Multidimensional Optimization Problem Research Articles

Behavioral analysis of the leader particle during stagnation in a particle swarm optimization algorithm

Concept of the particle swarms emerged from a simulation of the collective behavior of social creatures. It gradually evolved into a powerful derivative-free optimization techniques, now known as Particle Swarm Optimization (PSO) for solving multi-dimensional, multi-modal, and non-convex optimization problems. The dynamics governing the movement of the particles in PSO has invoked a great deal of research interest over the last decade. Theoretical investigations of PSO has mostly focused on particle trajectories in the search space and the parameter-selection. This work looks into the PSO algorithm from the perspective of the leader particle and takes into account stagnation, a situation where particles are trapped at less coveted local optima, thus preventing them from reaching more coveted global optima. We show that the points sampled by the leader particle satisfy a simple mathematical relation which demonstrates that they lie on a specific line. We demonstrate the condition under which for certain values of the parameters, particles stick to exploring one side of the stagnation point only and ignore the other side, and also the case where both sides are explored. We also obtain information about the gradient of the objective function during stagnation in PSO. We provide a large number of machine simulations which support our claims over several ranges of the control parameters. This sheds light on possible modifications to the basic PSO algorithm which would help future researchers to work with even more efficient and state-of-the-art PSO variants.

Parameter identification of fractional order systems using block pulse functions

In this paper, a novel method is proposed to identify the parameters of fractional-order systems. The proposed method converts the fractional differential equation to an algebraic one through a generalized operational matrix of block pulse functions. And thus, the output of the fractional system to be identified is represented by a matrix equation. The parameter identification of the fractional order system is converted to a multi-dimensional optimization problem, whose goal is to minimize the error between the output of the actual fractional order system and that of the identified system. The proposed method can simultaneously identify the parameters and the fractional differential orders of the fractional order system and avoid the drawbacks in the literature that the fractional differential orders should be known or commensurate. Furthermore, the proposed method avoids complex calculations of the fractional derivative of input and output signals. Illustrative examples covering both fractional and integer systems are given to demonstrate the validity of the proposed method.

Software prototype for solving multi-objective machining optimization problems: Application in non-conventional machining processes

For an effective and efficient application of machining processes it is often necessary to consider more than one machining performance characteristics for the selection of optimal machining parameters. This implies the need to formulate and solve multi-objective optimization problems. In recent years, there has been an increasing trend of using meta-heuristic algorithms for solving multi-objective machining optimization problems. Although having the ability to efficiently handle highly non-linear, multi-dimensional and multi-modal optimization problems, meta-heuristic algorithms are plagued by numerous limitations as a consequence of their stochastic nature. To overcome some of these limitations in the machining optimization domain, a software prototype for solving multi-objective machining optimization problems was developed. The core of the developed software prototype is an algorithm based on exhaustive iterative search which guarantees the optimality of a determined solution in a given discrete search space. This approach is justified by a continual increase in computing power and memory size in recent years. To analyze the developed software prototype applicability and performance, four case studies dealing with multi-objective optimization problems of non-conventional machining processes were considered. Case studies are selected to cover different formulations of multi-objective optimization problems: optimization of one objective function while all the other are converted into constraints, optimization of a utility function which combines all objective functions and determination of a set of Pareto optimal solutions. In each case study optimization solutions that had been determined by past researchers using meta-heuristic algorithms were improved by using the developed software prototype.

Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization

It is an important issue to estimate parameters of chaotic systems in nonlinear science. In this paper, delay time as well as parameters of time-delay chaotic system is considered by treating delay time as an additional parameter. The parameter estimation problem is formulated as a multidimensional optimization problem, and an effective hybrid biogeography-based optimization is developed to solve this problem. Numerical simulations are conducted on two typical time-delay chaotic systems to show the effectiveness of the proposed scheme.

Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm

This paper is concerned with the parameter estimation of nonlinear chaotic system, which could be essentially formulated as a multi-dimensional optimization problem. In this paper, a hybrid algorithm by combining differential evolution with artificial bee colony is implemented to solve parameter estimation for chaotic systems. Hybrid algorithm combines the exploration of differential evolution with the exploitation of the artificial bee colony effectively. Experiments have been conducted on Lorenz system and Chen system. The proposed algorithm is applied to estimate the parameters of two chaotic systems. Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to differential evolution, artificial bee colony, particle swarm optimization, and genetic algorithm from literature when considering the quality of the solutions obtained.

Parameter estimation of chaotic systems by an oppositional seeker optimization algorithm

The parameter estimation can be formulated as a multi-dimensional optimization problem. By combining the seeker optimization algorithm with the opposition-based learning method, an oppositional seeker optimization algorithm is proposed in this work, and is applied to the parameter estimation of chaotic systems. The seeker optimization algorithm provides a new alternative for population-based heuristic search. By considering an estimate and its opposite of current solutions at the same time, the opposition-based learning method is employed for population initialization and also for generation jumping in seeker optimization algorithm. Numerical simulations on two typical chaotic systems are conducted to show the effectiveness and robustness of the proposed scheme.

Cross-Layer MIMO Transceiver Optimization for Multimedia Streaming in Interference Networks

In this paper, we consider dynamic precoder/decorrelator optimization for multimedia streaming in MIMO interference networks. We propose a truly cross-layer framework in the sense that the optimization objective is the application level performance metrics for multimedia streaming, namely the playback interruption and buffer overflow probabilities. The optimization variables are the MIMO precoders/decorrelators at the transmitters and the receivers, which are adaptive to both the instantaneous channel condition and the playback queue length. The problem is a challenging multi-dimensional stochastic optimization problem and brute-force solution has exponential complexity. By exploiting the underlying timescale separation and special structure in the problem, we derive a closed-form approximation of the value function based on continuous time perturbation. Using this approximation, we propose a low complexity dynamic MIMO precoder/decorrelator control algorithm by solving an equivalent weighted MMSE problem. We also establish the technical conditions for asymptotic optimality of the low complexity control algorithm. Finally, the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved.

An Optimized Random Channel Access Policy in Cognitive Radio Networks under Packet Collision Requirement for Primary Users

We consider a distributed random channel access policy in a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage over available multiple primary user (PU) channels. In the random channel access policy each SU stochastically determines whether to access a channel based on the access probability (AP) which is adapted to the sensing results. It is then important to obtain the optimal AP values from the SUs' throughput performance perspective. In our analysis, we assume that all SUs acquire a common channel state information that is potentially erroneous. We analyze the throughput of an arbitrary SU and the packet collision probability of a PU due to the interference by SUs. By considering a requirement on the packet collision probability of a PU, we rigorously derive an explicit expression on the optimal AP values that maximize the throughput of an SU under the requirement for PUs. In the derivation we show that the multi-dimensional optimization problem with AP values can be converted into a one-dimensional optimization problem, so that the optimal AP values can be easily found. Numerical examples are provided to validate our analysis and to investigate the performance behavior of the optimal channel access policy.

Differential Evolution for Prediction of Longitudinal Dispersion Coefficients in Natural Streams

Differential evolution (DE) is a population-based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, a novel expression for the prediction of longitudinal dispersion coefficient in natural streams is proposed to minimize the sum-square error using differential evolution algorithm. The new expression considers the hydraulic and geometric characteristics of rivers. Datasets consisting 65 sets of observations from 29 rivers in the unite states are used to test the proposed algorithm, and results demonstrate the performance and applicability of the proposed differential evolution. Compared with the previous methods, the new expression using differential evolution is superior to other expressions. Moreover, 56.92 % of the prediction using the new expression lie with the 0.5 < Kpre/Kmeas < 1.5 that is better than other expressions.

Hybrid algorithm for dynamic economic dispatch with valve‐point effects

Dynamic economic dispatch problem in power system considering valve-point effects of generators is a non-smooth, non-convex and multi-dimensional constrained optimisation problem. In allusion to those characteristics, this study proposes a hybrid algorithm which integrates low-discrepancy sequences, improved shuffled frog leaping algorithm and sequential quadratic programming. The effectiveness of the proposed method has been verified by using case studies based on 5-unit, 10-unit and 30-unit test systems over a period of 24 h. The results show that the proposed method has improved solution quality and computation efficiency, compared with most current approaches.

A multidimensional tropical optimization problem with a non-linear objective function and linear constraints

We examine a multidimensional optimization problem in the tropical mathematics setting. The problem involves the minimization of a non-linear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality constraints. We start with an overview of known tropical optimization problems with linear and non-linear objective functions. A short introduction to tropical algebra is provided to offer a formal framework for solving the problem under study. As a preliminary result, a solution to a linear inequality with an arbitrary matrix is presented. We describe an example optimization problem drawn from project scheduling and then offer a general representation of the problem. To solve the problem, we introduce an additional variable and reduce the problem to the solving of a linear inequality, in which the variable plays the role of a parameter. A necessary and sufficient condition for the inequality to hold is used to evaluate the parameter, whereas the solution to the inequality is considered a solution to the problem. Based on this approach, a complete direct solution in a compact vector form is derived for the optimization problem under fairly general conditions. Numerical and graphical examples for two-dimensional problems are given to illustrate the obtained results.

Multi-dimensional sensor placement optimization for Canton Tower focusing on application demands

Optimal sensor placement (OSP) technique plays a key role in the structural health monitoring (SHM) of large-scale structures. According to the mathematical background and implicit assumptions made in the triaxial effective independence (EfI) method, this paper presents a novel multi-dimensional OSP method for the Canton Tower focusing on application demands. In contrast to existing methods, the presented method renders the corresponding target mode shape partitions as linearly independent as possible and, at the same time, maintains the stability of the modal matrix in the iteration process. The modal assurance criterion (MAC), determinant of the Fisher Information Matrix (FIM) and condition number of the FIM have been taken as the optimal criteria, respectively, to demonstrate the feasibility and effectiveness of the proposed method. Numerical investigations suggest that the proposed method outperforms the original EfI method in all instances as expected, which is looked forward to be even more pronounced should it be used for other multi-dimensional optimization problems.

A Novel Middleware-Based Model for Redundant Reader Elimination Using Genetic Algorithm

Eliminating redundant readers is important for the performance improvement of the radio frequency identification (RFID) networks. This paper proposes an efficient approach for redundant reader elimination. A middleware-based model, which is formulated as a multi-dimensional optimization problem, is developed to evaluate the network performance. The real-coded genetic algorithm (RGA) is employed to search the optimal adjustable parameters. The simulation results reveal that the proposed approach outperforms other algorithms in terms of optimization precision and computing time.

A fuzzy k-coverage approach for RFID network planning using plant growth simulation algorithm

Optimization of network planning is important for the performance improvement of the radio frequency identification (RFID) networks before deployment. This paper proposes an efficient approach for RFID network planning based on k-coverage. A k-coverage model, which is formulated as a multi-dimensional optimization problem with constraint conditions, is developed to evaluate the network performance. The plant growth simulation algorithm (PGSA) is used to optimize the RFID networks by determining the optimal adjustable parameters in the model. In the proposed approach, the objective function and the constraints are separately processed and no external control parameter is required. The simulation results demonstrate the effectiveness of the proposed approach using PGSA in comparison to other algorithms.

Power Optimization between sensing and signaling for Distributed Detection

The power of each sensor node in wireless sensor networks for signal detection applications is scarce and limited. Thus, the allocation of power resource of a node should make the detection performance of the whole network maximum, which is complex due to the detection probability of the whole system cannot be expressed explicitly. The ant colony optimization algorithm is good at solving multidimensional optimization problem. Consequently, continuous ant colony system (CACS) and ACO R proposed in literature are adopted to optimize the allocation of node’s power between sensing and communications. Simulation show that they can lead to a good power allocation. Meanwhile, the identical power allocation scheme (IPAS) that all sensor nodes have identical power assignment can achieve nearly the same detection performance as that achieved by the best scheme searched by CACS and ACO R . As a result, particularly for a large number of identical sensors, IPAS can be employed to achieve nearly the best detection performance. DOI: http://dx.doi.org/10.11591/telkomnika.v11i8.3032

Integrating bus services with mixed fleets

Conventional bus service (with fixed routes and schedules) has lower average cost than flexible bus service (with demand-responsive routes) at high demand densities. At low demand densities flexible bus service has lower average costs and provides convenient door-to-door service. Bus size and operation type are related since larger buses have lower average cost per passenger at higher demand densities. The operation type and other decisions are jointly optimized here for a bus transit system connecting a major terminal to local regions. Conventional and flexible bus sizes, conventional bus route spacings, areas of service zones for flexible buses, headways, and fleet sizes are jointly optimized in multi-dimensional nonlinear mixed integer optimization problems. To solve them, we propose a hybrid approach, which combines analytic optimization with a Genetic Algorithm. Numerical analysis confirms that the proposed method provides near-optimal solutions and shows how the proposed Mixed Fleet Variable Type Bus Operation (MFV) can reduce total cost compared to alternative operations such as Single Fleet Conventional Bus (SFC), Single Fleet Flexible Bus (SFF), Mixed Fleet Conventional Bus (MFC) and Mixed Fleet Flexible Bus (MFF). With consistent system-wide bus sizes, capital costs are reduced by sharing fleets over times and over regions. The sensitivity of results to several important parameters is also explored.

GPU-Based PSO Application in Multiuser Detection and Trajectory Parameter Estimation

The parallel character of particle swarm algorithm (PSO) and the Graphic Processing Unit (GPU) technology of Compute United Device Architecture (CUDA) from NVIDIA are analyzed. Two methods of the realization of PSO based on GPU are discussed. One method is using the module of open source particle swarm algorithm supporting the GPU, with the application of multiuser detector (MUD). The other method is using the module of MATLAB supporting the GPU with the application of the moving parameter estimation. The test results show that the PSO algorithm based on GPU technology can significantly improve the speed of system capacity, to solve the problem of multi-dimensional global optimization, with the poor real-time performance. It can be widely used in the project of high real-time requirements.

Software prototype for validation of machining optimization solutions obtained with meta-heuristic algorithms

Optimization of machining processes is of primary importance for increasing machining efficiency and economics. Determining optimal values of machining parameters is performed by applying optimization algorithms to mathematical models of relationships between machining parameters and machining performance measures. In recent years, there has been an increasing trend of using empirical models and meta-heuristic optimization algorithms. The use of meta-heuristic optimization algorithms is justified because of their ability to handle highly non-linear, multi-dimensional and multi-modal optimization problems. Meta-heuristic algorithms are powerful optimization tools which provide high quality solutions in a short amount of computational time. However, their stochastic nature creates the need to validate the obtained solutions. This paper presents a software prototype for single and multi-objective machining process optimization. Since it is based on an exhaustive iterative search, it guarantees the optimality of determined solution in given discrete search space. The motivation for the development of the presented software prototype was the validation of machining optimization solutions obtained by meta-heuristic algorithms. To analyze the software prototype applicability and performance, six case studies of machining optimization problems, both single and multi-objective, were considered. In each case study the optimization solutions that had been determined by past researchers using meta-heuristic algorithms were either validated or improved by using the developed software prototype.

Cogging Torque Optimization of Axial Flux Permanent Magnet Motor

The conventional climb method is difficult to apply for the multimodal and multi-dimensional optimization problem. To solve this problem, the improved climb method is proposed in this paper. The proposed algorithm can mitigate the time for the optimization and increase the reliability for the optimization. The proposed algorithm is verified through the optimization of an axial flux permanent magnet motor.

Parameter estimation for reaction kinetics model based on composite genetic algorithm

Through establishing an appropriate fitness function,the parameter estimation problem for residue hydrofining reaction kinetics model was formulated as a multi-dimensional functional optimization problem,which can be solved by Composite Genetic Algorithm(CGA).Chaotic sequences design method was introduced to construct the initialization population that was scattered uniformly over the entirely search space in order to maintain the diversity.The CGA randomly combined several effective crossover strategies with some suitable mutation strategies at each generation to create new offspring individuals.The simulation results on four benchmark problems demonstrate the effectiveness and robustness of the proposed algorithm.Taking a catalytic cracking unit in oil refinery as an example,a numerical application of the parameter estimation for residue hydrofining reaction kinetics model was solved.Satisfactory results were obtained.