·5 at 60 rpm on a bicycle ergometer, and was increased by 0·5 kg each two minutes until the subject would no longer turn.the ergometer, or when the rate fell to 40 to 50 rev/min).,In contrast, the endurance performance test was of the ‘ steady- pace ’ type in which all of the subjects began pedalling at the same initial rate of 69. pedal rpm at a work rate of 1656 kgm/min for 12 minutes. Although the rate of pedalling (and thus the Work rate) declined as fatigue developed, the friction load remained constant at124 kg throughout the test. There were 12 endurance scores for each individual, endurance being measured as the cumulated work done up to a particular minute. The 12 scores ranged from no decrement in the case of a few subjects with complete endurance to 24 percent in the subjeots with least endurance.

The validity correlations (i.e., the min-by-min correlations between, max [Vdot]o₂and the 12 endurance scores), progressively increased to Y = 0·78 at minute 12. An empirical equation of the form, Y =C ? at, was used to fit. a smooth curve to the trend of the correlations so its' changing rate of curvature could be determined quantitatively. The rate of change was found to slow down considerably in the; later stages of performance, especially after minutes 7 or 8, where the change, was less than 0·04 correlation units.

It was concluded that max [Vdot]o₂ does hot predict endurance performance effectively unless the performance is continued for a least 8 minutes under the conditions of the present experiment. With a,12 minute test, the validity is 96 percent of the asymptotic value, suggesting little further gains can be expected beyond 12 minutes.     

The relationship between heart rate and oxygen uptake during non-steady state exercise

In this study the validity of using heart rate (HR) responses to estimate oxygen uptake ([Vdot]O₂) during varying non-steady state activities was investigated. Dynamic and static exercise engaging large and small muscle masses were studied in four different experiments. In the first experiment, 16 subjects performed an interval test on a cycle ergometer, and 12 subjects performed a field test consisting of various dynamic leg exercises. Simultaneous HR and [Vdot]O₂ measurements were made. Linear regression analyses revealed high correlations between HR and [Vdot]O₂ during both the interval test (r= 0.90±0.07) and the field test (r= 0.94±0.04). In the second experiment, 14 non-wheelchair-bound subjects performed both an interval wheelchair test on a motor driven treadmill, and a wheelchair field test consisting of dynamic and static arm exercise. Significant relationships were found for all subjects during both the interval test (r = 0.91±0.06) and the field test (r= 0.86±0.09). During non-steady state exercise using both arms and legs in a third experiment, contradictory results were found. For 11 of the 15 subjects who performed a field test consisting of various nursing tasks no significant relationship between HR and [Vdot]O₂ was found (r= 0.42±0.16). All tasks required almost the same physiological strain, which induced a small range in data points. In a fourth experiment, the influence of a small data range on the HR-[Vdot]O₂ relationship was investigated: five subjects performed a field test that involved both low and high physiological strain, non-steady state arm and leg exercise. Significant relationships were found for all subjects (r = 0.86±0.04). Although the r-values found in this study were less than under steady state conditions, it can be concluded that [Vdot]O₂ may be estimated from individual HR-[Vdot]O₂ regression lines during non-steady state exercise.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Computation of infimal H∞ norm over a finite horizon

In this paper we develop necessary conditions for a minimax problem involving control and exogenous inputs. The problem can be regarded as a finite horizon version of the H_∞ optimal control problem. We consider problems involving generalized cost functional and non-zero initial conditions. A criterion for the evaluation of the performance index is given in these cases. Our computational experience shows that the finite horizon performance is useful in computing the infimal H_∞ norm in the infinite horizon case, as the final time becomes large. Also, expressions are derived for the variation in performance in terms of system parameter variations. These linear expressions are useful in the evaluation of the robustness of the proposed control strategy.     

Uq(sl(2)) Satisfies a Bernstein Duality

It is well known that in some cases the functorExt_R^μ( − , R) defines a duality between module categories. In earlier papers we studied when this duality can be represented by a bimodule and have characterized when this happens. In this paper, using some computational methods of noncommutative Gröbner bases in the construction of projective resolutions of irreducible finite-dimensional representations, we show new examples of algebras satisfying this property.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

The computational complexity of rules for the character table of Sn

The Murnaghan–Nakayama rule is the classical formula for computing the character table of S_n. Y. Roichman (Adv. Math. 129 (1997) 25) has recently discovered a rule for the Kazhdan–Lusztig characters of q Hecke algebras of type A, which can also be used for the character table of S_n. For each of the two rules, we give an algorithm for computing entries in the character table of S_n. We then analyze the computational complexity of the two algorithms, and in the case of characters indexed by partitions in the (k,ℓ) hook, compare their complexities to each other. It turns out that the algorithm based on the Murnaghan–Nakayama rule requires far less operations than the other algorithm. We note the algorithms’ complexities’ relation to two enumeration problems of Young diagrams and Young tableaux.     

Nonlinear L2-by-3 transform for PAPR reduction in OFDM systems

Orthogonal frequency division multiplexing (OFDM), the multicarrier modulation technique with high bandwidth efficiency and robustness against multipath fading, is used in several high-speed broadband communication systems including digital video broadcasting (DVB), digital audio broadcasting (DAB), asymmetric digital subscriber line (ADSL), wireless local area network (WLAN IEEE 802.11a,g), high performance radio local area network (HIPERLAN 2), and worldwide interoperability for microwave access (WiMAX IEEE 802.16). However, the transmit signal in OFDM system has a high peak-to-average power ratio (PAPR), one of the major drawbacks of multicarrier transmission, and therefore high dynamic range is required in both the digital to analog converter (DAC) and the power amplifier (PA) for proper operation. Otherwise, the nonlinearities of PA cause out-of-band distortion and increase in bit error rate (BER). Therefore, the reduction in PAPR in OFDM system is desirable in order to obtain power efficiency and increase BER performance. In this paper, a new parametric PAPR reduction technique, L₂-by-3 transform from sliding norm transform (SNT) family is proposed. Based on its parameter, a significant PAPR reduction is obtained. This paper presents the analysis of power saving and computational complexity of the proposed method L₂-by-3 and comparison to two other methods; selected mapping and partial transmit sequence.     

On the gap between H2 and entropy performance measures in H∞ control design

Recent papers have considered the problem of minimizing an entropy functional subject to an H_∞ performance constraint. Since the entropy is an upper bound for the H₂ cost, there remains a gap between entropy minimization and H₂ minimization. In this paper we consider a generalized cost functional involving both H₂ and entropy aspects. This approach thus provides a means for optimizing H₂ performance within H_∞ control design.     

Heuristic algorithms for two machine re-entrant flow shop

This paper focuses on a two machine re-entrant flow shop scheduling problem with the objective of minimizing makespan. In the re-entrant flow shop considered here, each job has the processing route (M₁, M₂, M₁, M₂, …, M₁, M₂). We present heuristic algorithms, some are modified from existing algorithms and some are newly developed. Extensive computational experiments are performed to evaluate the performance of the heuristics. Results of the experiments show that the performance of heuristics is significantly affected by the distribution of workloads on machines and some of them are excellent.     

A re-evaluation of the minimum altitude at which hypoxic performance decrements can be detected

Denison et al. reported an initial transient increase in reaction time on a spatial transformation task while exercising at 27?W at an altitude of 2438 m (8000?ft). This increase was attributed to ‘task novelty’. However, subsequent experiments using different performance tests have failed to demonstrate a reliable effect at this altitude. In experiment 1 the spatial transformation task was performed at 27?W with SaO₂ (percentage arterial oxyhaemoglobin saturation) held at the equivalent of 2438?m while breathing a low-oxygen mixture. Initial reaction time did not increase. In experiment 2, SaO₂ was first stabilized at 2438?m, then the 27?W workload was applied while SaO₂ was allowed to vary freely and the spatial transformation task performed. There was an increase in reaction time which was attributed to an accompanying decrease in SaO₂. These results lead to the conclusion that the minimum altitude at which hypoxic performance decrements can be detected is greater than 2438?m and they raise doubts about the ‘task novelty’ hypothesis. The decreased SaO₂ in experiment 2 can be explained by a combination of hypoxia, exercise and hypoventilation due to breathing resistance. It is argued that this combination may have been a factor in the increased reaction time found by Denison et al.     

New approaches to robust l2?l∞ and H∞ filtering for uncertain discrete-time systemsfiltering for uncertain discrete-time systems

The problems of robust l ₂−l _∞ and H _∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l ₂−l _∞ or H _∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.     

2D Bilinear programming for robust PID/DD controller design

A new design method of PID structured controllers to achieve robust performance is developed. Both robust stabilization and performance conditions are losslessly expressed by bilinear constraints in the proportional‐double derivative variable ( k _P, k _DD) and the integral‐derivative variable ( k _I, k _D). Therefore, the considered control design can be efficiently solved by alternating optimization between ( k _P, k _DD) and ( k _I, k _D), which is a 2D computationally tractable program. The proposed method works equally efficiently whenever even higher order differential or integral terms are included in PID control to improve its robustness and performance. Numerical examples are provided to show the viability of the proposed development. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ filtering for a class of uncertain nonlinear systems

This paper investigates the problem of H_∞ filtering for a class of uncertain continuous-time nonlinear systems with real time-varying parameter uncertainty and unknown initial state. We develop an infinite horizon H_∞ filtering methodology which provides both robust stability and a guaranteed H_∞ performance for the filtering error irrespective of the parameter uncertainty.     

Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

Network‐based robust H∞ control of continuous‐time systems with uncertainty

This paper studies the problem of robust H_∞ control for continuous‐time networked control systems (NCSs). A new type of Lyapunov functionals is exploited to derive sufficient conditions for guaranteeing the robust exponential stability and H_∞ performance of the considered system. It is shown that the new result is less conservative than the existing corresponding ones. Meanwhile, a method of eliminating redundant variables to reduce computational complexity is given, which is also applied to design state feedback H_∞ controllers, and the design condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust p stability and performance

In this paper we study robust stability, in the _p sense, against structured perturbations of bounded _p norm. The perturbations may be either linear time-varying, nonlinear time-varying, or nonlinear time-invariant. We develop exact tests for robust stability for each case in terms of convex optimization problems. These results are extended to solve the corresponding robust performance problems, with performance measured via the induced _p norm.