Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

An Improved Flower Pollination Algorithm for Global and Local Optimization

Meta-heuristic algorithms have emerged as a powerful optimization tool for handling non-smooth complex optimization problems and also to address engineering and medical issues. However, the traditional methods face difficulty in tackling the multimodal non-linear optimization problems within the vast search space. In this paper, the Flower Pollination Algorithm has been improved using Dynamic switch probability to enhance the balance between exploitation and exploration for increasing its search ability, and the swap operator is used to diversify the population, which will increase the exploitation in getting the optimum solution. The performance of the improved algorithm has investigated on benchmark mathematical functions, and the results have been compared with the Standard Flower pollination Algorithm (SFPA), Genetic Algorithm, Bat Algorithm, Simulated annealing, Firefly Algorithm and Modified flower pollination algorithm. The ranking of the algorithms proves that our proposed algorithm IFPDSO has outperformed the above-discussed nature-inspired heuristic algorithms.

A Global Optimization Algorithm for Unconstrained Non-linear Optimization Problems Using Chaotic Neuron Map and Golden Number

This paper presents aninnovative global multi-variable optimization algorithm using one of the best chaotic sequences, the neuron map, a description of which is also provided in the paper. The algorithm uses neuron map in the first stage to move near the global minimum point, as well as in each iteration of the second stage of local search that is done using the N-dimensional golden section search algorithm. The generation and mapping of the neuron variables to the optimization variables along with the stagewise search for the global minimum is explained conscientiously in the work. Numerical results on some benchmark functions and the comparison with a latest state-of-the-art algorithm ispresented in order to demonstrate the efficiency of the proposed algorithm.

A new parameter in three-term conjugate gradient algorithms for unconstrained optimization

<span>In this study, we develop a different parameter of three term conjugate gradient kind, this scheme depends principally on pure conjugacy condition (PCC), Whereas, the conjugacy condition (PCC) is an important condition in unconstrained non-linear optimization in general and in conjugate gradient methods in particular. The proposed method becomes converged, and satisfy conditions descent property by assuming some hypothesis, The numerical results display the effectiveness of the new method for solving test unconstrained non-linear optimization problems compared to other conjugate gradient algorithms such as Fletcher and Revees (FR) algorithm and three term Fletcher and Revees (TTFR) algorithm. and as shown in Table (1) from where in a number of iterations and evaluation of function and in Figures (1), (2) and (3) from where in A comparison of the number of iterations, A comparison of the number of times a function is calculated and A comparison of the time taken to perform the functions.</span>

Inner Product of Fuzzy Vectors

The inner product of vectors of non-normal fuzzy intervals will be studied in this paper by using the extension principle and the form of decomposition theorem. The membership functions of inner product will be different with respect to these two different methodologies. Since the non-normal fuzzy interval is more general than the normal fuzzy interval, the corresponding membership functions will become more complicated. Therefore, we shall establish their relationship including the equivalence and fuzziness based on the a-level sets. The potential application of inner product of fuzzy vectors is to study the fuzzy linear optimization problems.

System Identification of Dampers Using Chaotic Accelerated Particle Swarm Optimization

Aims: Different chaotic APSO-based algorithms are developed to deal with high non-linear optimization problems. Then, considering the difficulty of the problem, an adaptation of these algorithms is presented to enhance the algorithm. Background: : Particle swarm optimization (PSO) is a population-based stochastic optimization technique suitable for global optimization with no need for direct evaluation of gradients. The method mimics the social behavior of flocks of birds and swarms of insects and satisfies the five axioms of swarm intelligence, namely proximity, quality, diverse response, stability, and adaptability. There are some advantages to using the PSO consisting of easy implementation and a smaller number of parameters to be adjusted; however, it is known that the original PSO had difficulties in controlling the balance between exploration and exploitation. In order to improve this character of the PSO, recently, an improved PSO algorithm, called the accelerated PSO (APSO), was proposed, and preliminary studies show that the APSO can perform superiorly. Objective: This paper presents several chaos-enhanced accelerated particle swarm optimization methods for high non-linear optimization problems. Method: Some modifications to the APSO-based algorithms are performed to enhance their performance. Then, the algorithms are employed to find the optimal parameters of the various types of hysteretic Bouc-Wen models. The problems are solved by the standard PSO, APSO, different CAPSO, and adaptive CAPSO, and the results provide the most useful method. Result: Seven different chaotic maps have been investigated to tune the main parameter of the APSO. The main advantage of the CAPSO is that there is a fewer number of parameters compared with other PSO variants. In CAPSO, there is only one parameter to be tuned using chaos theory. Conclusion: To adapt the new algorithm for susceptible parameter identification algorithm, two series of Bouc-Wen model parameters containing standard and modified Bouc-Wen models are used. Performances are assessed on the basis of the best fitness values and the statistical results of the new approaches from 20 runs with different seeds. Simulation results show that the CAPSO method with Gauss/mouse, Liebovitch, Tent, and Sinusoidal maps performs satisfactorily. Other: The sub-optimization mechanism is added to these methods to enhance the performance of the algorithm.