Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Observations Regarding Choice Behaviour in Interactive Multiple Criteria Decision-Making Environments: An Experimental Investigation
1989
Many interactive procedures have been developed for solving optimization problems having multiple criteria. In such procedures, an exploration over the feasible or efficient region is conducted for locating the most preferred solution. As Steuer (1986) notes, interactive procedures are characterized by phases of decision-making alternating with phases of computation. Generally a pattern is established that we keep repeating until termination. At each iteration, a solution, or group of solutions, is generated for a decision-maker’s (DM’s) examination. Based on the examination, the DM inputs information to the solution procedure in the form of tradeoffs, pairwise comparisons, aspiration level…
Experiments on a Prey Predators System
2003
The paper describes a prey-predators system devoted to perform experiments on concurrent complex environment. The problem has be treated as an optimization problem. The prey goal is to escape from the predators reaching its lair, while predators want to capture the prey. At the end of the 19th century, Pareto found an optimal solutions for decision problems regarding more than one criterion at the same time. In most cases this ‘Pareto-set’ cannot be determined analytically or the computation time could be exponential. In such cases, evolutionary Algorithms (EA) are powerful optimization tools capable of finding optimal solutions of multi-modal problems. Here, both prey and predators learn i…
Adaptive and Dynamic Ant Colony Search Algorithm for Optimal Distribution Systems Reinforcement Strategy
2006
The metaheuristic technique of Ant Colony Search has been revised here in order to deal with dynamic search optimization problems having a large search space and mixed integer variables. The problem to which it has been applied is an electrical distribution systems management problem. This kind of issues is indeed getting increasingly complicated due to the introduction of new energy trading strategies, new environmental constraints and new technologies. In particular, in this paper, the problem of finding the optimal reinforcement strategy to provide reliable and economic service to customers in a given time frame is investigated. Utilities indeed need efficient software tools to take deci…
Interactive Multiobjective Optimization of Superstructure SMB Processes
2009
We consider multiobjective optimization problems arising from superstructure formulation of Simulated Moving Bed (SMB) processes. SMBs are widely used in many industrial separations of chemical products and they are challenging from the optimization point of view. We employ efficient interactive multiobjec-tive optimization which enables considering several conflicting objectives simultaneously without unnecessary simplifications as have been done in previous studies. The interactive IND-NIMBUS software combined with the IPOPT optimizer is used to solve multiobjective SMB design problems. The promising results of solving a superstructure SMB optimization problem with four objectives demonst…
Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems
2009
Evolutionary multi-objective optimization algorithms are commonly used to obtain a set of non-dominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficient and convergent procedure. In this paper, we test an augmented local search based EMO procedure rigorously on a test suite of constrained and unconstrained multi-objective optimization problems. The success of our approach on most of the test problems not only provides confidence but also stresses the importance of hybrid evolutionary algorithms in solving multi-objective optimization problems.
Towards Better Integration of Surrogate Models and Optimizers
2019
Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been proven to be very effective in solving (synthetic and real-world) computationally expensive optimization problems with a limited number of function evaluations. The two main components of SAEAs are: the surrogate model and the evolutionary optimizer, both of which use parameters to control their respective behavior. These parameters are likely to interact closely, and hence the exploitation of any such relationships may lead to the design of an enhanced SAEA. In this chapter, as a first step, we focus on Kriging and the Efficient Global Optimization (EGO) framework. We discuss potentially profitable ways of a better integration of…
Using a TSP heuristic for routing order pickers in warehouses
2010
In this paper, we deal with the sequencing and routing problem of order pickers in conventional multi-parallel-aisle warehouse systems. For this NP-hard Steiner travelling salesman problem (TSP), exact algorithms only exist for warehouses with at most three cross aisles, while for other warehouse types literature provides a selection of dedicated construction heuristics. We evaluate to what extent reformulating and solving the problem as a classical TSP leads to performance improvements compared to existing dedicated heuristics. We report average savings in route distance of up to 47% when using the LKH (Lin-Kernighan-Helsgaun) TSP heuristic. Additionally, we examine if combining problem-sp…
Optimal positioning of irregular shapes in stamping die strip
2010
The nesting of two-dimensional shapes is a common problem, where raw material has to be economically cut. As for the single-pass single-row strip layout, several algorithms, based on established methods, have been proposed. Moreover, it should be noticed that the optimum layout should also consider a few constraints, like grain orientation for subsequent forming operation, correct bridge width, and the commercial roll of metal width in order to make solutions applicable in real industrial environments. Most of the procedures until now shown in literature are quite complex and often ignore these real constraints. They usually make use of sliding techniques and are not able to effectively wor…
Construction and optimality of a special class of balanced designs
2006
The use of balanced designs is generally advisable in experimental practice. In technological experiments, balanced designs optimize the exploitation of experimental resources, whereas in marketing research experiments they avoid erroneous conclusions caused by the misinterpretation of interviewed customers. In general, the balancing property assures the minimum variance of first-order effect estimates. In this work the authors consider situations in which all factors are categorical and minimum run size is required. In a symmetrical case, it is often possible to find an economical balanced design by means of algebraic methods. Conversely, in an asymmetrical case algebraic methods lead to e…
Design of a Permanent Magnet Synchronous Generator using Interactive Multiobjective Optimization
2017
We consider an analytical model of a permanent magnet synchronous generator and formulate a mixed-integer constrained multiobjective optimization problem with six objective functions. We demonstrate the usefulness of solving such a problem by applying an interactive multiobjective optimization method called NIMBUS. In the NIMBUS method, a decision is iteratively involved in the optimization process and directs the solution process in order to find her/his most preferred Pareto optimal solution for the problem. We also employ a commonly used noninteractive evolutionary multiobjective optimization method NSGA-II to generate a set of solutions that approximates the Pareto set and demonstrate t…