We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along row...

The Antlion Optimization (ALO) algorithm is a meta-heuristic optimization based on the hunting of ants by antlions. basic inadequacy this that it has long run time because random walk model used for ant's movement. We improved some mechanisms in ALO algorithm, such as ants' walking, reproduction, sliding towards antlion, elitism, and selection procedure. This proposed called Improved (IALO) alg...

Reducing manufacturing lead times and minimizing work-in-process (WIP) inventories are the cornerstones of popular manufacturing strategies such as Lean, Quick Response, and Just-inTime Manufacturing. In this paper, we present a model that captures the relationship between facility layout and congestion-related measures of performance. We use the model to introduce a formulation of the facility...

Evolutionary algorithms solve problems by simulating the evolution of a population candidate solutions. We focus on evolving permutations for ordering such as traveling salesperson problem (TSP), well assignment quadratic (QAP) and largest common subgraph (LCS). propose cycle mutation, new mutation operator whose inspiration is well-known crossover operator, concept permutation cycle. use fitne...

Variances of solution values that can be calculated in polynomial time may be associated with an instance of the Quadratic Assignment Problem (QAP). The problem of graph isomorphism can be modeled as a QAP, associating each data matrix with each graph. In this work, we look for invariant edge weight functions for the graphs composing the instances in order to try to find quantitative difference...

The quadratic assignment problem (QAP) is one of the nondeterministic polynomial (NP)-hard combinatorial optimization problems. One of the heuristic algorithms for the QAP is tabu-search. Exponential tabusearch, which is one of improved versions of the tabu search, was proposed using a neural network, and it was further extended to chaotic tabu search with a chaotic neural network. Chaotic dyna...

Hospital facilities are known as functionally complex buildings. There usually configurational problems that lead to inefficient transportation processes for patients, medical staff, and/or logistics of materials. The Quadratic Assignment Problem (QAP) is a well-known problem in the field Operations Research from category facility's location/allocation problems. However, it has rarely been util...

In this paper, we describe an approach for solving the quadratic assignment problem (QAP) that is based on genetic algorithms (GA). It will be shown that a standard canonical GA (SGA), which involves genetic operators of selection, reproduction, crossover, and mutation, tends to fall short of the desired performance expected of a search algorithm. The performance deteriorates significantly as t...

In this paper we address the Adjacent Quadratic Assignment Problem (AQAP) which is a variant of the QAP where the cost coefficient matrix has a particular structure. Motivated by strong lower bounds obtained by applying Reformulation Linearization Technique (RLT) to the classical QAP, we propose two special RLT representations for the problem. The first is based on a “flow” formulation whose li...

Facility layout planning is an indispensable part of the manufacturing and service operations. In literature, there are two main different approaches for solution facility problem: While first one aims to minimize both total transportation assignment costs in a quantitative way, second maximize closeness relationship more qualitative way. this study, we use these model multi-objective optimizat...