Multi-objective Performance Measures Research Articles

A multi-objective two-echelon location-routing problem for cash logistics: A metaheuristic approach

This study proposes a two-echelon location routing framework for cash-in-transit. In order to mitigate the risk of robbery in cash transportation, a dynamic risk index is considered. The utilized risk function encompasses both the amount of cash carried by a vehicle and the travel time of a route, and it relaxes a pre-defined parameter of risk threshold in the literature. Multiple exact and metaheuristic methodologies are utilized and evaluated on several small to medium-sized instances and a case study. The effectiveness of the proposed methods is evaluated and shown by examining various multi-objective performance measures. The case study is researched in more depth to obtain managerial insights, and the results show that depending on the risk or cost efficiency of the solutions on a Pareto frontier, the risk of traversing longer routes or transporting larger amounts of cash can be determining in locating new bank vaults.

A tuned NSGA-II to optimize the total cost and service level for a just-in-time distribution network

Distribution network planning has attracted the attention of many studies during last decades. Just-in-time (JIT) distribution has a key role in efficient delivery of products within distribution networks. In modeling of JIT distribution networks, the most frequently applied objectives are related to cost and service level. However, evaluating the impact of simultaneously minimizing total costs and balance between distribution network entities in different echelons still rarely complies with the current literature. To remedy this shortcoming and model reality more accurately, this paper develops a multi-objective mixed-integer nonlinear optimization model for a JIT distribution in three-echelon distribution network. The aims are minimization of total logistics cost along with maximization of capacity utilization balance for distribution centers and manufacturing plants. A non-dominated sorting genetic algorithm-II (NSGA-II) with three different mutation operators namely swap, reversion and insertion is employed to provide a set of near-optimal Pareto solutions. Then, the provided solutions are verified with non-dominated ranked genetic algorithm (NRGA) as well. The Taguchi method in design of experiments tunes the parameters of both algorithms, and their performances are then compared in terms of some multi-objective performance measures. In addition, a genetic algorithm is used to assess Pareto optimal solutions of NSGA-II. Different problems with different sizes are considered to compare the performance of the suggested algorithms. The results show that the proposed solution approach performs efficiently. Finally, the conclusion and some directions for future research are proposed.

Discrete multi-objective differential evolution algorithm for routing in wireless mesh network

The wireless mesh network (WMN) is a challenging technology that offers high quality services to the end users. With growing demand for real-time services in the wireless networks, quality-of-service-based routing offers vital challenges in WMNs. In this paper, a discrete multi-objective differential evolution (DMODE) approach for finding optimal route from a given source to a destination with multiple and competing objectives is proposed. The objective functions are maximization of packet delivery ratio and minimization of delay. For maintaining good diversity, the concepts of weight mapping crossover (WMX)-based recombination and dynamic crowding distances are implemented in the DMODE algorithm. The simulation is carried out in NS-2 and it is observed that DMODE substantially improves the packet delivery ratio and significantly minimizes the delay for various scenarios. The performance of DMODE, DEPT and NSGA-II is compared with respect to multi-objective performance measures namely as `spread'. The results demonstrate that DMODE generates true and well-distributed Pareto-optimal solutions for the multi-objective routing problem in a single run.

Chaotic improved PSO-based multi-objective optimization for minimization of power losses and L index in power systems

Multi-objective optimal reactive power dispatch (MOORPD) seeks to not only minimize power losses, but also improve the stability of power system simultaneously. In this paper, the static voltage stability enhancement is achieved through incorporating L index in MOORPD problem. Chaotic improved PSO-based multi-objective optimization (MOCIPSO) and improved PSO-based multi-objective optimization (MOIPSO) approaches are proposed for solving complex multi-objective, mixed integer nonlinear problems such as minimization of power losses and L index in power systems simultaneously. In MOCIPSO and MOIPSO based optimization approaches, crossover operator is proposed to enhance PSO diversity and improve their global searching capability, and for MOCIPSO based optimization approach, chaotic sequences based on logistic map instead of random sequences is introduced to PSO for enhancing exploitation capability. In the two approaches, constrain-prior Pareto-dominance method (CPM) is proposed to meet the inequality constraints on state variables, the sorting and crowding distance methods are considered to maintain a well distributed Pareto optimal solutions, and moreover, fuzzy set theory is employed to extract the best compromise solution over the Pareto optimal curve. The proposed approaches have been examined and tested in the IEEE 30 bus and the IEEE 57 bus power systems. The performances of MOCIPSO, MOIPSO, and multi-objective PSO (MOPSO) approaches are compared with respect to multi-objective performance measures. The simulation results are promising and confirm the ability of MOCIPSO and MOIPSO approaches for generating lower power losses and smaller L index than MOPSO method.

Evolutionary Optimum Design for a Task Specified 6-Link Planar Robot

Optimal structure design for robots is fundamentally important, as it stands first in the order of robotic system design. The structure of industrial robots should be robust, versatile and strong enough – to withstand a variety of forces/loads, guarantee stability and security in operation. To achieve best solution, it is desirable to perform structure design optimization. Here, it is proposed to determine optimal geometric dimensions for a task specified 6-link planar robot considering pick and place operation. The aim is to minimize torque required for defined motion and to maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints. Links physical characteristics (length and cross sectional area parameters) are design variables. Five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Evolutionary algorithms viz. Elitist Nondominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Differential Evolution (MODE), Multiobjective Genetic Algorithm (MOGA) are used. Normalized weighting objective functions and average fuzzy membership functions are used to select the best optimal solution. Multiobjective performance measures, namely, Solution Spread Measure (SSM) and Ratio of Non-dominated Individuals (RNI) are used to evaluate Pareto optimal fronts. Two other multiobjective performance measures, namely, Optimizer Overhead (OO) and Algorithm effort are used to find computational effort of optimization algorithms. Results obtained from various techniques are compared and analyzed.

Multi-objective job shop scheduling problem with sequence dependent setup times using a novel metaheuristic

The job shop problem is the most complicated and typical problem of all kinds of production scheduling problems, the allocation of resources over time to perform a collection of tasks. This paper studies multi-objective job shop scheduling problems where the setup times is sequence dependent to minimise two objective functions simultaneously. Since the problem is NP-hard and difficult to find an optimal solution in a reasonable computational time an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. An electromagnetism algorithm is known as a flexible and effective population-based algorithm utilising an attraction/repulsion mechanism to move the particles towards optimality. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. All the results demonstrate that our MOEA is very effective for the problem.

Multi-objective metaheuristic algorithms for the resource-constrained project scheduling problem with precedence relations

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multi-objective Variable Neighborhood Search (MOVNS) and Pareto Iterated Local Search (PILS) methods. The proposed algorithms use strategies based on the concept of Pareto Dominance to search for solutions and determine the set of non-dominated solutions. The solutions obtained by the algorithms, from a set of instances adapted from the literature, are compared using four multi-objective performance measures: distance metrics, hypervolume indicator, epsilon metric and error ratio. The computational tests have indicated an algorithm based on MOVNS as the most efficient one, compared to the distance metrics; also, a combined feature of MOG and MOVNS appears to be superior compared to the hypervolume and epsilon metrics and one based on PILS compared to the error ratio. Statistical experiments have shown a significant difference between some proposed algorithms compared to the distance metrics, epsilon metric and error ratio. However, significant difference between the proposed algorithms with respect to hypervolume indicator was not observed.

A multi-objective electromagnetism algorithm for a bi-objective hybrid no-wait flowshop scheduling problem

This article studies multi-objective hybrid no-wait flowshop scheduling problems to minimize both makespan and total tardiness. This article mathematically formulates the problem using an effective multi-objective mixed integer linear programming models. Since the problem is NP-hard and it is difficult to find an optimal solution in a reasonable computational time, an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilizing an attraction/repulsion mechanism to move the particles towards optimality. MOEA is carefully evaluated for its performance against multi-objective immune algorithms and the adaptation of a well-known multi-objective simulated annealing in the relevant literature by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.

A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: An NSGA-II with tuned parameters

In this research, a bi-objective vendor managed inventory model in a supply chain with one vendor (producer) and several retailers is developed, in which determination of the optimal numbers of different machines that work in series to produce a single item is considered. While the demand rates of the retailers are deterministic and known, the constraints are the total budget, required storage space, vendor's total replenishment frequencies, and average inventory. In addition to production and holding costs of the vendor along with the ordering and holding costs of the retailers, the transportation cost of delivering the item to the retailers is also considered in the total chain cost. The aim is to find the order size, the replenishment frequency of the retailers, the optimal traveling tour from the vendor to retailers, and the number of machines so as the total chain cost is minimized while the system reliability of producing the item is maximized. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimization algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. The parameters of both algorithms are first calibrated using the Taguchi approach. Then, the performances of the two algorithms are compared in terms of some multi-objective performance measures. Moreover, a local searcher, named simulated annealing (SA), is used to improve NSGA-II. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.

Scheduling multi-objective open shop scheduling using a hybrid immune algorithm

Despite their importance, hardly ever have multi-objective open shop problems been the topic of researches. This paper studies the mentioned problem and proposes some novel multi-objective solution methods centered on the idea behind artificial immune and simulated annealing algorithms incorporating with powerful and fast local search engines. First, the algorithms are tuned and then carefully evaluated for their performance by means of multi-objective performance measures and statistical tools. An available ant colony optimization is also brought into the experiment. Among the proposed algorithms, the results show that the variant of enhanced artificial immune algorithm outperforms the others.

Multi-objective no-wait flowshop scheduling problems: models and algorithms

This article studies multi-objective no-wait flowshop scheduling problems to minimise both makespan and total tardiness. This problem is commonly denoted by . This article mathematically formulates the problem using two effective multi-objective mixed integer linear programming models. The multi-objective mathematical models are then solved by a multiple criteria decision making approach, called Fuzzy programming method. Moreover, the article proposes a novel multi-objective iterated local search algorithm incorporating three types of local search engine: greedy, moderate and curtailed fashions. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.

An improved generalized differential evolution algorithm for multi-objective reactive power dispatch

An improved multi-objective generalized differential evolution (I-GDE3) approach to solve optimal reactive power dispatch (ORPD) with multiple and competing objectives is proposed in this article. The objective functions are minimization of real power loss and bus voltage profile improvement. For maintaining good diversity, the concepts of simulated binary crossover (SBX) based recombination and dynamic crowding distance (DCD), are implemented in the GDE3 algorithm. I-GDE3 obtains the Pareto-solution set for ORPD that is impervious to load drifts and perturbations. The performance of the proposed approach is tested in standard IEEE 118-bus and IEEE 300-bus test systems and the result demonstrates the capability of the I-GDE3 algorithm in generating diverse and well distributed Pareto-optimal solutions that are less sensitive to various loading conditions along with load perturbations. The performance of I-GDE3 is compared with respect to multi-objective performance measures namely span, hyper-volume and C-measure. The results show the effectiveness of I-GDE3 and confirm its potential to solve the multi-objective RPD problem.

Multi-objective no-wait hybrid flowshop scheduling problem with transportation times

This paper studies multi-objective no-wait hybrid flowshop scheduling problems to minimise both makespan and total tardiness. Furthermore, we consider transportation times between machines. This transportation time can be either job-dependent or job-independent. We consider that all transportations are job-independent; and transportations between two machines have to be done by one transporter. This paper presents a new multi-objective electromagnetism algorithm (MOEA). Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilising an attraction/repulsion mechanism to move the particles towards optimality. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.

Application of modified NSGA-II algorithm to multi-objective reactive power planning

This paper discusses the application of Modified Non-Dominated Sorting Genetic Algorithm-II (MNSGA-II) to multi-objective Reactive Power Planning (RPP) problem. The three objectives considered are minimization of combined operating and VAR allocation cost, bus voltage profile improvement and voltage stability enhancement. For maintaining good diversity in nondominated solutions, Dynamic Crowding Distance (DCD) procedure is implemented in NSGA-II and it is called as MNSGA-II. The standard IEEE 30-bus test system, practical 69-bus Indian system and IEEE 118-bus system are considered to analyze the performance of MNSGA-II. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference pareto-front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD) in 15 independent runs. The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPP problem. A decision-making procedure based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used for finding best compromise solution from the set of pareto-solutions obtained through MNSGA-II.

A multi-objective electromagnetism algorithm for a bi-objective flowshop scheduling problem

This paper deals with a bi-objective flowshop scheduling problem minimizing the makespan and total weighted tardiness, in which all jobs may not be processed by all machines. Furthermore, we consider transportation times between machines. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new multi-objective electromagnetism algorithm (MOEM). The motivation behind this algorithm has risen from the attraction–repulsion mechanism of electromagnetic theories. Along with MOEA, we apply simulated annealing to solve the given problem. A set of experimental instances are carried out to evaluate the algorithm by advanced multi-objective performance measures. The related results show that a variant of our proposed MOEM provides sound performance comparing with other algorithms.

Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method are 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 the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.

Simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection

Tolerance specification is an important part of mechanical design. Design tolerances strongly influence the functional performance and manufacturing cost of a mechanical product. Tighter tolerances normally produce superior components, better performing mechanical systems and good assemblability with assured exchangeability at the assembly line. However, unnecessarily tight tolerances lead to excessive manufacturing costs for a given application. The balancing of performance and manufacturing cost through identification of optimal design tolerances is a major concern in modern design. Traditionally, design tolerances are specified based on the designer’s experience. Computer-aided (or software-based) tolerance synthesis and alternative manufacturing process selection programs allow a designer to verify the relations between all design tolerances to produce a consistent and feasible design. In this paper, a general new methodology using intelligent algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Particle Swarm Optimization (MOPSO) for simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection is presented. The problem has a multi-criterion character in which 3 objective functions, 3 constraints and 5 variables are considered. The average fitness factor method and normalized weighted objective functions method are separately 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 the computational effort of NSGA-II and MOPSO algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

This paper addresses an application of modified NSGA-II (MNSGA-II) by incorporating controlled elitism and dynamic crowding distance (DCD) strategies in NSGA-II to multiobjective optimal reactive power dispatch (ORPD) problem by minimizing real power loss and maximizing the system voltage stability. To validate the Pareto-front obtained using MNSGA-II, reference Pareto-front is generated using multiple runs of single objective optimization with weighted sum of objectives. For simulation purposes, IEEE 30 and IEEE 118 bus test systems are considered. The performance of MNSGA-II, NSGA-II and multiobjective particle swarm optimization (MOPSO) approaches are compared with respect to multiobjective performance measures. TOPSIS technique is applied on obtained non-dominated solutions to determine best compromise solution (BCS). Karush–Kuhn–Tucker (KKT) conditions are also applied on the obtained non-dominated solutions to substantiate a claim on optimality. Simulation results are quite promising and the MNSGA-II performs better than NSGA-II in maintaining diversity and authenticates its potential to solve multiobjective ORPD effectively.

Concurrent multi-objective tolerance allocation of mechanical assemblies considering alternative manufacturing process selection

Concurrent design of tolerances by considering both the manufacturing cost and quality loss of each component by alternate processes of the assemblies may ensure the manufacturability, reduce the manufacturing costs, decrease the number of fraction nonconforming (or defective rate), and shorten the production lead time. Most of the current tolerance design research does not consider the quality loss. In this paper, a novel multi-objective optimization method is proposed to enhance the operations of the non-traditional algorithms (Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO)) and systematically distribute the tolerances among various the components of mechanical assemblies. The problem has a multi-criterion character in which three objective functions, one constraint, and three variables are considered. The average fitness factor method and normalized weighted objective function method are 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 optimizer overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto-optimal fronts and results obtained from various techniques are compared and analysed. Both NSGA-II and MOPSO algorithms are best for this problem.

Evolutionary trajectory planning for an industrial robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator (AdeptOne XL robot) in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE), have been used for the optimization. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.