Infeasible Regions Research Articles

Iterative Training of Dynamic Skills Inspired by Human Coaching Techniques

Inspired by how humans learn dynamic motor skills through a progressive process of coaching and practices, we introduce an intuitive and interactive framework for developing dynamic controllers. The user only needs to provide a primitive initial controller and high-level, human-readable instructions as if s/he is coaching a human trainee, while the character has the ability to interpret the abstract instructions, accumulate the knowledge from the coach, and improve its skill iteratively. We introduce “control rigs” as an intermediate layer of control module to facilitate the mapping between high-level instructions and low-level control variables. Control rigs also utilize the human coach's knowledge to reduce the search space for control optimization. In addition, we develop a new sampling-based optimization method, Covariance Matrix Adaptation with Classification (CMA-C), to efficiently compute-control rig parameters. Based on the observation of human ability to “learn from failure”, CMA-C utilizes the failed simulation trials to approximate an infeasible region in the space of control rig parameters, resulting a faster convergence for the CMA optimization. We demonstrate the design process of complex dynamic controllers using our framework, including precision jumps, turnaround jumps, monkey vaults, drop-and-rolls, and wall-backflips.

Feasibility Evaluation of Quinary Heterogeneous Reactive Extractive Distillation

This study addresses a feasibility evaluation method for the heterogeneous reactive extractive distillation of azeotropic quinary mixtures based on visualization in composition space. A critical composition region, that is, thermodynamically infeasible region for heterogeneous reactive extractive distillation, is determined by the constraint of reaction and phase equilibria. In addition, operating constraints are imposed on the feasibility evaluation in terms of the upper and lower internal reflux boundaries. Using these two kinds of feasibility constraints, we examine how the ethyl and isopropyl acetate reactive distillation systems, which cannot produce pure products because of four minimum-boiling azeotropes, lead to a full conversion and pure product recovery with the introduction of an external entrainer inducing L–L splits. The pure acetate production in a single reactive extractive distillation column is possible because the composition trajectory approaches the desired region in composition space ...

Enchanted Multi-Objective Differential Evolutional Algorithm for Economic/Environmental Dispatch

An enchanted multi-objective differential evolutional algorithm was proposed, and was applied to solve the environmental economic dispatch problem. Duo to the weakness of random initial population, the orthogonal method was used in the initialization. Based on survival of the fittest, improved differential operation was proposed, combined with the corresponding parameters control method proposed. With the combination of B-coefficient method and restrain dominance, the process of solving equation and selection operation were used to make the individuals meet the equality constrain. Then the algorithm was tested on the IEEE-30 test system, the results are compared with the results of non-dominated genetic algorithm-II、multi-objective differential evolution and the known results in the papers, and the validity is verified. Keywords: Security constrained economic/environmental dispatch,Constrained multi-objective differential evolution,Feasible region and infeasible region

A Generalized Water-Filling Algorithm with Linear Complexity and Finite Convergence Time

This letter presents an algorithm with linear complexity and finite convergence time for solving the generalized water-filling (WF) problem. The WF problem is generalized by using a weighted-sum-rate, weighted-sum-power, and peak power constraints. The proposed algorithm solves the optimization problems with concave (power and rate) or quasi-concave (energy-efficiency) objective functions. Additionally, it can simultaneously use maximum-power and minimum-rate constraints and give a priority to one of the constraints in the event they generate an infeasible region. Through this generalization, the algorithm can be applied to many WF-based methods proposed in the literature. Moreover, this letter shows multiple ways to further reduce the computational complexity and, via simulation, illustrates the effectiveness of the proposed algorithm.

Strategic robust supply chain design based on the Pareto-optimal tradeoff between efficiency and risk

The strategic design of a robust supply chain has to determine the configuration of the supply chain so that its performance remains of a consistently high quality for all possible future conditions. The current modeling techniques often only consider either the efficiency or the risk of the supply chain. Instead, we define the strategic robust supply chain design as the set of all Pareto-optimal configurations considering simultaneously the efficiency and the risk, where the risk is measured by the standard deviation of the efficiency. We model the problem as the Mean–Standard Deviation Robust Design Problem (MSD-RDP). Since the standard deviation has a square root expression, which makes standard maximization algorithms based on mixed-integer linear programming non-applicable, we show the equivalency to the Mean–Variance Robust Design Problem (MV-RDP). The MV-RDP yields an infinite number of mixed-integer programming problems with quadratic objective (MIQO) when considering all possible tradeoff weights. In order to identify all Pareto-optimal configurations efficiently, we extend the branch-and-reduce algorithm by applying optimality cuts and upper bounds to eliminate parts of the infeasible region and the non-Pareto-optimal region. We show that all Pareto-optimal configurations can be found within a prescribed optimality tolerance with a finite number of iterations of solving the MIQO. Numerical experience for a metallurgical case is reported.

Reporting gamma-ray spectrometric measurement results near the natural limit: primary measurement results, best estimates calculated with the Bayesian posterior and best estimates calculated with the probability density distribution resembling shifting

When reporting best estimates as measurement results, systematic influences near the natural limit are introduced that originate not only in the possible inconsistency of the analytical procedure but also in the conversion of the primary measurement results to best estimates. It has been shown that the probability density distribution resembling shifting of values observed in the unfeasible region to the limit of the feasible range (the natural limit) introduces a smaller systematic influence than the Bayesian posterior, resembling censoring with repetition of the measurements that result in observed values in the unfeasible region. The drawback that the uncertainty intervals calculated with the Bayesian posterior do not encompass the natural limit and may not encompass the observed value, although it lies within the feasible region, is avoided by using the probability density distribution resembling shifting. Therefore, such best estimates introduce a smaller systematic influence into the measurement results and are better suited as inputs for subsequent analyses.

Solving a Location, Allocation, and Capacity Planning Problem with Dynamic Demand and Response Time Service Level

Logistic systems with uncertain demand, travel time, and on-site processing time are studied here where sequential trip travel is allowed. The relationship between three levels of decisions: facility location, demand allocation, and resource capacity (number of service units), satisfying the response time requirement, is analysed. The problem is formulated as a stochastic mixed integer program. A simulation-based hybrid heuristic is developed to solve the dynamic problem under different response time service level. An initial solution is obtained from solving static location-allocation models, followed by iterative improvement of the three levels of decisions by ejection, reinsertion procedure with memory of feasible and infeasible service regions. Results indicate that a higher response time service level could be achieved by allocating a given resource under an appropriate decentralized policy. Given a response time requirement, the general trend is that the minimum total capacity initially decreases with more facilities. During this stage, variability in travel time has more impact on capacity than variability in demand arrivals. Thereafter, the total capacity remains stable and then gradually increases. When service level requirement is high, the dynamic dispatch based on first-come-first-serve rule requires smaller capacity than the one by nearest-neighbour rule.

Constrained Multiobjective Biogeography Optimization Algorithm

Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.

Constraint Programming and Ant Colony System for the Component Deployment Problem

Contemporary motor vehicles have increasing numbers of automated functions to augment the safety and comfort of a car. The automotive industry has to incorporate increasing numbers of processing units in the structure of cars to run the software that provides these functionalities. The software components often need access to sensors or mechanical devices which they are designed to operate. The result is a network of hardware units which can accommodate a limited number of software programs, each of which has to be assigned to a hardware unit. A prime goal of this deployment problem is to find software-to-hardware assignments that maximise the reliability of the system. In doing so, the assignments have to observe a number of constraints to be viable. This includes limited memory of a hardware unit, collocation of software components on the same hardware units, and communication between software components. Since the problem consists of many constraints with a significantly large search space, we investigate an ACO and constraint programming (CP) hybrid for this problem. We find that despite the large number of constraints, ACO on its own is the most effective method providing good solutions by also exploring infeasible regions.

Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures

This work develops an augmented particle swarm optimization (AugPSO) algorithm using two new strategies,: boundary-shifting and particle-position-resetting. The purpose of the algorithm is to optimize the design of truss structures. Inspired by a heuristic, the boundary-shifting approach forces particles to move to the boundary between feasible and infeasible regions in order to increase the convergence rate in searching. The purpose of the particle-position-resetting approach, motivated by mutation scheme in genetic algorithms (GAs), is to increase the diversity of particles and to prevent the solution of particles from falling into local minima. The performance of the AugPSO algorithm was tested on four benchmark truss design problems involving 10, 25, 72 and 120 bars. The convergence rates and final solutions achieved were compared among the simple PSO, the PSO with passive congregation (PSOPC) and the AugPSO algorithms. The numerical results indicate that the new AugPSO algorithm outperforms the simple PSO and PSOPC algorithms. The AugPSO achieved a new and superior optimal solution to the 120-bar truss design problem. Numerical analyses showed that the AugPSO algorithm is more robust than the PSO and PSOPC algorithms.

Robust expected violation criterion for constrained robust design problems and its application in automotive lightweight design

Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.

Extension of the constrained particle swarm optimization algorithm to optimal operation of multi-reservoirs system

Three constrained versions of Particle Swarm Optimization (PSO) algorithm are presented in this paper for the efficient optimal operation of multi-reservoir systems using storage/release volumes as decision variables of the problem. Proposed algorithms are based on identifying and excluding the infeasible region of the search space before and during the search which has already proposed and used by the author for the operation of single reservoirs [5]. In the first version named Partially Constrained Particle Swarm Optimization I (PCPSO1), the sequential nature of the solution building procedure of PSO is used to explicitly enforce the release/storage constraints of the problem during solution construction. For this, the continuity equation is used at each period of the operation of each reservoir to define a new set of bounds for decision variable of the next period which satisfy release/storage constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for some rare cases. In the second version named Partially Constrained Particle Swarm Optimization Two (PCPSO2), the periods of the operations for upstream reservoirs, reservoirs with known inflow, are treated in a reverse order prior to the PCPSO1 search to define new set of bounds for storage volumes such that PCPSO1 algorithm is not given any chance of producing infeasible operations regarding upstream reservoirs. In the third version, the PCPSO2 search is augmented with a mechanism similar to that used in PCPSO2 for all downstream reservoirs by which all the infeasible operation of the downstream dams are also excluded from the search process and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. Proposed methods are used to solve two benchmark problems of hydropower operations of multi-reservoir system namely Four and Ten reservoir systems and the results are presented and compared with those of the conventional unconstrained PSO and other methods in the literature. The methods are shown to be very effective in locating optimal or near optimal solutions and efficient in terms of the convergence characteristics of the resulting algorithms. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original algorithm.

On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients

In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.

Reporting measurement results of activities near the natural limit: note and extension of the article “Interpretation of measurement results near the detection limit in gamma-ray spectrometry using Bayesian statistics”

When reporting activity measurement results near the natural limit for activities, (zero), care must be taken not to report observed values from the unfeasible region and not to report confidence intervals extending beyond the limit of the feasible range. This can be achieved by reporting best estimates, where the requirements that the best-estimate values remain in the feasible range and that the confidence intervals do not extend beyond its limit are taken into account. The use of the truncated and renormalized normal distribution, defined by the primary measurement result, as the posterior in the calculation of the best estimates fulfills both requirements, but suffers in that it introduces a bias into the measurement results reported, that is, the observed value may not lie within the interval, centered at the best-estimate value and having a width equal to twice its uncertainty, and that, consequently, the use of best estimates may lead to unacceptable results. Therefore, a posterior, comprising the Dirac delta function distribution δ(a) and the truncated normal distribution, is used for the calculation of the best estimate. It is shown that here the bias introduced is smaller; the observed value lies within the interval centered on the best-estimate value and has a width equal to twice its uncertainty, and that these best estimates perform better when used in calculations of the mean.

Constrained Multi-Objective Differential Evolution for Security Constrained Economic/Environmental Dispatch

A newly constrained multi-objective differential evolution optimization technique (CMODE) for security constrained economic/environmental dispatch (EED) was proposed. The proposed CMODE evolved a constrained multi-objective version of differential evolution (DE) by employing the traditional multi-objective differential evolution (DEMO) and constrain handle technique to balance the search between feasible region and infeasible region. The proposed CMODE method had been applied to solve the security constrained EED problem. Experiments had been carried on a standard test system. The results demonstrate the high efficiency of the proposed method to solve security constrained EED problem, and the necessary of taking security constrains into consideration.

Binary trie coding scheme: an intelligent genetic algorithm avoiding premature convergence

The multi-dimensional knapsack problems (MKP) have a landscape called a rugged landscape, which may lead to local optima without any progress to optimal solution. Optimization requirement often involves searching amongst various solutions under multi-objective situations. Maintaining diversity and avoiding premature convergence while keeping the population size small and unique is one of the prime approaches to meet the requirements. In this paper, we propose a practical solution to the duplicity as well as premature convergence problem. We have introduced the concept of virtually compressed binary trie (VCBT) and tried to show that the VCBT can be naturally integrated with the genetic algorithm (GA) so that duplicates are completely eliminated while the trie size is kept reasonably small and practically feasible. Our binary trie coding scheme (BTCS) relies on problem-specific knowledge in fragmenting the search space into feasible and infeasible regions, and thus pruning the infeasible areas. Pruning of the trie occurs frequently and is dependent upon many parameters (other than the infeasibility) and the trie size is kept small throughout the whole process. Comparison tables are given for the performance of the BTCS and other good performing evolutionary algorithms found in literature for the MKP. Here, the optimization ability of the BTCS is compared against the GA given by Chu and Beasley; in particular, on a suite of standard MKP test instances from the OR library. The simulation results show that the proposed strategy significantly improves the computational efficiency of GA and generates robust and near-optimal solutions.

Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem

Evolutionary algorithms (EAs) have been applied successfully to many water resource problems, such as system design, management decision formulation, and model calibration. The performance of an EA with respect to a particular problem type is dependent on how effectively its internal operators balance the exploitation/exploration trade‐off to iteratively find solutions of an increasing quality. For a given problem, different algorithms are observed to produce a variety of different final performances, but there have been surprisingly few investigations into characterizing how the different internal mechanisms alter the algorithm's searching behavior, in both the objective and decision space, to arrive at this final performance. This paper presents metrics for analyzing the searching behavior of ant colony optimization algorithms, a particular type of EA, for the optimal water distribution system design problem, which is a classical NP‐hard problem in civil engineering. Using the proposed metrics, behavior is characterized in terms of three different attributes: (1) the effectiveness of the search in improving its solution quality and entering into optimal or near‐optimal regions of the search space, (2) the extent to which the algorithm explores as it converges to solutions, and (3) the searching behavior with respect to the feasible and infeasible regions. A range of case studies is considered, where a number of ant colony optimization variants are applied to a selection of water distribution system optimization problems. The results demonstrate the utility of the proposed metrics to give greater insight into how the internal operators affect each algorithm's searching behavior.

A novel direct search approach for combined heat and power dispatch

A novel approach based on the direct search method (DSM) is proposed for the solution of combined heat and power (CHP) dispatch problem. To deal with the mutual dependency of multiple-demand and heat–power capacity of cogeneration units, the penalty functions should be considered in DSM to enforce the corresponding violated constraints from the infeasible region into the feasible region. Many nonlinear characteristics of the generator can be handled properly in the direct search procedure. To increase the possibility of exploring the search space where the global optimal solution exists, another effective strategy based on a successive refinement search technique is also proposed to guarantee a possibly complete examination of the solution space. Numerical experiments are included to demonstrate the proposed direct search approach can obtain a higher quality solution than many existing techniques.

Feasibility classification of new design points using support vector machine trained by reduced dataset

In this paper, we propose to use a support vector machine (SVM) for the classification of design data. Although the SVM is a very popular technique in data mining, it is rarely applied to an industrial design process that may require information regarding the feasibility of the design point of interest. To check the feasibility, the designer must conduct experiments or computer simulations, which may incur considerable cost. Therefore, the SVM can be an effective tool for predicting feasible and infeasible regions because it only uses the cumulative design data. In this paper, we used the SVM to classify sample datasets drawn from mathematical test problems and from an air-conditioner pipe design example. Our results indicate that the SVM is capable of very accurately identifying feasible and infeasible regions in the design space. Further, we were able to reduce the training time of the SVM by using the k-means clustering algorithm to reduce the amount of training data, taking advantage of the powerful generalization abilities of the SVM. Consequently, we conclude that the SVM can be an effective tool to assess feasibility at certain design points, avoiding some of the high computational costs of the analysis.

A stochastic framework for inequality constrained estimation

Quality description is one of the key features of geodetic inference. This is even more true if additional information about the parameters is available that could improve the accuracy of the estimate. However, if such additional information is provided in the form of inequality constraints, most of the standard tools of quality description (variance propagation, confidence ellipses, etc.) cannot be applied, as there is no analytical relationship between parameters and observations. Some analytical methods have been developed for describing the quality of inequality constrained estimates. However, these methods either ignore the probability mass in the infeasible region or the influence of inactive constraints and therefore yield only approximate results. In this article, a frequentist framework for quality description of inequality constrained least-squares estimates is developed, based on the Monte Carlo method. The quality is described in terms of highest probability density regions. Beyond this accuracy estimate, the proposed method allows to determine the influence and contribution of each constraint on each parameter using Lagrange multipliers. Plausibility of the constraints is checked by hypothesis testing and estimating the probability mass in the infeasible region. As more probability mass concentrates in less space, applying the proposed method results in smaller confidence regions compared to the unconstrained ordinary least-squares solution. The method is applied to describe the quality of estimates in the problem of approximating a time series with positive definite functions.