Multi-Objective Optimization of Multi-Product Parallel Disassembly Line Balancing Problem Considering Multi-Skilled Workers Using a Discrete Chemical Reaction Optimization Algorithm

This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers.A mathematical model for the parallel disassembly line is established to achieve maximized disassembly profit and minimized workstation cycle time.Based on a product’s AND/OR graph,matrices for task-skill,worker-skill,precedence relationships,and disassembly correlations are developed.A multi-objective discrete chemical reaction optimization algorithm is designed.To enhance solution diversity,improvements are made to four reactions:decomposition,synthesis,intermolecular ineffective collision,and wall invalid collision reaction,completing the evolution of molecular individuals.The established model and improved algorithm are applied to ball pen,flashlight,washing machine,and radio combinations,respectively.Introducing a Collaborative Resource Allocation(CRA)strategy based on a Decomposition-Based Multi-Objective Evolutionary Algorithm,the experimental results are compared with four classical algorithms:MOEA/D,MOEAD-CRA,Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ),and Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ).This validates the feasibility and superiority of the proposed algorithm in parallel disassembly production lines.

Optimization of volume to point conduction problem based on a novel thermal conductivity discretization algorithm

A conduction heat transfer process is enhanced by filling prescribed quantity and optimized-shaped high thermal conductivity materials to the substrate. Numerical simulations and analyses are performed on a volume to point conduction problem based on the principle of minimum entropy generation. In the optimization, the arrangement of high thermal conductivity materials is variable, the quantity of high thermal-conductivity material is constrained, and the objective is to obtain the maximum heat conduction rate as the entropy is the minimum.A novel algorithm of thermal conductivity discretization is proposed based on large quantity of calculations.Compared with other algorithms in literature, the average temperature in the substrate by the new algorithm is lower, while the highest temperature in the substrate is in a reasonable range. Thus the new algorithm is feasible. The optimization of volume to point heat conduction is carried out in a rectangular model with radiation boundary condition and constant surface temperature boundary condition. The results demonstrate that the algorithm of thermal conductivity discretization is applicable for volume to point heat conduction problems.

Novel Discrete Particle Swarm Optimization Based on Huge Value Penalty for Solving Engineering Problem

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 discrete particle swarm optimization algorithm for capacitated vehicle routing problem

Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid ap- proximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimiza- tion (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.

A New Clustering Algorithm Using Adaptive Discrete Particle Swarm Optimization in Wireless Sensor Network

Wireless sensor networks (WSNs) are mainly characterized by their limited and non-replenishable energy supply. Hence, the energy efficiency of the infrastructure greatly affects the network lifetime. Clustering is one of the methods that can expand the lifespan of the whole network by grouping the sensor nodes according to some criteria and choosing the appropriate cluster heads(CHs). The balanced load of the CHs has an important effect on the energy consumption balancing and lifespan of the whole network. Therefore, a new CHs election method is proposed using an adaptive discrete particle swarm optimization (ADPSO) algorithm with a fitness value function considering the load balancing and energy consumption. Simulation results not only demonstrate that the proposed algorithm can have better performance in load balancing than low-energy adaptive clustering hierarchy (LEACH), hybrid energy-efficient distributed clustering (HEED), and dynamic clustering algorithm with balanced load (DCBL), but also imply that the proposed algorithm can extend the network lifetime more.

A branch-and-bound algorithm for discrete multi-factor portfolio optimization model

In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

Discrete Optimization on Unsteady Pressure Fluctuation of a Centrifugal Pump Using ANN and Modified GA

Pressure fluctuation due to rotor-stator interaction in turbomachinery is unavoidable,inducing strong vibration in the equipment and shortening its lifecycle.The investigation of optimization methods for an industrial centrifugal pump was carried out to reduce the intensity of pressure fluctuation to extend the lifecycle of these devices.Considering the time-consuming transient simulation of unsteady pressure,a novel optimization strategy was proposed by discretizing design variables and genetic algorithm.Four highly related design parameters were chosen,and 40 transient sample cases were generated and simulated using an automatic program.70%of them were used for training the surrogate model,and the others were for verifying the accuracy of the surrogate model.Furthermore,a modified discrete genetic algorithm(MDGA)was proposed to reduce the optimization cost owing to transient numerical simulation.For the benchmark test,the proposed MDGA showed a great advantage over the original genetic algorithm regarding searching speed and effectively dealt with the discrete variables by dramatically increasing the convergence rate.After optimization,the performance and stability of the inline pump were improved.The efficiency increased by more than 2.2%,and the pressure fluctuation intensity decreased by more than 20%under design condition.This research proposed an optimization method for reducing discrete transient characteristics in centrifugal pumps.

RESEARCH ON OPTIMIZING THE MERGING RESULTS OF MULTIPLE INDEPENDENT RETRIEVAL SYSTEMS BY A DISCRETE PARTICLE SWARM OPTIMIZATION

The result merging for multiple Independent Resource Retrieval Systems (IRRSs), which is a key component in developing a meta-search engine, is a difficult problem that still not effectively solved. Most of the existing result merging methods, usually suffered a great influence from the usefulness weight of different IRRS results and overlap rate among them. In this paper, we proposed a scheme that being capable of coalescing and optimizing a group of existing multi-sources-retrieval merging results effectively by Discrete Particle Swarm Optimization (DPSO). The experimental results show that the DPSO, not only can overall outperform all the other result merging algorithms it employed, but also has better adaptability in application for unnecessarily taking into account different IRRS's usefulness weight and their overlap rate with respect to a concrete query. Compared to other result merging algorithms it employed, the DPSO's recognition precision can increase nearly 24.6%, while the precision standard deviation for different queries can decrease about 68.3%.

Parallel discrete lion swarm optimization algorithm for solving traveling salesman problem

As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.

Service composition based on discrete particle swarm optimization in military organization cloud cooperation

This paper addresses the problem of service composition in military organization cloud cooperation（MOCC）. Military service providers（MSP） cooperate together to provide military resources for military service users（MSU）. A group of atom services, each of which has its level of quality of service（QoS）, can be combined together into a certain structure to form a composite service. Since there are a large number of atom services having the same function, the atom service is selected to participate in the composite service so as to fulfill users＇ will. In this paper a method based on discrete particle swarm optimization（DPSO） is proposed to tackle this problem. The method aims at selecting atom services from service repositories to constitute the composite service, satisfying the MSU＇s requirement on QoS. Since the QoS criteria include location-aware criteria and location-independent criteria, this method aims to get the composite service with the highest location-aware criteria and the best-match location-independent criteria. Simulations show that the DPSO has a better performance compared with the standard particle swarm optimization（PSO） and genetic algorithm（GA）.

A Min-Max Strategy to Aid Decision Making in a Bi-Objective Discrete Optimization Problem Using an Improved Ant Colony Algorithm

A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

A COMBINAT0RIAL ALGORITHM FOR THE DISCRETE OPTIMIZATION OF STRUCTURES

The definition of local optimum solution of the discrete optimization is first given.and then a comprehensive combinatorial algorithm is proposed in this paper. Two-leveloptimum method is used in the algorithm. In the first level optimization, anapproximate local optimum solution X is found by using the heuristic algorithm,relative difference quotient algorithm. with high computational efficiency and highperformance demonstrated by the performance test of random samples. In the secondlevel, a mathematical model of (- 1, 0, 1) programming is established first, and then itis changed into (0, 1) programming model. The local optimum solution X will befrom the (0. 1) programming by using the delimitative and combinatorial algorithm orthe relative difference quotient algorithm. By this algorithm, the local optimumsolution can be obtained certainly, and a method is provnded to judge whether or notthe approximate optimum solution obtained by heuristic algorithm is an optimumsolution. The above comprehensive combinatorial algorithm has higher computationalefficiency.

Binary discrete method of topology optimization

The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate, even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements, meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.

Numerical Solution of a Class of Nonlinear Optimal Control Problems Using Linearization and Discretization

In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

Generalized Algorithms of Discrete Optimization and Their Power Engineering Applications

Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal and heuristic procedures. This allows one to obtain quasi-optimal solutions after a small number of steps, overcoming the NP-completeness of discrete optimization problems. Questions of constructing so-called “duplicate” algorithms are considered to improve the quality of discrete problem solutions. An approach to solving discrete problems with fuzzy coefficients in objective functions and constraints on the basis of modifying the generalized algorithms is considered. Questions of applying the generalized algorithms to solve multicriteria discrete problems are also discussed. The results of the paper are of a universal character and can be applied to the design, planning, operation, and control of systems and processes of different purposes. The results of the paper are already being used to solve power engineering problems.

Circular Obstacle Avoidance Control of the Compass-Type Biped Robot Based on a Blending Method of Discrete Mechanics and Nonlinear Optimization

This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the circular obstacle is derived. Next, an optimal control problem for the discrete compass-type robot is formulated and a solving method of the problem by the sequential quadratic programming is presented in order to calculate a discrete control input. Then, a transformation method that converts a discrete control input into a continuous zero-order hold input via discrete Lagrange-d’ Alembert principle is explained. From the results of numerical simulations, it turns out that obstacle avoidance control for the continuous compass-type robot can be achieved by the proposed method.