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Abstract: The aim of this paper is to establish that there exist suitable objective functions for mathematical programming formulations of dynamic user equilibrium assignment in the sense of . Recently, showed that we cannot necessarily calculate a dynamic user equilibrium assignment by minimising the integral over time of Beckmann’s objective function that is widely used to solve for static user equilibrium assignment. In the present paper, two distinct objective functions are presented that result from formulations of assignment either as a variational inequality or as an infinitesimal optimisation: each of these formulations can be solved as a forward dynamic programme. With these formulations and solution approaches, we solve an example based upon Lin and Lo’s one correctly. [Copyright &y& Elsevier]

• A novel optimizer called Chimp Optimization Algorithm (ChOA) is proposed. • ChOA is inspired by individual intelligence and sexual motivation of chimps. • ChOA alleviates the problems of slow convergence rate and trapping in local optima. • The four main steps of Chimp hunting are implemented. This paper proposes a novel metaheuristic algorithm called Chimp Optimization Algorithm (ChOA) inspired by the individual intelligence and sexual motivation of chimps in their group hunting, which is different from the other social predators. ChOA is designed to further alleviate the two problems of slow convergence speed and trapping in local optima in solving high-dimensional problems. In this paper, a mathematical model of diverse intelligence and sexual motivation of chimps is proposed. In this regard, four types of chimps entitled attacker, barrier, chaser, and driver are employed for simulating the diverse intelligence. Moreover, four main steps of hunting, i.e. driving, chasing, blocking, and attacking, are implemented. The proposed ChOA algorithm is evaluated in 3 main phases. First, a set of 30 mathematical benchmark functions is utilized to investigate various characteristics of ChOA. Secondly, ChOA was tested by 13 high-dimensional test problems. Finally, 10 real-world optimization problems were used to evaluate the performance of ChOA. The results are compared to several newly proposed meta-heuristic algorithms in terms of convergence speed, the probability of getting stuck in local minimums, and exploration, exploitation. Also, statistical tests were employed to investigate the significance of the results. The results indicate that the ChOA outperforms the other benchmark optimization algorithms. [ABSTRACT FROM AUTHOR]

In the last decades, a number of novel meta-heuristics and hybrid algorithms have been proposed to solve a great variety of optimization problems. Among these, constrained optimization problems are considered of particular interest in applications from many different domains. The presence of multiple constraints can make optimization problems particularly hard to solve, thus imposing the use of specific techniques to handle fitness landscapes which generally show complex properties. In this paper, we introduce a modified Covariance Matrix Adaptation Evolution Strategy (CMA-ES) specifically designed for solving constrained optimization problems. The proposed method makes use of the restart mechanism typical of most modern variants of CMA-ES, and handles constraints by means of an adaptive penalty function. This novel CMA-ES scheme presents competitive results on a broad set of benchmark functions and engineering problems, outperforming most state-of-the-art algorithms as for both efficiency and constraint handling. [ABSTRACT FROM AUTHOR]

Abstract: To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps. [Copyright &y& Elsevier]

Abstract: Second-order cone programs are a class of convex optimization problems. We refer to them as deterministic second-order cone programs (DSCOPs) since data defining them are deterministic. In DSOCPs we minimize a linear objective function over the intersection of an affine set and a product of second-order (Lorentz) cones. Stochastic programs have been studied since 1950s as a tool for handling uncertainty in data defining classes of optimization problems such as linear and quadratic programs. Stochastic second-order cone programs (SSOCPs) with recourse is a class of optimization problems that defined to handle uncertainty in data defining DSOCPs. In this paper we describe four application models leading to SSOCPs. [Copyright &y& Elsevier]

Abstract: Aiming at distributed energy system (DES) with energy storage device, the mathematical models of major equipments are established in this paper. With the objective functions of the daily minimum operation cost and the minimum equipment quantity, a mixed integer nonlinear multistage objective function is established, which is solved by the means of dynamic programming and penalty function and then the system optimization is completed. According to the case of a hospital in Tianjin, the optimized result is compared with the other two modes, which are DES without energy storage device and sub-production system (the existing system of the hospital). The result shows that the system with energy storage device is better than the system without energy storage device, and the economy of DES is superior to sub-production system significantly. [Copyright &y& Elsevier]

Abstract: In this paper, the strictly convex quadratic program (QP) arising in model predictive control (MPC) for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has considerable merits when applied to MPC over standard active set or interior point algorithms. Its performance is tested and compared against state-of-the-art QP solvers on a series of benchmark problems. The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons. For example, for the challenging crude distillation unit model of with 252 states, 32 inputs, and 90 outputs, the average running time of the proposed approach is 1.57 ms. [Copyright &y& Elsevier]

Abstract: In this paper, an interactive segmentation method is proposed, which is based on an improved Chan–Vese model, i.e. multiple piecewise constant model with geodesic active contour. The k-means method is used to learn the models of the foreground and background, which are the optimal piecewise constant approximation of the original image according to the input seeds clue by the user. Based on the piecewise constant models of the foreground and background, the multiple piecewise constant with a geodesic active contour energy function can be minimized by effective graph cuts algorithm, and the minimum cuts can be used to partition the image into the foreground and background. Numerical experiments demonstrate the superior performance of the proposed interactive foreground extraction method based on the improved Chan–Vese model compared to the original Chan–Vese model by simple user interaction. [Copyright &y& Elsevier]

Abstract: In this paper, by introducing a new nonmonotone line search technique and combining it with the spectral projected gradient method, we propose a solution method for solving the bound constrained optimization problems. Under mild conditions, we obtain the global convergence even without requiring a prior of the existence of a limit point. Numerical tests are also given to show the efficiency of the proposed method. [Copyright &y& Elsevier]