Rough‐fuzzy quadratic minimum spanning tree problem

A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study, a bi‐objective rough‐fuzzy quadratic minimum spanning tree problem has been proposed for a connected graph, where the linear and the quadratic weights are represented as rough‐fuzzy variables. The proposed model is formulated by using rough‐fuzzy chance‐constrained programming technique. Subsequently, three related theorems are also proposed for the crisp transformation of the proposed model. The crisp equivalent models are solved with a classical multi‐objective solution technique, the epsilon‐constraint method and two multi‐objective evolutionary algorithms: (a) nondominated sorting genetic algorithm II (NSGA‐II) and (b) multi‐objective cross‐generational elitist selection, heterogeneous recombination, and cataclysmic mutation (MOCHC) algorithm. A numerical example is provided to illustrate the proposed model when solved with different methodologies. A sensitivity analysis of the example is also performed at different confidence levels. The performance of NSGA‐II and MOCHC are analysed on five randomly generated instances of the proposed model. Finally, a numerical illustration of an application of the proposed model is also presented in this study.     

Multiobjective pseudo‐variable neighborhood descent for a bicriteria parallel machine scheduling problem with setup time

A multiobjective variable neighborhood descent (VND) based heuristic is developed to solve a bicriteria parallel machine scheduling problem. The problem considers two objectives, one related to the makespan and the other to the flow time, where the setup time depends on the sequence, and the machines are identical. The heuristic has a set of neighborhood structures based on swap, remove, and insertion moves. We propose changing the local search inside the VND to a sequential search through the neighborhoods to obtain nondominated points for the Pareto‐front quickly. In the numerical tests, we consider a single‐objective version of the heuristic, comparing the results on 510 benchmark instances to show that it is quite effective. Moreover, new instances are generated in accordance with the literature for the bicriteria problem, showing the ability of the proposed heuristic to return an efficient set of nondominate solutions compared with the well‐known nondominated sorting genetic algorithm II.     

Multiobjective model for solving resource‐leveling problem with discounted cash flows

Nowadays, executers are struggling to improve the economic and scheduling situation of projects. Construction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are inefficient and costly to implement on site. The objective of the resource‐leveling problem is to reduce resource fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, minimizing the discounted costs of resource fluctuations and minimizing the project makespan are considered in a multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the optimization problem is NP‐hard, we propose multiobjective evolutionary algorithms, namely nondominated sorting genetic algorithm‐II (NSGA‐II), strength Pareto evolutionary algorithm‐II (SPEA‐II), and multiobjective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order to study the performance of these algorithms, three criteria are proposed and compared with each other to demonstrate the strengths of each applied algorithm. To validate the results obtained for the suggested model, we compared the results of the first objective function with a well‐tuned genetic algorithm and differential algorithm, and we also compared the makespan results with one of the popular algorithms for the resource constraints project scheduling problem. Finally, we can observe that the NSGA‐II algorithm presents better solutions than the other two algorithms on average.     

ADAPTIVE RANKS CLONE AND k‐NEAREST NEIGHBOR LIST–BASED IMMUNE MULTI‐OBJECTIVE OPTIMIZATION

Artificial immune systems (AIS) are computational systems inspired by the principles and processes of the vertebrate immune system. The AIS‐based algorithms typically exploit the immune system's characteristics of learning and adaptability to solve some complicated problems. Although, several AIS‐based algorithms have proposed to solve multi‐objective optimization problems (MOPs), little focus have been placed on the issues that adaptively use the online discovered solutions. Here, we proposed an adaptive selection scheme and an adaptive ranks clone scheme by the online discovered solutions in different ranks. Accordingly, the dynamic information of the online antibody population is efficiently exploited, which is beneficial to the search process. Furthermore, it has been widely approved that one‐off deletion could not obtain excellent diversity in the final population; therefore, a k‐nearest neighbor list (where k is the number of objectives) is established and maintained to eliminate the solutions in the archive population. The k‐nearest neighbors of each antibody are founded and stored in a list memory. Once an antibody with minimal product of k‐nearest neighbors is deleted, the neighborhood relations of the remaining antibodies in the list memory are updated. Finally, the proposed algorithm is tested on 10 well‐known and frequently used multi‐objective problems and two many‐objective problems with 4, 6, and 8 objectives. Compared with five other state‐of‐the‐art multi‐objective algorithms, namely NSGA‐II, SPEA2, IBEA, HYPE, and NNIA, our method achieves comparable results in terms of convergence, diversity metrics, and computational time.     

MRMOGA: a new parallel multi‐objective evolutionary algorithm based on the use of multiple resolutions

In this paper, we introduce MRMOGA (Multiple Resolution Multi‐Objective Genetic Algorithm), a new parallel multi‐objective evolutionary algorithm which is based on an injection island approach. This approach is characterized by adopting an encoding of solutions which uses a different resolution for each island. This approach allows us to divide the decision variable space into well‐defined overlapped regions to achieve an efficient use of multiple processors. Also, this approach guarantees that the processors only generate solutions within their assigned region. In order to assess the performance of our proposed approach, we compare it to a parallel version of an algorithm that is representative of the state‐of‐the‐art in the area, using standard test functions and performance measures reported in the specialized literature. Our results indicate that our proposed approach is a viable alternative to solve multi‐objective optimization problems in parallel, particularly when dealing with large search spaces. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimizing a bi‐objective vehicle routing problem that appears in industrial enterprises

In this paper, a new solution method is implemented to solve a bi‐objective variant of the vehicle routing problem that appears in industry and environmental enterprises. The solution involves designing a set of routes for each day in a period, in which the service frequency is a decision variable. The proposed algorithm, a muti‐start multi‐objective local search algorithm (MSMLS), minimizes total emissions produced by all vehicles and maximizes the service quality measured as the number of times that a customer is visited by a vehicle in order to be served. The MSMLS is a neighbourhood‐based metaheuristic that obtains high‐quality solutions and that is capable of achieving better performance than other competitive algorithms. Furthermore, the proposed algorithm is able to perform rapid movements thanks to the easy representation of the solutions.     

Solving scalarized multi‐objective network flow problems using an interior point method

In this paper, we present a primal‐dual interior‐point algorithm to solve a class of multi‐objective network flow problems. More precisely, our algorithm is an extension of the single‐objective primal infeasible dual feasible inexact interior point method for multi‐objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi‐objective instances are reported. The multi‐objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision‐making methods.     

The r‐interdiction selective multi‐depot vehicle routing problem

The protection of critical facilities has been attracting increasing attention in the past two decades. Critical facilities involve physical assets such as bridges, railways, power plants, hospitals, and transportation hubs among others. In this study we introduce a bilevel optimization problem for the determination of the most critical depots in a vehicle routing context. The problem is modeled as an attacker–defender game (Stackelberg game) from the perspective of an adversary agent (the attacker) who aims to inflict maximum disruption on a routing network. We refer to this problem as the r‐interdiction selective multi‐depot vehicle routing problem (RI‐SMDVRP). The attacker is the decision maker in the upper level problem (ULP) who chooses r depots to interdict with certainty. The defender is the decision maker in the lower level problem (LLP) who optimizes the vehicle routes in the wake of the attack. The defender has to satisfy all customer demand either using the remaining depots or through outsourcing to a third party logistics service provider. The ULP is solved through exhaustive enumeration, which is viable when the cardinality of interdictions does not exceed five among nine depots. For the LLP we implement a tabu search heuristic adapted to the selective multi‐depot VRP. Our results are obtained on a set of RI‐SMDVRP instances synthetically constructed from standard MDVRP test instances.     

Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping method

This paper presents a study of multi‐objective optimal design of nonlinear control systems and has validated the control design with a twin rotor model helicopter. The gains of the porportional integral differential (PID) control are designed in the framework of multi‐objective opitmization. Eight design paramaters are optimized to minimize six time‐domain objective objective functions. The study of multi‐objective optimal design of feedback control with such a number of design paramaters and objective functions is rare in the literature. The Pareto optimal solutions are obtained by the proposed parallel simple cell mapping method consisting of a robust Pareto set recovery algorithm and a rolling subdivision technique. The proposed parallel simple cell mapping algorithm has two features: the number of cells in the invariant set grows linearly with the rolling subdivisions, and the Pareto set is insensitive to the inital set of seed cells. The current control design is compared with the classical LQE control for linear systems, and is also experimentally validated. The current design provides improved control performance as compares with the LQR control, and is applicable to complex nonlinear systems.     

Multi‐objective memetic algorithm: comparing artificial neural networks and pattern search filter method approaches

In this work, two methodologies to reduce the computation time of expensive multi‐objective optimization problems are compared. These methodologies consist of the hybridization of a multi‐objective evolutionary algorithm (MOEA) with local search procedures. First, an inverse artificial neural network proposed previously, consisting of mapping the decision variables into the multiple objectives to be optimized in order to generate improved solutions on certain generations of the MOEA, is presented. Second, a new approach based on a pattern search filter method is proposed in order to perform a local search around certain solutions selected previously from the Pareto frontier. The results obtained, by the application of both methodologies to difficult test problems, indicate a good performance of the approaches proposed.     

Engineering an efficient two‐phase local search algorithm for the co‐rotating twin‐screw extruder configuration problem

The twin‐screw configuration problem arises during polymer extrusion and compounding. It consists in defining the location of a set of pre‐defined screw elements along the screw axis in order to optimize different, typically conflicting objectives. In this paper, we present a simple yet effective stochastic local search (SLS) algorithm for this problem. Our algorithm is based on efficient single‐objective iterative improvement algorithms, which have been developed by studying different neighborhood structures, neighborhood search strategies, and neighborhood restrictions. These algorithms are embedded into a variation of the two‐phase local search framework to tackle various bi‐objective versions of this problem. An experimental comparison with a previously proposed multi‐objective evolutionary algorithm shows that a main advantage of our SLS algorithm is that it converges faster to a high‐quality approximation to the Pareto front.     

Multi‐objective optimization using metaheuristics: non‐standard algorithms

In recent years, the application of metaheuristic techniques to solve multi‐objective optimization problems has become an active research area. Solving this kind of problems involves obtaining a set of Pareto‐optimal solutions in such a way that the corresponding Pareto front fulfils the requirements of convergence to the true Pareto front and uniform diversity. Most of the studies on metaheuristics for multi‐objective optimization are focused on Evolutionary Algorithms, and some of the state‐of‐the‐art techniques belong this class of algorithms. Our goal in this paper is to study open research lines related to metaheuristics but focusing on less explored areas to provide new perspectives to those researchers interested in multi‐objective optimization. In particular, we focus on non‐evolutionary metaheuristics, hybrid multi‐objective metaheuristics, parallel multi‐objective optimization and multi‐objective optimization under uncertainty. We analyze these issues and discuss open research lines.     

An iterative approach to H−/H∞ Fault Detection Observer Design for Discrete‐Time Uncertain Systems

In this paper, H _?/H _∞ multi‐objective fault detection observer design problem for linear discrete‐time systems is studied. Owing to the model inaccuracy in practical situations, system uncertainty is considered as well as the structure of the uncertainty. Sufficient conditions for the existence of the observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented. A new iterative linear matrix inequality (LMI) algorithm for the observers are proposed to obtain the solutions. In order to reduce the conservativeness, the observer design problem in finite frequency domain is also investigated. Simulation results illustrate the effectiveness of the proposed methods.     

A novel local search algorithm with configuration checking and scoring mechanism for the set k‐covering problem

The set k‐covering problem, an extension of the classical set covering problem, is an important NP‐hard combinatorial optimization problem with extensive applications, including computational biology and wireless network. The aim of this paper is to design a new local search algorithm to solve this problem. First, to overcome the cycling problem in local search, the set k‐covering configuration checking (SKCC) strategy is proposed. Second, we use the cost scheme of elements to define the scoring mechanism so that our algorithm can find different possible good‐quality solutions. Having combined the SKCC strategy with the scoring mechanism, a subset selection strategy is designed to decide which subset should be selected as a candidate solution component. After that, a novel local search framework, as we call DLL_ccsm (diversion local search based on configuration checking and scoring mechanism), is proposed. DLL_ccsm is evaluated against two state‐of‐the‐art algorithms. The experimental results show that DLL_ccsm performs better than its competitors in terms of solution quality in most classical instances.     

Hepta‐band coupled‐fed antenna for metal‐ring‐frame WWAN/LTE smartphone applications

A small‐size 40 mm × 10 mm coupled‐fed antenna for hepta‐band WWAN/LTE metal‐ring‐frame (MRF) smartphone applications is investigated. Unlike conventional solutions that remove the redundant resonances excited by the MRF, the proposed antenna makes full use of the MRF resonances. By meticulously co‐design the antenna and MRF, multi‐resonance frequencies are excited and integrated, which results in achieving hepta‐band operation for an MRF smartphone antenna. Detail design considerations and experimental results of the proposed antenna are provided and analyzed. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:633–639, 2016.     

Boundary‐based optimization strategies for design of fragment‐type isolation structure in compact MIMO systems

Fragment‐type structures have been used to acquire high isolation in compact multiple‐input and multiple‐output (MIMO) systems. In this paper, two novel optimization strategies, boundary‐based two‐dimensional (2D) median filtering operator and boundary‐based 2D weighted sum filtering operator, are proposed to design fragment‐type isolation structures first when specific boundary conditions are considered in engineering designs. Second, two computer aided optimization techniques are proposed through combining these two operators with MOEA/D‐GO (multi‐objective evolutionary algorithm based on decomposition combined with enhanced genetic operators), respectively. Finally, fragment‐type isolation structures of a compact MIMO PIFAs (planar inverted‐F antennas) system operating at 2.345‐2.36 GHz are designed. Comparison results show that more alternative designs could be found at the expense of searching speed, and both better front‐back‐ratio and wider impedance bandwidth are observed.     

An evolutionary approach to generalized biobjective traveling salesperson problem

We consider the generalized biobjective traveling salesperson problem, where there are a number of nodes to be visited and each node pair is connected by a set of edges. The final route requires finding the order in which the nodes are visited (tours) and finding edges to follow between the consecutive nodes of the tour. We exploit the characteristics of the problem to develop an evolutionary algorithm for generating an approximation of nondominated points. For this, we approximate the efficient tours using approximate representations of the efficient edges between node pairs in the objective function space. We test the algorithm on several randomly-generated problem instances and our experiments show that the evolutionary algorithm approximates the nondominated set well.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

Graphics processing unit‐accelerated bounding for branch‐and‐bound applied to a permutation problem using data access optimization

Branch‐and‐bound (B&B) algorithms are attractive methods for solving to optimality combinatorial optimization problems using an implicit enumeration of a dynamically built tree‐based search space. Nevertheless, they are time‐consuming when dealing with large problem instances. Therefore, pruning tree nodes (subproblems) is traditionally used as a powerful mechanism to reduce the size of the explored search space. Pruning requires to perform the bounding operation, which consists of applying a lower bound function to the subproblems generated during the exploration process. Preliminary experiments performed on the Flow‐Shop scheduling problem (FSP) have shown that the bounding operation consumes over 98% of the execution time of the B&B algorithm. In this paper, we investigate the use of graphics processing unit (GPU) computing as a major complementary way to speed up the search. We revisit the design and implementation of the parallel bounding model on GPU accelerators. The proposed approach enables data access optimization. Extensive experiments have been carried out on well‐known FSP benchmarks using an Nvidia Tesla C2050 GPU card. Compared to a CPU‐based single core execution using an Intel Core i7‐970 processor without GPU, speedups higher than 100 times faster are achieved for large problem instances. At an equivalent peak performance, GPU‐accelerated B&B is twice faster than its multi‐core counterpart. Copyright © 2013 John Wiley & Sons, Ltd.