Evolutionary trajectory planning for an industrial robot

SUMMARYA general new methodology using evolutionary algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Differential Evolution (MODE), for obtaining optimal trajectory planning of an industrial robot manipulator (PUMA 560 robot) in the presence of fixed and moving obstacles with payload constraint is presented. The problem has a multi-criterion character in which six objective functions, 32 constraints and 288 variables are considered. A cubic NURBS curve is used to define the trajectory. The average fuzzy membership function method is used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find computational effort of the NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed. Both NSGA-II and MODE are best for this problem.

This paper proposes two multi-objective trajectory planning optimization algorithms, namely, Multi-objective differential evolution (MODE) and Elitist Non-dominated sorting genetic algorithm (NSGA-II). They are applied for a differential drive wheels mobile robot (DDWMR). A cubic NURBS curve is utilized to constitute the mobile robot’s path. The objective functions considered are travel time, traveled length, and actuators efforts. All objective functions are to be minimized. The constraints considered are mobile robot’s kinematic limits, obstacle avoidance, and dynamic limits. Two stationary and five moving obstacles are present around the robot. Numerical simulation results are examined and compared.

Naphtha pyrolysis is one of the important routes for simultaneous production of ethylene and propylene. With recent increase in demand of both ethylene and propylene, understanding of naphtha pyrolysis becomes important for producing with increasing yield of these valuable products. Simultaneous maximization of yield of these two products is mathematically formulated as a multiobjective optimization (MOO) problem. Improved selected scheme is incorporated in the existing multiobjective differential evolution (MODE) algorithm and a new evolutionary algorithm is proposed. Both the evolutionary algorithms [i.e., MODE III and MODE-III with improved selection scheme (MODE III-ISS)] are used for MOO of industrial naphtha cracker unit. Two objectives (maximization of ethylene yield and propylene yield) and decision variables [pressure of the reactor tube (P), temperature of the reactor (T), initial flow rate of naphtha (F 0), and steam to naphtha ratio (SOR)] are considered for MOO study. MODE III and MODE III-ISS algorithms results are compared and presented, which clearly shows that the proposed MODE III-ISS algorithm possesses certain advantages over the MODE III algorithm (such as number of successful selections and percentage convergence with respect to initial number of population points, the quality of the obtained nondominated [ND] solutions).

Simultaneous optimization of two or more objectives is an instance of multi-objective optimization (MOO). However, for most of the Multi-Objective Problems (MOPs), no single solution can optimize all the objective functions simultaneously. Evolutionary algorithms are a type of optimization algorithm used for constructing a well-distributed optimal front more quickly than a much more efficient approach. One of the most commonly used algorithms in this regard is differential evolution (DE). To solve the problem of non-dominated sorting for Multi-Objective DE (MODE), an approach is proposed that reduces the time complexity. DE is commonly recognized as one of the best methods for solving the MOPs. Several versions of DEs have been proposed for MOPs. This article proposes a novel mutation technique, named Environmental Parameter-based Multi-Objective Differential Evolution (EP-MODE) that acquires two additional environmental parameters to preserve diversity and accelerate the convergence. The proposed approach also reduces the time complexity of non-dominated sorting for Multi-Objective DE (MODE). The proposed mutation's performance has been evaluated on DTLZ series and ZDT series benchmark test functions on the Pareto-optimal front and compared with existing multi-objective algorithms (MODE and MODE-RMO). The solution comparatively verifies that the proposed EP-MODE outperforms most of the MODEs for lower dimension functions and higher functions. HIGHLIGHTS New environmental parameters-based mutation has been introduced in a differential evolution algorithm to solve multi-objective optimization problems (EP-mode) The addition of two additional environmental parameters to EP-mode has been found to be appropriate for maintaining diversity while also accelerating the convergence rate EP-MODE evaluated on bi-objective (DTLZ series) and tri-objective (ZDT series) benchmark test functions on the Pareto-optimal front and found EP-MODE's efficiency is higher than that of the MODE algorithm and the MODE algorithm with a ranking-based mutation operator GRAPHICAL ABSTRACT

This paper presents an application of the Multiobjective Differential Evolution (MoDE) algorithm for the optimal operation of a complex multipurpose reservoir system. The developed algorithm (MoDE) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the case study. The case study includes part of a complex water supply system located in southwest Brazil that provides water for approximately 20 million people in the Sao Paulo metropolitan area (SPMA). The objectives of the case study include minimization of demand shortage (the difference between demand for water and available water supply), maximization of water quality (or minimization of the deviation from the water quality standards), and minimization of pumping cost. MoDE is applied to the case study using two inflow scenarios: (1) a drought period with inflows below historical average; and (2) a wet period with inflows above historical average. Multiobjective analysis is done by comparing two pairs of objective functions: minimization of demand shortage versus minimization of pumping cost and minimization of demand shortage versus minimization of the deviation from water quality standards. The constraints for the analysis are reservoir capacity, tunnels and channel limitations, and minimum downstream flow for all reservoirs. The proposed MoDE algorithm is outperforming NSGA-II as it converges closer to and provides better spread coverage of the true Pareto front.

Parameter estimation of a pressure swing adsorption model for air separation using multi-objective optimisation and support vector regression model

The parameter estimation tuning is one of the procedures of system identification. One of the identification problems is to find an optimal model structure especially for representing the complex multivariable dynamic systems. Therefore, this problem needs to be solved by using multi-objective optimization with two objective functions namely minimum predictive error and model complexity. In this paper, the tuning of control parameters is studied before comparing multi-objective evolutionary algorithms. The framework is based on the system identification problems. In parameter tuning, two main qualitative parameters of evolutionary algorithms are focused on crossover rate and mutation rate. The multi-objective evolutionary algorithms used for this study are an elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective optimization using differential evolution (MOODE). The different parameter settings are compared in order to obtain good parameter setting for NSGA-II and MOODE. Then, the performance for both algorithms is also compared using Pareto front. The plotted graphs of two objective functions show the non-dominated fronts achieved by the algorithms. The results proved that MOODE shows an advantage in solving system identification problems in a multivariable nonlinear dynamic system.

MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

The combination optimization of the train operation plan is an ongoing challenge: while computing power has improved, it is difficult to obtain a complete train operation plan system. With the aim of generating system-optimal operation strategies, a new collaborative optimization method is proposed for line planning problem. Through a set of constraints, the problem is formulated as a two-objective model with the objectives of economic benefits and market effects. An optimization approach with adaptive improvement of control parameters based on the multi-objective differential evolution (MODE) algorithm is proposed to solve the model, and a heuristic algorithm is designed to get a better initial solution. Finally, computational results on benchmark multi-objective problems show that the improvements of the strategies are positive and the optimization result of the improved algorithm has better stability. Meanwhile, based on a numerical example of a practical case study involving a 397-kilometer railway corridor to demonstrate the effectiveness of the proposed model and solution. As the basis of successive decisions, this method can adjust the number of trains according to the passenger flow demand, which greatly saves operating costs.

Optimization of an operating domestic wastewater treatment plant using elitist non-dominated sorting genetic algorithm

Optimization of the inspection intervals of a safety system in a nuclear power plant by Multi-Objective Differential Evolution (MODE)

Two-dimensional heat transfer in a fin was modeled with acceptable accuracy and optimized. Bezier curve was used to estimate the fin geometry. The finite volume method coupled with the artificial neural network was developed to predict the temperature distribution through the fin with -1.5% to +1% and ± 0.5% accuracy for fin efficiency and rate of heat transfer, respectively. Locations of four control points in the Bezier curve were considered as design variables. Then, fast and elitist non-dominated sorting genetic algorithm (NSGA-II) was applied to find the maximum fin efficiency and the rate of heat transfer as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The maximum 72 percent for fin efficiency was found with 739W as its rate of heat transfer while the maximum rate of heat transfer was 962.3 W with 57 percent efficiency. In addition, the optimum results of two-dimensional heat transfer were compared with one-dimensional and the average 14.7 percent decreases in fin efficiency and the rate of heat transfer was found that show the deficiency of the one-dimension modeling. In the second case study, the Pareto front was derived for the rate of heat transfer and fin surface area as two objective functions. It was observed that the results of optimum fin configuration in the case of fin efficiency as objective function are the same with the results of fin surface area as objective function.

A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC) is presented for a 5-degree of freedom (DOF) hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions) subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II). A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.

Differential evolution based on network structure for feature selection