New Optimization Techniques in Engineering

For the purpose of solving the engineering constrained discrete optimization problem, a novel discrete particle swarm optimization(DPSO) is proposed. The proposed novel DPSO is based on the idea of normal particle swarm optimization(PSO), but deals with the variables as discrete type, the discrete optimum solution is found through updating the location of discrete variable. To avoid long calculation time and improve the efficiency of algorithm, scheme of constraint level and huge value penalty are proposed to deal with the constraints, the stratagem of reproducing the new particles and best keeping model of particle are employed to increase the diversity of particles. The validity of the proposed DPSO is examined by benchmark numerical examples, the results show that the novel DPSO has great advantages over current algorithm. The optimum designs of the 100?1 500 mm bellows under 0.25 MPa are fulfilled by DPSO. Comparing the optimization results with the bellows in-service, optimization results by discrete penalty particle swarm optimization(DPPSO) and theory solution, the comparison result shows that the global discrete optima of bellows are obtained by proposed DPSO, and confirms that the proposed novel DPSO and schemes can be used to solve the engineering constrained discrete problem successfully.

Hybrid scatter search and path relinking for the capacitated p-median problem

Particle Swarm Optimization (PSO) is a commonly used optimization to solve many problems. The PSO, which is developed for continuous optimization, is updated to solve discrete problems and Discrete PSO (DPSO) is obtained in this study. With DPSO, the Traveling Salesman Problem (TSP), which is well-known in the literature as a discrete problem, is solved. In order to improve the results, the swap method, the shift method, and the symmetry method are added to DPSO. The symmetry method is a new and successful method. The variations of the DPSO occurred according to the selected method type (DPSO1 (swap method), DPSO2 (shift method), DPSO3 (swap and shift methods), DPSO4 (symmetry method), DPSO5 (swap, shift, and symmetry methods), DPSO6 (swap, shift, symmetry, and 2-opt methods)). The effect of each method on the performance of the DPSO has been studied in detail. To demonstrate the success of the variations of the DPSO, the results are additionally compared with many well-known and new discrete algorithms in the literature. The results showed that the performance of DPSO has improved with the symmetry method and it has achieved better results than the discrete heuristic algorithms recently proposed in the literature.

The classical Particle Swarm Optimization is a powerful method to find the minimum of a numerical function, on a continuous definition domain. As some binary versions have already successfully been used, it seems quite natural to try to define a framework for a discrete PSO. In order to better understand both the power and the limits of this approach, we examine in detail how it can be used to solve the well known Traveling Salesman Problem, which is in principle very “bad” for this kind of optimization heuristic. Results show Discrete PSO is certainly not as powerful as some specific algorithms, but, on the other hand, it can easily be modified for any discrete/combinatorial problem for which we have no good specialized algorithm.

The probabilistic travelling salesman problem (PTSP) is an extension of the well-known travelling salesman problem (TSP), which has been extensively studied in the field of combinatorial optimization. The goal of the TSP is to find the minimum length of a tour to all customers, given the distances between all pairs of customers whereas the objective of the PTSP is to minimize the expected length of the a priori tour where each customer requires a visit only with a given probability (Bertsimas, 1988; Bertsimas et al., 1990; Jaillet, 1985). The main difference between the PTSP and the TSP is that in the PTSP the probability of each node being visited is between 0.0 and 1.0 while in TSP the probability of each node being visited is 1.0. Due to the fact that the element of uncertainty not only exists, but also significantly affects the system performance in many real-world transportation and logistics applications, the results from the PTSP can provide insights into research in other probabilistic combinatorial optimization problems. Moreover, the PTSP can also be used to model many real-world applications in logistical and transportation planning, such as daily pickup-delivery services with stochastic demand, job sequencing involving changeover cost, design of retrieval sequences in a warehouse or in a cargo terminal operations, meals on wheels in senior citizen services, trip-chaining activities, vehicle routing problem with stochastic demand, and home delivery service under e-commerce (Bartholdi et al., 1983; Bertsimas et al., 1995; Campbell, 2006; Jaillet, 1988; Tang & Miller-Hooks, 2004). Early PTSP computational studies, dating from 1985, adopted heuristic approaches that were modified from the TSP (e.g., nearest neighbor, savings approach, spacefilling curve, radial sorting, 1-shift, and 2-opt exchanges) (Bartholdi & Platzman, 1988; Bertsimas, 1988; Bertsimas & Howell, 1993; Jaillet, 1985, 1987; Rossi & Gavioli, 1987). With its less than satisfactory performance in yielding solution quality, researchers in the recent years switch to metaheuristic methods, such as ant colony optimization (Bianchi, 2006; Branke & Guntsch, 2004), evolutionary algorithm (Liu et al., 2007), simulated annealing (Bowler et al., 2003), threshold accepting (Tang & Miller-Hooks, 2004) and scatter search (Liu, 2006, 2007, 2008). Because the genetic algorithm (GA), a conceptual framework of the population-based metaheuristic method, has been shown to yield promising outcomes for solving various complicated optimization problems in the past three decades (Back et al., 1997; Davis, 1991; O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

An Improved discrete particle swarm optimization (DPSO)-based algorithm for the traveling salesman problem (TSP) is proposed. In order to overcome the problem of premature convergence, a novel depressor is proposed and a diversity measure to control the swarm is also introduced which can be used to switch between the attractor and depressor. The proposed algorithm has been applied to a set of benchmark problems and compared with the existing algorithms for solving TSP using swarm intelligence. The results show that it can prevent premature convergence to a high degree, but still keeps a rapid convergence like the basic DPSO.

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

Objectives: A well-known NP-complete problem is the travelling salesman problem (TSP). It has numerous engineering and scientific applications. In this article, we have proposed a multi-conveyance TSP where different conveyances are present to travel from one city to another city. This is an extension to classical TSP. In this TSP, the salesman visits all the cities only once during his/her tour, using different conveyances to travel from one city to another. The cost of travelling between cities using various modes of conveyance varies. The objective of this research is to find the minimum cost tour using an ant colony optimization (ACO) based approach by satisfying the constraints of the proposed multi-conveyance TSP. Method: The considered TSP has been solved using a novel ACO technique. The proposed ACO is adopted with the Roulette-wheel selection and “tuning solution” techniques. We have used a few benchmark datasets from TSPLIB to check the effectiveness of the proposed algorithm. The experimental findings for a few benchmarks TSP instances show that almost always, the proposed ACO is able to find a better result. Then, we used some redefined and randomly generated datasets for experiments. The experimental outcomes for various input datasets are also very encouraging. Findings: The goal of the proposed TSP is to find a complete tour with a minimum cost without exceeding the total travel cost and total travel time. Thus, there are two novel constraints in the classical TSP. Novelty: A unique aspect of the proposed research is the use of several conveyance facilities and a fixed total travel time and cost. This is new, as these three factors are integrated into a single TSP model. Keywords: Travelling Salesman Problem; Travel Cost; Travel Time; MultiConveyance TSP; Ant Colony Optimization

The Scatter Search is one of the population-based metaheuristics, which can be used to solve a wide range of problems including Traveling Salesman Problem (TSP), Routing Protocol, and End-to-End QoS, while Bees Algorithm can be applied to optimize the solution of these problems. In this paper, an improved Scatter Search algorithm based on Bees Algorithm has been presented. The improvement provides Scatter Search with random exploration for search space of problem and more of intensification for promising solutions. The original and improved Scatter Search has been tested on Traveling Salesman Problem. A computational experiment with benchmark instances is reported. The results demonstrate that the improved Scatter Search algorithm produces better performance than original Scatter Search algorithm. The developed algorithm has been compared with other algorithms for the same problem, and the result was competitive with some algorithm and insufficient with another.

The paper presents a novel discrete search optimisation technique to dynamically and optimally select the capacitor-bank size for loss reduction and energy management system of distribution/utilisation systems using either fixed or switched capacitor bank stages selected online using a discrete multi-objective particle swarm optimisation (DMOPSO) technique. The novel search and optimisation approach is implemented to compromise a number of conflicting objectives/ goals including minimum load-bus voltage deviation, minimisation of source root-mean-square current for feeder-capacity release, reduction of feeder loss and total harmonic distortion of currents and voltages as well as the maximum power factor in a global complex optimality-search multi-objective problem. The correct (on-off) timing/switching intervals for the four solid-state switches for capacitor bank switching stages in addition to the fixed base-capacitor bank originally selected by the DMOPSO search and optimisation technique.

AIChE JournalVolume 18, Issue 4 p. 867-869 Communication to the Editor Trajectory optimization techniques in chemical reaction engineering. II. Comparison of the methods R. K. Jaspan, R. K. Jaspan Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Search for more papers by this authorJ. Coull, Corresponding Author J. Coull Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Search for more papers by this author R. K. Jaspan, R. K. Jaspan Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Search for more papers by this authorJ. Coull, Corresponding Author J. Coull Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15213Search for more papers by this author First published: July 1972 https://doi.org/10.1002/aic.690180440Citations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume18, Issue4July 1972Pages 867-869 RelatedInformation

The Traveling Salesman Problem (TSP) is an NP-hard graph search problem. Despite having numerous modifications of the original abstract problem, Time Dependent Traveling Salesman Problem (TD TSP) was one of the most realistic extensions under real traffic conditions. In TD TSP the edges between nodes are assigned higher costs (weights), if they were traveled during the rush hour periods, or crossed the traffic jam regions, such as the city center(s). In this paper we introduce an even more real-life motivated approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem (IFTD TSP), which is a further extension of the TSP, and also of the classic TD TSP, with the additional notion of using intuitionistic fuzzy sets for the definition of uncertain costs, time, and space of the rush hour—traffic jam region affecting graph sections. In IFTD TSP we use fuzzy memberships and non-memberships sets for estimating the vague costs between nodes in order to quantify the behavior of traffic jam regions, and the rush hour periods. Since intuitionistic fuzzy sets are generalizations of classic fuzzy sets, our approach may be considered an extension and substitution of the original abstract TD TSP problem, even, of the (classic) Fuzzy TD TSP. Lastly, DBMEA (Discrete Bacterial Memetic Evolutionary Algorithm) was applied on the IFTD TSP model, the results of the simulation runs based on some extensions of the benchmarks generated from the original TD TSP data set showed quite good and promising preliminary results.

Integrated decisions on merchandise image display and inventory planning are closely related to operational performance of online stores. A visual-attention-dependent demand (VADD) model has been developed to support online stores make the decisions. In the face of evolving products, customer needs, and competitors in an e-commerce environment, the benefits of using VADD model depend on how fast the model runs on the computer. As a result, a discrete particle swarm optimization (DPSO) method is employed to solve the VADD model. To verify the usability and effectiveness of DPSO method, it was compared with the existing methods for large-scale, medium-scale, and small-scale problems. The comparison results show that both GA and DPSO method perform well in terms of the approximation rate, but the DPSO method takes less time than the GA method. A sensitivity is conducted to determine the model parameters that influence the above comparison result.

Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) algorithms have attracted the interest of researchers due to their simplicity, effectiveness and efficiency in solving real world optimization problems. Swarm-inspired optimization has recently become very popular. Both ACO and PSO are successfully applied in the Traveling Salesman Problem (TSP). Our approach consists in combining Fuzzy Logic with ACO (FACO - Fuzzy Ant Colony Optimization) and PSO (FPSO - Fuzzy Particle Swarm Optimization) for solving the TSP. Experimental results and comparative studies illustrate the importance of Fuzzy logic in reducing the time and the best length for the TSP problems considered.

This paper proposes a discrete particle swarm optimization (DPSO) to solve the multiple destination routing (MDR) problems. The problem has been proven to be NP-complete and the traditional heuristics (e.g., the SPH, DNH and ADH) are inefficient in solving it. The particle swarm optimization (PSO) is an efficient global search algorithm and is promising in dealing with complex problems. This paper extends the PSO to a discrete PSO and uses the DPSO to solve the MDR problem. The global search ability and fast convergence ability of the DPSO make it efficient to the problem. Experiments based on the benchmarks from the OR-library show that the DPSO obtains better results when compared with traditional heuristic algorithms, and also outperforms the GA-based algorithm with faster convergence speed.KeywordsParticle swarm optimization (PSO)multiple destination routing problemsSteiner tree problem