Kind Of Optimization Problem Research Articles

Volumes Constrained Layout Optimization of a Continuum with Multiple Materials

A sequencing approach is presented to deal with the layout optimization of a continuum with multiple materials. Commonly, a structure may not have only one type of solid phase, e.g., steel-reinforced concrete structure. To have an excellent mechanical performance of the structure, the layout of the steel-lips should be optimized. It is difficult to solve such kind of optimization problem by traditional method, especially, the number of phases is big. In this work, a criterion method is presented and the essentials of the method are as follows. For example, a structure with many materials, however, initially is set to be with the same solid which is stiffest among the materials. Firstly, the field of strain energy density (SED) of structure is obtained by finite element analysis (FEA). Secondly, the sequence of the SEDs of elements is complemented. Thirdly, according to the order of the SEDs, the material of the elements with lower SED is replaced with the softer material. To keep the stability of algorithm, only a small part of elements is changed in each update. As the amount of a material reaches its critical values, the final layout of the material in structure is obtained. Fourthly, repeat the process for different phases, the layout optimization of the structure is completed until all of the amounts of materials reach their critical values. Finally, numerical examples on volumes constrained optimizations are given to demonstrate the validity and efficiency of the present method.

The Application of Genetic Algorithm on Optimization Problem for Mayonnaise Compositions

For some function optimization problems of non-linear, multi-model and multi-objective, they are difficult to solve by other optimization methods, however, genetic algorithm is easy to find good results, so a kind of optimization problem for mayonnaise compositions based on genetic algorithm is introduced. This termination condition is selected according to the iteration number of maximum generation, the optimal solution of last generation in the evolution is the final result with genetic algorithm to solve optimization problem. The population size is 20, crossover rate is 0.7, and mutation rate is 0.04. Via the evolution of 100 generations, the optimization solution is gotten, which has certain guiding significance for the production.

Optimization Design of Steel-Concrete Composite Beams Considering Bond-Slip Effect

The optimization methodology of the steel-concrete composite beam was proposed in this paper. The objective function is the cost of the composite beams, and the design variables are the geometry parameters, including height and width of the concrete deck, as well as thickness of the steel flange and web. The constraint conditions are main requirements stated in Chinese code for the design of composite beam, reasonable calculating theories and indispensable constructions, as well as some mature and consistent conclusions confirmed by experimental studies. Stiffness reduction coefficient is used to consider the effect of bond-slip effect between concrete and steel when calculating the beam deformation. The optimization for composite beam under uniform loads is given as a demonstration example finally. The methodology proposed in this paper should be useful for obtaining the solution of this kind of optimization problem.

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.

Hybrid of genetic algorithm and simulated annealing for multiple project scheduling with multiple resource constraints

Since scheduling of multiple projects is a complex and time-consuming task, a large number of heuristic rules have been proposed by researchers for such problems. However, each of these rules is usually appropriate for only one specific type of problem. In view of this, a hybrid of genetic algorithm and simulated annealing (GA-SA Hybrid) is proposed in this paper for generic multi-project scheduling problems with multiple resource constraints. The proposed GA-SA Hybrid is compared to the modified simulated annealing method (MSA), which is more powerful than genetic algorithm (GA) and simulated annealing (SA). As both GA and SA are generic search methods, the GA-SA Hybrid is also a generic search method. The random-search feature of GA, SA and GA-SA Hybrid makes them applicable to almost all kinds of optimization problems. In general, these methods are more effective than most heuristic rules. Three test projects and three real projects are presented to show the advantage of the proposed GA-SA Hybrid method. It can be seen that GA-SA Hybrid has better performance than GA, SA, MSA, and some most popular heuristic methods.

Evolutionary techniques for optimization problems in integrated manufacturing system: State-of-the-art-survey

Integrated manufacturing system (IMS) is a novel manufacturing environment which has been developed for the next generation of manufacturing and processing technologies. It consists of engineering design, process planning, manufacturing, quality management, and storage and retrieval functions. Improving the decision quality in those fields give rise to complex combinatorial optimization problems, unfortunately, most of them fall into the class of NP-hard problems. Find a satisfactory solution in an acceptable time play important roles. Evolutionary techniques (ET) have turned out to be potent methods to solve such kind of optimization problems. How to adapt evolutionary technique to the IMS is very challenging but frustrating. Many efforts have been made in order to give an efficient implementation of ET to optimize the specific problems in IMS. In this paper, we address four crucial issues in IMS, including design, planning, manufacturing, and distribution. Furthermore, some hot topics in these issues are selected to demonstrate the efficiency of ET’s application, such as layout design (LD) problem, flexible job-shop scheduling problem (fJSP), multistage process planning (MPP) problem, and advanced planning and scheduling (APS) problem. First, we formulate a generalized mathematic models for all those problems; several evolutionary algorithms which adapt to the problems have been proposed; some test instances based on the practical problems demonstrate the effectiveness and efficiency of our proposed approach.

A genetic approach to joint routing and link scheduling for wireless mesh networks

Wireless mesh networks are an attractive technology for providing broadband connectivity to mobile clients who are just on the edge of wired networks, and also for building self-organized networks in places where wired infrastructures are not available or not deemed to be worth deploying. This paper investigates the joint link scheduling and routing issues involved in the delivery of a given backlog from any node of a wireless mesh network towards a specific node (which acts as a gateway), within a given deadline. Scheduling and routing are assumed to be aware of the physical interference among nodes, which is modeled in the paper by means of a signal-to-interference ratio. Firstly, we present a theoretical model which allows us to formulate the task of deriving joint routing and scheduling as an integer linear programming problem. Secondly, since the problem cannot be dealt with using exact methods, we propose and use a technique based on genetic algorithms. To the best of our knowledge, these algorithms have never been used before for working out these kinds of optimization problems in a wireless mesh environment. We show that our technique is suitable for this purpose as it provides a good trade-off between fast computation and the overall goodness of the solution found. Our experience has in fact shown that genetic algorithms would seem to be quite promising for solving more complex models than the one dealt with in this paper, such as those including multiple flows and multi-radio multi-channels.

1208 船体中央断面の多段階最適設計に関する研究

There are more than 100 design variables and 2000 constraint conditions in designing mid-ship section of ship structure, and hence, it is very difficult to determine all design variables with satisfying all constraint conditions and having a reasonable value of objective function, or construction cost. Since this kind of optimization problem has so many design variables and a huge number of constraint conditions, it takes unbelievably large computational effort for obtaining an optimal solution when all design variables are solved simultaneously. A multi-step optimization method is introduced here with the aim of reducing the computational time. Since the design process of a mid-ship section is divided into three stages, double bottom, bilge hopper tank and topside tank stages, traditionally, three-step optimization may be rational and is introduced. But, when design variables in each step are determined separately, the solution obtained after the final step is far form the optimal solution obtained by solving all design the variables at once. In order to resolve this problem, characteristic design variable method is introduced and investigated here. The proposed method gives good solutions with satisfying all constraint conditions and having reasonable value of the objective function instead of solving all design variables at once. Genetic algorithm is used for optimization procedure in this study.

A hybrid immigrants scheme for genetic algorithms in dynamic environments

Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution(s) of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.

A novel splicing/decomposable binary encoding and its operators for genetic and evolutionary algorithms

In this paper, we introduce a new genetic representation — a splicing/decomposable (S/D) binary encoding, which was proposed based on some theoretical guidance and existing recommendations for designing efficient genetic representations. The S/D binary representation can be spliced and decomposed to describe potential solutions of the problem with different precisions by different number of uniform-salient building blocks (BBs). According to the characteristics of the S/D binary representation, genetic and evolutionary algorithms (GEAs) can be applied from the high scaled to the low scaled BBs sequentially to avoid a noise from the competing BBs and improve GEAs’ performance. Our theoretical and empirical investigations reveal that the S/D binary representation is more proper than other existing binary encodings for GEAs searching. Moreover, we define a new genotypic distance on the S/D binary space, which is equivalent to the Euclidean distance on the real-valued space during GEAs convergence. Based on the new genotypic distance, GEAs can reliably and predictably solve problems of bounded complexity and the methods depended on the Euclidean distance for solving different kinds of optimization problems can be directly used on the S/D binary space.

Optimal Design of Magnitude Responses of Rational Infinite Impulse Response Filters

This correspondence considers a design of magnitude responses of optimal rational infinite impulse response (IIR) filters. The design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters (the error function reflects a ripple square magnitude) is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband, as well as the stability condition. Since the cost function is nonsmooth and nonconvex, while the constraints are continuous, this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem. To address this issue, our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints. Then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method. The solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem. Hence, small transition bandwidth filters can be obtained

A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Analysis of Interior-Point Paths.

Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning the existence of these paths, their analyticity and the limiting behavior of their derivatives as r ↓ 0, and this also for degenerate problems in the areas of linear programming, linear complementarity problems, and semi-definte programming.

A Superlinearly Convergent SSLE Algorithm for Optimization Problems with Linear Complementarity Constraints

In this paper we study a special kind of optimization problems with linear complementarity constraints. First, by a generalized complementarity function and perturbed technique, the discussed problem is transformed into a family of general nonlinear optimization problems containing parameters. And then, using a special penalty function as a merit function, we establish a sequential systems of linear equations (SSLE) algorithm. Three systems of equations solved at each iteration have the same coefficients. Under some suitable conditions, the algorithm is proved to possess not only global convergence, but also strong and superlinear convergence. At the end of the paper, some preliminary numerical experiments are reported.

Optimization of Catalytic Processes and Reactors

Efficient methods and algorithms have been developed for the optimization of catalytic processes and reactors. In mathematical terms, these problems reduce to finding the extremum of a functional of a large number of variables whose domain of variation is subject to various constraints as sets of partial differential equations and algebraic inequalities. This implies solving problems in which the domain of extremals is closed. Applying Pontryagin's maximum principle to catalytic processes described by sets of differential equations with constrained phase and control variables allows the necessary set of optimal conditions to be found. A numerical algorithm has been developed for solving nonlinear boundary-value problems that arise when the maximum principle is employed. The efficiency of this algorithm is demonstrated by the example of the catalytic oligomerization of α-methylstyrene, a typical process requiring various kinds of optimization problems to be solved. The theoretical optimization of the process has served as the basis for the engineering optimization of an industrial reactor. Optimal controls were determined in both the theoretical and engineering optimization steps.

Optimal Design of Sensor Parameters in PLC-Based Control System Using Mixed Integer Programming

Programmable Logic Controller (PLC) has been widely used in the industrial control. Inherently, the PLC-based system is a class of Hybrid Dynamical System (HDS) in which continuous state of the plant is controlled by the discrete logic-based controller. This paper firstly presents the formal algebraic model of the PLC-based control systems which enable the designer to formulate the various kinds of optimization problem. Secondly, the optimization problem of the 'sensor parameters,' such as the location of the limit switch in the material handling system, the threshold temperature of the thermostat in the temperature control system, is addressed. Finally, we formulate this problem as Mixed Logical Dynamical Systems (MLDS) form which enables us to optimize the sensor parameters by applying the Mixed Integer Programming.

A hybrid genetic algorithm–neural network strategy for simulation optimization

Abstract Simulation optimization aims at determining the best values of input parameters, while the analytical objective function and constraints are not explicitly known in terms of design variables and their values only can be estimated by complicated analysis or time-consuming simulation. In this paper, a hybrid genetic algorithm–neural network strategy (GA–NN) is proposed for such kind of optimization problems. The good approximation performance of neural network (NN) and the effective and robust evolutionary searching ability of genetic algorithm (GA) are applied in hybrid sense, where NNs are employed in predicting the objective value, and GA is adopted in searching optimal designs based on the predicted fitness values. Numerical simulation results and comparisons based on a well-known pressure vessel design problem demonstrate the feasibility and effectiveness of the framework, and much better results are achieved than some existed literature results.

OPTIMIZATION OF COMPLEX SYSTEM RELIABILITY BY A MODIFIED GREAT DELUGE ALGORITHM

In this paper, a global optimization meta-heuristic, the great deluge algorithm, is extended and applied to optimize the reliability of complex systems. Two different kinds of optimization problems (i) Reliability optimization of a complex system with constraints on cost and weight (ii) Optimal redundancy allocation in a multi-stage mixed system with constraints on cost and weight are solved to demonstrate the effectiveness of the algorithm. A software developed in ANSI C, implements the algorithm. In terms of both accuracy and speed, it is observed that the present algorithm, the modified great deluge algorithm (MGDA) yielded far superior results compared to those obtained by the simulated annealing, the improved non-equilibrium simulated annealing and other optimization algorithms. Further, when both accuracy and speed are considered simultaneously, both MGDA and another meta-heuristic, ant colony optimization (ACO) yielded comparable results. In conclusion, the MGDA, can be used as an efficient alternative to ACO and other existing optimization techniques.

Representability of convex sets by analytical linear inequality systems

The solution sets of analytical linear inequality systems posed in the Euclidean space form a transition class between the polyhedral convex sets and the closed convex sets, which are representable by means of linear continuous systems. The constraint systems of many semi-infinite programming problems are analytical, and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems. The Euclidean closed n-dimensional balls admit analytical representation if and only if n<3. This paper solves, in a negative way, the analytical representation problem for a wide class of n-dimensional convex sets, with n⩾3, which includes quasi-polyhedral sets and smooth convex bodies.

A (μ + λ) evolutionary algorithm for reconstruction of SPECT data

Algorithms used to reconstruct single photon emission computed tomography (SPECT) data are based on one of two principles: filtered back projection or iterative methods. In this paper, an evolution strategy (ES) was applied to reconstruct transaxial slices of SPECT data. Evolutionary algorithms are stochastic global search methods that have been used successfully for many kinds of optimization problems. The newly developed reconstruction algorithm consisting of /spl mu/ parents and /spl lambda/ children uses a random principle to readjust the voxel values, whereas other iterative reconstruction methods use the difference between measured and simulated projection data. The (/spl mu/ + /spl lambda/)-ES was validated against a test image, a heart, and a Jaszczak phantom. The resulting transaxial slices show an improvement in image quality, in comparison to both the filtered back projection method and a standard iterative reconstruction algorithm.