Separate Objective Function Research Articles

Complete coverage problem of multiple robots with different velocities

Complete coverage, which is integral to many robotic applications, aims to cover an area as quickly as possible. In such tasks, employing multiple robots can reduce the overall coverage time by appropriate task allocation. Several multi-robot coverage approaches divide the environment into balanced subareas and minimize the maximum subarea of all robots. However, balanced coverage in many situations, such as in the cases of robots with different velocities and heterogeneous multi-robot systems, may have inefficient results. This study addresses the unbalanced complete coverage problem of multiple robots with different velocities for a known environment. First, we propose a novel credit model to transform the unbalanced coverage problem into a set of single-objective optimization problems, which can find a combinational optimal solution by optimizing each separate objective function of the single-objective optimization problem to alleviate the computational complexity. Then, we propose a credit-based algorithm composed of a cyclic region growth algorithm and a region fine-tuning algorithm. The cyclic region growth algorithm finds an initial solution to the single-objective optimization problems set by a regional growth strategy with multiple restricts, whereas the region fine-tuning algorithm reallocates the tasks of the partitions with too many tasks to the partitions with too few tasks by constructing a search tree, thereby converging the initial solution to the optimal solution. Simulation results indicate that compared with conventional multi-robot complete coverage problem algorithms, the credit-based algorithm can obtain the optimal solution with the increased number of robots and enlarged size of the mission environment.

Stochastic modelling of gravity data for 2D basement reliefs, free of regularization coefficient

In this paper, a modified version of strength Pareto evolutionary algorithm SPEA (II) is used as a multi-objective optimization method in gravity data modelling. In this method, a two-dimensional gravity inversion problem is solved by iteratively random creation of forward models. It is shown that it can be used as a fast and effective inversion tool in the depth-modelling of two-dimensional layer problems with applications in depth-to-basements, Geometry of bedrocks and sedimentary basins modelling cases. As a result of direct use of the regularization term as a separate objective function, smooth models have a high chance of being selected as final solutions, which makes the results more acceptable and easier to interpret. The most important advantages of this method are that it works independently of the regularization coefficient; so there is no need to run the algorithm so many times to find a proper regularization parameter. Furthermore, there is no need to directly deal with inverse formulations. and the last but not the least, by using a multi-objective algorithm as a global optimization method, convergence to a stable solution does not depend on the initial model, the way classical inversion methods do. For testing the algorithm, a synthetic model is used for layer boundary modelling. To assess the stability of this algorithm, white Gaussian noise added to the synthetic model, Finally, to evaluate the validity of this method, real data from the Reconcavo basin in Brazil considered for processing and inversion, and the results are compared to the ones from previous studies. All computations have been done in the GNU Octave 5.1.0 environment.

Developing a New Multi-Objective Mathematical Model for Electric Vehicles Routing with Charging Stations and Time Windows

To provide an optimal products distribution system, it is important to consider the cost of transportation and customer satisfaction and provide timely services to them. In this paper, in order to deal with the mentioned challenges, a two-objective mathematical model of the problem of routing an inhomogeneous electric vehicle with a time window with the possibility of recharging is presented. In the proposed model, in addition to the objective function of minimizing the route traveled and the costs associated with vehicles, a soft time window is provided for vehicles to reach the destination depot to minimize their latency in a separate objective function. Moreover, this objective function will lead to vehicles arriving at customer points sooner and will increase their satisfaction. To solve the proposed mathematical model, the epsilon constraint method is used to achieve the exact solutions and due to the NP-hard nature of the mathematical model, the multi objective particle swarm optimization (MOPSO) algorithm is used to solve the model in large scale. The results of numerical comparisons show that the MOPSO algorithm can show high efficiency in finding Pareto solutions.

An effective multi-objective particle swarm optimization for the multi-item capacitated lot-sizing problem with set-up times and backlogging

ABSTRACTIn this article, a multi-item capacitated lot-sizing problem (MICLSP) with consideration of set-up times and backlogging, which is one of the key issues in production planning, is addressed. The inventory is formulated as a separate objective function representing its level instead of integrating it into a total cost function for effective control of this objective. The proposed model attempts to minimize simultaneously the total cost and the total inventory level. The developed model shows high performance compared to its mono-objective version. An efficient multi-objective particle swarm optimization (MOPSO) is developed to generate a representative set of Pareto-optimal solutions. A numerical example is given to illustrate the application of the proposed algorithm. The algorithm’s effectiveness is proven based on two experiments conducted on a set of 28 instances. The experiments compare the proposed algorithm’s results with those of the augmented epsilon-constraint method and the basic version of MOPSO.

Energy storage management strategy in distribution networks utilised by photovoltaic resources

Large penetration of electrical energy storage (EES) units and renewable energy resources in distribution systems can help to improve network profiles (e.g. bus voltage and branch current profiles), and to reduce operational cost as well as power losses. On the other hand, unsecure system operation as a result of involving these units is another challenge to network operators. Therefore, establishing a trade-off between operational cost and security is very important. This study presents a new approach to determine the optimal charging/discharging schedule of EES units in distribution systems by employing multi-objective optimisation methods, which will effectively reduce operational cost and enhance distribution network security. In this regard, a voltage stability index (VSI) is converted into a security index to improve the radial network security. This VSI index is treated as a separate objective function, and a multi-objective strategy is implemented to obtain a set of non-dominated solutions instead of a single optimal solution, which simultaneously minimise both of the operational cost and security index. In order to assess the effectiveness and applicability of the proposed method, it is applied to IEEE standard 33-bus and 136-bus distribution test systems, and then the obtained results are compared with those of existing methodologies.

Power Quality Improvement Utilizing PV Fed Unified Power Quality Conditioner Based on UV-PI and PR-R Controller

This paper presents control and configuration of photovoltaic fed unified power quality conditioner for the purpose of power quality enhancement. Literature studies convey that fixed PI gains used in the control schemes of Unified Power Quality Conditioners (UPQC) and PV-UPQC cannot easily adapt to various dynamic conditions. In this paper a novel online tunings method for PI control gains is adopted in the controllers of series and shunt converters of PV-UPQC. Unlike the previously implemented JAYA algorithm which has a single objective function utilized in the controller of DSTATCOM for improvement of only current quality, the new adaptive JAYA algorithm has two separate objective function, employed in shunt and series inverter control of PV-UPQC system for improvement of both current and voltage quality under various operational scenarios for power quality issues. The experimental results verify that implementation of JAYA based auto tuning PI controller increases the adaptivity of PV-UPQC system towards various dynamic conditions. Results obtained are compared with conventional optimization algorithms with fixed PI gains pertaining to a distribution system for validating its efficacy.

HUMANOID ROBOT MOTION PLANNING – A MULTIPLE CONSTRAINS APPROACH

In this paper, we present a new method for humanoid robot motion planning under multiple constraints. In our method, the multiple constraints humanoid robot motion is formulated as a multiobjective optimization problem, considering each constraint as a separate objective function. Three different constrains are considered: (1) minimum energy consumption; (2) stability; and (3) walking speed. The advantage of the proposed method is that in a single run of multiobjective evolution, are generated humanoid robot motions satisfying each constraint. The results show that optimal humanoid robot gaits have a large similarity with that of humans. In order to further verify the performance of optimal motions they are transferred to the “Bonten-Maru” humanoid robot.

Twin Kernel Embedding

In most existing dimensionality reduction algorithms, the main objective is to preserve relational structure among objects of the input space in a low dimensional embedding space. This is achieved by minimizing the inconsistency between two similarity/dissimilarity measures, one for the input data and the other for the embedded data, via a separate matching objective function. Based on this idea, a new dimensionality reduction method called Twin Kernel Embedding (TKE) is proposed. TKE addresses the problem of visualizing non-vectorial data that is difficult for conventional methods in practice due to the lack of efficient vectorial representation. TKE solves this problem by minimizing the inconsistency between the similarity measures captured respectively by their kernel Gram matrices in the two spaces. In the implementation, by optimizing a nonlinear objective function using the gradient descent algorithm, a local minimum can be reached. The results obtained include both the optimal similarity preserving embedding and the appropriate values for the hyperparameters of the kernel. Experimental evaluation on real non-vectorial datasets confirmed the effectiveness of TKE. TKE can be applied to other types of data beyond those mentioned in this paper whenever suitable measures of similarity/dissimilarity can be defined on the input data.

Multiobjective Evolution of Neural Controllers and Task Complexity

Robots operating in everyday life environments are often required to switch between different tasks. While learning and evolution have been effectively applied to single task performance, multiple task performance still lacks methods that have been demonstrated to be both reliable and efficient. This paper introduces a new method for multiple task performance based on multiobjective evolutionary algorithms, where each task is considered as a separate objective function. In order to verify the effectiveness, the proposed method is applied to evolve neural controllers for the Cyber Rodent (CR) robot that has to switch properly between two distinctly different tasks: 1) protecting another moving robot by following it closely and 2) collecting objects scattered in the environment. Furthermore, the tasks and neural complexity are analyzed by including the neural structure as a separate objective function. The simulation and experimental results using the CR robot show that the multiobjective-based evolutionary method can be applied effectively for generating neural networks that enable the robot to perform multiple tasks simultaneously.

Multiobjective batch process design aiming at robust performances

The most common batch design approach in practice and literature is a deterministic one. However, given the uncertainties prevailing in early stages of process design, a deterministically calculated productivity is not sufficient to select one of the large number of optional designs. Therefore, we propose a Tabu Search multiobjective optimization framework, which allows to approximate the Pareto-optimal set of designs while considering uncertain variables in the initial recipe. As a novel technique, we include performance robustness as a separate objective function within the multiobjective optimization alongside with productivity of a design, thus obtaining not only designs with high productivity or solely robust designs, but both high productivity and robust designs in one set of solutions. We examined several robustness criteria as a possible quantification of performance deviations under uncertain recipe variables. The implementation of a Tabu Search framework in combination with Monte-Carlo simulation and Latin Hypercube sampling provides a huge flexibility in the problem specification, in particular in the definition of parameter uncertainties. As a result we successfully demonstrate that metaheuristic optimization techniques are capable to approximate the Pareto-optimal set under uncertainty and are able to capture potentially antagonistic solution qualities such as high productivity and robustness by multiobjective optimization. With the help of this approach, parameters can be identified that have to be put into the focus of process research and development efforts in order to obtain high performance batch process designs.