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The facility layout problem (FLP) is a very important class of NP-hard problems in operations research that deals with the optimal assignment of facilities to minimize transportation costs. The quadratic assignment problem (QAP) can model the FLP effectively. One of the FLPs is the hospital facility layout problem that aims to place comprehensive clinics, laboratories, and radiology units within predefined boundaries in a way that minimizes the cost of movement of patients and healthcare personnel. We are going to develop a hybrid method based on discrete differential evolution (DDE) algorithm for solving the QAP. In the existing DDE algorithms, certain issues such as premature convergence, stagnation, and exploitation mechanism have not been properly addressed. In this study, we first aim to discover the issues that make the current problem worse and to identify the best solution to the problem, and then we propose to develop a hybrid algorithm (HDDETS) by combining the DDE and tabu search (TS) algorithms to enhance the exploitation mechanism in the DDE algorithm. Then, the performance of the proposed HDDETS algorithm is evaluated by implementing on the benchmark instances from the QAPLIB website and by comparing with DDE and TS algorithms on the benchmark instances. It is found that the HDDETS algorithm has better performance than both the DDE and TS algorithms where the HDDETS has obtained 42 optimal and best-known solutions from 56 instances, while the DDE and TS algorithms have obtained 15 and 18 optimal and best-known solutions out of 56 instances, respectively. Finally, we propose to apply the proposed algorithm to find the optimal distributions of the advisory clinics inside the Azadi Hospital in Iraq that minimizes the total travel distance for patients when they move among these clinics. Our application shows that the proposed algorithm could find the best distribution of the hospital’s rooms, which are modeled as a QAP, with reduced total distance traveled by the patients.

The Travelling Salesman Problem (TSP) is an NP-hard problem with high number of possible solutions. The complexity increases with the factorial of n nodes in each specific problem. Meta-heuristic algorithms are an optimization algorithm that able to solve TSP problem towards a satisfactory solution. To date, there are many meta-heuristic algorithms introduced in literatures which consist of different philosophies of intensification and diversification. This paper focuses on 6 heuristic algorithms: Nearest Neighbor, Genetic Algorithm, Simulated Annealing, Tabu Search, Ant Colony Optimization and Tree Physiology Optimization. The study in this paper includes comparison of computation, accuracy and convergence.

The quadratic assignment problem (QAP) is a combinatorial optimization problem that arises in many real-world applications, such as equipment allocation in industry. The QAP is NP-hard and, in practice, one of the hardest combinatorial optimization problems to solve to optimality. Exact solutions of QAP are typically obtained by the branch-and-bound method. This method, however, potentially requires a high computational effort, and the use of good lower bounds is essential to prune the search tree. Branch-and-bound algorithms that use the dual-ascent procedure based on the level-2 reformulation linearization technique (RLT2) belong to the state of the art on exactly solving QAP. In this work, we propose a parallel implementation of that branch-and-bound algorithm. Our approach uses the Auction Algorithm of Bertsekas and Castañon to solve the linear assignment problems of RLT2, which allows us to take advantage of the massive parallel environment of graphics processing units to speed up the lower bound computation and implement some memory optimization techniques to address large-size problems. We report experimental results that show significant execution time reductions compared to previous works and allow us to provide, for the first time, exact solutions for two instances of QAP: tai35b and tai40b.

A new version of BLS algorithm is introduced.Levenshtein Distance (LD) metric is applied to the BLS heuristic.The QAP is optimized with several processors using OpenMP.Significant improvements are obtained.The BLS-OpenMP can be reported as one of the best heuristics for the QAP. The Quadratic Assignment Problem (QAP) is one of the most challenging NP-Hard combinatorial optimization problems. Circuit-layout design, transportation/traffic engineering, and assigning gates to airplanes are some of the interesting applications of the QAP. In this study, we introduce an enhanced version of a recent local search heuristic, Breakout Local Search Algorithm (BLS), by using the Levenshtein Distance metric for checking the similarity of the new starting points to previously explored QAP permutations. The similarity-checking process prevents the local search algorithm, BLS, from getting stuck in already-explored areas. In addition, the proposed BLS Algorithm (BLS-OpenMP) incorporates multi-threaded computation using OpenMP. The stagnation-aware search for the optimal solutions of the QAP is executed concurrently on several cores with diversified trajectories while considering their similarity to already-discovered local optima. The exploration of the search space is improved by selecting the starting points intelligently and speeding up the fitness evaluations linearly with number of processors/threads. BLS-OpenMP has been tested on the hardest 59 problem instances of the QAPLIB, and it obtained 57 of the best known results. The overall deviation of the achieved solutions from the best known results is 0.019% on average, which is a significant improvement compared with state-of-the-art algorithms.

In this paper, we address continuous, integer and combinatorial k-sum optimization problems. We analyze different formulations of this problem that allow to solve it through the minimization of a relatively small number of minisum optimization problems. This approach provides a general tool for solving a variety of k-sum optimization problems and at the same time, improves the complexity bounds of many ad-hoc algorithms previously reported in the literature for particular versions of this problem. Moreover, the results developed for k-sum optimization have been extended to the more general case of the convex ordered median problem, improving upon existing solution approaches.

In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted data" in which this basic correspondence has been lost. Several recent papers have considered this situation without further assumptions on the underlying permutation. In applications, the latter is often to known to have additional structure that can be leveraged. Specifically, we herein consider the common scenario of "sparsely permuted data" in which only a small fraction of the data is affected by a mismatch between response and predictors. However, an adverse effect already observed for sparsely permuted data is that the least squares estimator as well as other estimators not accounting for such partial mismatch are inconsistent. One approach studied in detail herein is to treat permuted data as outliers which motivates the use of robust regression formulations to estimate the regression parameter. The resulting estimate can subsequently be used to recover the permutation. A notable benefit of the proposed approach is its computational simplicity given the general lack of procedures for the above problem that are both statistically sound and computationally appealing.

We consider a relaxation of the quadratic assignment problem without the constraint on the number of objects assigned to a specific position. This problem is NP-hard in the general case. To solve the problem, we propose a polynomial algorithm with guaranteed posterior accuracy estimate; we distinguish a class of problems with special assignment cost functions where the algorithm is 2-approximate. We show that if the graph in question contains one simple loop, and the set of assignment positions is a metric space, the proposed algorithm is 2-approximate and guaranteed to be asymptotically exact. We conduct a computational experiment in order to analyze the algorithm's errors and evaluate its accuracy.

This study proposes a new approach combining the chemical reaction optimization framework with the unified tabu search (UTS) heuristic to solve the capacitated vehicle routing problem (CVRP). The CVRP is one of the most well-studied problems not only because of its real-life applications but also due to the fact that the CVRP could be used to evaluate the efficiency of new algorithms and optimization methods. Chemical reaction optimization (CRO) is a new optimization framework mimicking the nature of chemical reactions. The CRO method has proved to be very effective for solving NP-hard optimization problems such as the quadratic assignment problem, neural network training, the knapsack problem, and the traveling salesman problem. We also present the design of elementary chemical reaction operations, the adaptation of the UTS algorithm to educate solutions in these operations. Finally, a thorough testing against well-known benchmark problems has been conducted. Experimental results show that the proposed algorithm is efficient and highly competitive in comparison with several prominent algorithms for this problem. The presented methodology may be a fine approach for developing similar algorithms to address other routing variants.

In this paper we introduce a new approach to solve fuzzy assignment problem namely, ones assignment method. Considering each fuzzy cost as a triangular fuzzy numbers the fuzzy assignment problem has been transformed into crisp values by using linguistic variables and ranking techniques and then it is solved by ones assignment method. The proposed method is a systematic procedure, easy to apply and can be utilized for all types of assignment problem with maximize or minimize objective functions. At the end, this method is illustrated with some numerical example

The doubly constrained entropy distribution/assignment (DEDA) problem that combines a gravity-based trip distribution (TD) problem and a traffic assignment (TA) problem has long been formulated as an optimization model and solved by two solution algorithms, i.e., partial- and full-linearization solution algorithms. As an alternative, this research first treats the DEDA problem by the augmented Lagrangian dual (ALD) method as the singly constrained entropy distribution/assignment (SEDA) problem, which in turn is addressed, via a tactical supernetwork representation, as an “extended” 1-origin-to-1-destination TA problem. A quick-precision TA solution algorithm, − called TAPAS (Traffic Assignment by Paired Alternative Segments), − is then adopted for solutions. The proposed approach is demonstrated with a numerical example for the correctness of the result, using Lingo 11 solver and the partial linearization solution (PLS) algorithm. Moreover, through the use of TAPAS in the innermost loop, the proposed approach also has the merit of generating unique path flow solution, which is very useful in route guidance under the intelligent transportation systems environment, among other academic applications. In addition, the proposed approach can be easily applied, or with minor modification at most, to various combined models in travel demand forecasting.

Generally, the optimal solution of assignment problem can be obtained by Hungarian algorithm of two-sided optimization with time complexity . This paper suggests one-sided optimal assignment and swap optimization algorithm with time complexity can be achieve the goal of two-sided optimization. This algorithm selects the minimum cost for each row, and reassigns over-assigned to under-assigned cell. Next, that verifies the existence of swap optimization candidates, and swap optimizes with . For 27 experimental data, the swap-optimization performs only 22% of data, and 78% of data can be get the two-sided optimal result through one-sided optimal result. Also, that can be improves on the solution of best known solution for partial problems.

We consider the bilevel assignment problem in which each decision maker (i.e., the leader and the follower) has its own objective function and controls a distinct set of edges in a given bipartite graph. The leader acts first by choosing some of its edges. Subsequently, the follower completes the assignment process. The edges selected by the leader and the follower are required to constitute a perfect matching. In this paper we propose an exact solution approach, which is based on a branch-and-bound framework and exploits structural properties of the assignment problem. Extensive computational experiments with linear sum and linear bottleneck objective functions are conducted to demonstrate the performance of the developed methods. While the considered problem is known to be NP-hard in general, we also describe some restricted cases that can be solved in polynomial time.

Graphical abstractDisplay Omitted HighlightsA hybrid method combining great deluge and tabu search algorithms is proposed.This hybrid is supported with a two-stage external memory.First stage of acts as a short term memory that is frequently updated.Second stage acts as a long term memory that is updated less frequently.Elements of the second stage are maximally dissimilar in variable space. A two-stage memory architecture is maintained within the framework of great deluge algorithm for the solution of single-objective quadratic assignment problem. Search operators exploiting the accumulated experience in memory are also implemented to direct the search towards more promising regions of the solution space. The level-based acceptance criterion of the great deluge algorithm is applied for each best solution extracted in a particular iteration. The use of short- and long-term memory-based search supported by effective move operators resulted in a powerful combinatorial optimization algorithm. A successful variant of tabu search is employed as the local search method that is only applied over a few randomly selected memory elements when the second stage memory is updated. The success of the presented approach is illustrated using sets of well-known benchmark problems and evaluated in comparison to well-known combinatorial optimization algorithms. Experimental evaluations clearly demonstrate that the presented approach is a competitive and powerful alternative for solving quadratic assignment problems.

We propose an exact algorithm to find the optimal solution to the grey pattern problem which is a special instance of the quadratic assignment problem. A very effective branch and bound algorithm is constructed. The special structure of the problem is exploited and optimal solutions for many problem instances established. One instance based on 64 facilities, organized in an 8 by 8 pattern, that was extensively researched in the literature was optimally solved in 15 s of computer time while existing papers report solution times of hours.

Display Omitted A major optimization problem in synthesis of sequential circuits is State Assignment (SA).Cuckoo search optimization (CSO) algorithm is employed for solving the SA problem.CSO targets area minimization of synthesized sequential circuits.CSO results outperform deterministic and non-deterministic heuristic optimization methods. A major optimization problem in the synthesis of sequential circuits is State Assignment or State Encoding in Finite State Machines (FSMs). The state assignment of an FSM determines the complexity of its combinational circuit and thus area, delay, testability and power dissipation. Since optimal state assignment is an NP-hard problem and existing deterministic algorithms produce solutions far from best known solutions, we resort to the use of non-deterministic iterative optimization heuristics. This paper proposes the use of cuckoo search optimization (CSO) algorithm for solving the state assignment problem (SAP) of FSMs with the aim of minimizing area of the resulting sequential circuit. Results obtained from the CSO algorithm are compared with those obtained from binary particle swarm optimization (BPSO) algorithm, genetic algorithm (GA), and the well-known deterministic methods of NOVA and JEDI. The results indicate that CSO outperforms deterministic methods as well as other non-deterministic heuristic optimization methods.

Instead of using traditional (two-parent) crossover operator, multi-parent crossover operator is used in genetic algorithms to improve solution quality for many numerical optimization problems. However, very few literatures are available on multi-parent crossover operator for combinatorial optimization problems, especially, quadratic assignment problem (QAP). This paper proposes a multi-parent extension of the sequential constructive crossover (MPSCX), which is a generalization of the traditional sequential constructive crossover (SCX), for the QAP. Then a multi-parent genetic algorithm (MPGA) using MPSCX is developed. Experimental results on ten QAPLIB instances show that our MPGA significantly improves GA using SCX by up to 1.75 % in average assignment cost with maximum of 2.79 % away from the best known solution value. Finally, the efficiency of our MPGA is compared against MPGA using an existing multi-parent crossover for the problem. Experimental results show that our MPGA is better.

We address the solution of a very challenging (and previously unsolved) instance of the quadratic 3-dimensional assignment problem, arising in digital wireless communications. The paper describes the techniques developed to solve this instance to optimality, from the choice of an appropriate mixed-integer programming formulation, to cutting planes and symmetry handling. Using these techniques we were able to solve the target instance with moderate computational effort (2.5 million nodes and 1 week of computations on a standard PC).

The assignment problem (AP) is to optimally solve the task of assigning n jobs to n individuals, such that minimum cost or maximum profit can be obtained. It is a vitally important NP-complete problem in operation management and applied mathematics, having a wide range of applications. In this paper, we present a new parallel DNA algorithm to solve the assignment problem using DNA molecular operations. Meanwhile, we design flexible length DNA strands to represent different jobs and individuals, take appropriate steps and get the solutions of the AP in proper length range and with O ( n 2 ) time complexity. We extend the application of DNA molecular operations and simultaneity reduce the complexity of the computation.

We present a hyper-heuristic algorithm for solving combinatorial black-box optimization problems. The algorithm named CMA-VNS stands for a hybrid of variants of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and Variable Neighborhood Search (VNS). The framework design and the design profiles of variants of CMA-VNS are introduced to enhance the intensification of searching for conventional CMA-ES solvers. We explain the parameter configuration details, the heuristic profile selection, and the rationale of incorporating machine learning methods during the study. Experimental tests and the results of the first and the second Combinatorial Black-Box Optimization Competitions (CB-BOC 2015, 2016) confirmed that CMA-VNS is a competitive hyper-heuristic algorithm.

There are many nature-inspired algorithms being proposed and researched to solve combinatorial optimization problems. The theory of Five-elements in Chinese traditional culture implies a possible approach to solve present-day problems of science and engineering. In this paper, the Five-elements Cycle Model (FECM) is developed based on the mechanism of generation and restriction among five elements, and Five-elements Cycle Optimization (FECO) algorithm is proposed for finding the optimal solution of travelling salesman problems. The performance and parameter comparison of FECO is given by experiments, the comparison with 7 optimization algorithms based on various mechanisms for some TSP instances from TSPLIB are also given, which indicate the availability of FECO.

Combinatorial optimization problems such as the Travelling Salesman Problem, Quadratic Assignment Problem and Sliding-Tile Puzzle have structure that can be described algebraically and exploited to improve search quality. In particular, heuristic functions for these problems can be described in terms of symmetric groups. By employing techniques from the emerging field of algebraic machine learning, we investigate the harmonic decomposition of popular sliding-tile puzzle heuristics via the extension of the Fourier Transform to noncommutative groups. The Fourier-space representation for these heuristics can then be manipulated by multiplication with a real-valued weight vector. By performing such a reweighting and then taking the inverse transform, we obtain a ‘filtered’ version of the original heuristic. Taking the 8-puzzle as a case study, we demonstrate that heuristic accuracy is related to harmonic spectral density and further that the heuristic functions given by the Hamming and Manhattan distance metrics on puzzle state can be transformed into significantly better heuristics by performing a search in the weight space.

This paper presents the analysis of the 2-sum problem and the spectral algorithm. The spectral algorithm was proposed by Barnard, Pothen and Simon in [1]; its heuristic properties have been advocated by George and Pothen in [4] by formulation of the 2-sum problem as a Quadratic Assignment Problem. In contrast to that analysis another approach is proposed: permutations are considered as vectors of Euclidian space. This approach enables one to prove the bound results originally obtained in [4] in an easier way. The geometry of permutations is considered in order to explain what are ‘good’ and ‘pathological’ situations for the spectral algorithm. Upper bounds for approximate solutions generated by the spectral algorithm are proved. The results of numerical computations on (graphs of) large sparse matrices from real-world applications are presented to support the obtained results and illustrate considerations related to the ‘pathological’ cases.

The aim of Land-use Suitability Analysis and Planning Problem (LSAPP) is to identify the most suitable parcels of land for future land-uses considering several conflicting criteria. LSAPP can be modeled using a variant of a well-known combinatorial optimization problem called Quadratic Assignment Problem (QAP). In this paper, a multi-objective mathematical model is developed for LSAPP based on QAP modeling. The large-size instances of the proposed multi-objective mathematical model are difficult to solve in a reasonable CPU time using exact algorithms. So, an efficient three-phase hybrid solution procedure is proposed. In the first phase, the compensatory objectives are integrated using Analytic Hierarchy Process (AHP) and Decision-Making Trial and Evaluation Laboratory. Then, based on the aforementioned suitability objective function and other spatial objectives and constraints, a multi-objective LSAPP is constructed. Finally, a hybrid multiple objective meta-heuristic algorithm is proposed to solve the ...

Combined with quantum computing and genetic algorithm, quantum genetic algorithm (QGA) shows considerable ability of parallelism. Experiments have shown that QGA performs quite well on TSP, job shop problem and some other typical combinatorial optimization problems. The other problems like nutritional diet which can be transformed into specific combinational optimization problem also can be solved through QGA smoothly. This paper sums up the main points of QGA for general combinatorial optimization problems. These points such as modeling of the problem, qubit decoding and rotation strategy are useful to enhance the convergence speed of QGA and avoid premature at the same time.

Performance comparisons between algorithms have a long tradition in metaheuristic research. An early example is comparisons between Tabu Search (TS) and Simulated Annealing (SA) algorithms for tackling the Quadratic Assignment Problem (QAP). The results of these comparisons are to a certain extent inconclusive, even when focusing on only these two types of algorithms. While comparisons of SA and TS algorithms were based on rather small-sized instances, here we focus on possible dependencies of the relative performance between SA and TS algorithms on instance size. In fact, our experimental results show that the assertion whether one algorithm is better than the other can depend strongly on QAP instance size even if one focuses on instances with otherwise same characteristics.

Ant colony optimization is a meta-heuristic that has been widely used for solving combinatorial optimization problems, and most real-world applications are concerned with multi-objective optimization problems. The Pareto strength ant colony optimization (PSACO) algorithm, which uses the concepts of Pareto optimality and also the domination concept, has been shown to be very effective in optimizing any number of objectives simultaneously. This paper modifies the PSACO algorithm to solve two combinatorial optimization problems: the travelling salesman problem (TSP); and the job-shop scheduling problem (JSSP). It uses the random-weight based method as an improvement. The proposed method achieved a better performance than the original PSACO algorithm for both combinatorial optimization problems and obtained well-distributed Pareto-optimal fronts.

Quadratic assignment problems (QAPs) is a NP-hard combinatorial optimization problem. QAPs are often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator that can be used for benchmarking for heuristic algorithms. Our QAP generator combines small size QAPs with known optimum solution into a larger size QAP instance. We call these instances composite QAPs (cQAPs), and we show that the cost function of composite QAPs is additively decomposable. We give mild conditions for which a composite QAP instance has known optimum solution. We generate cQAP instances using uniform distributions with different bounds for the component QAPs and for the rest of the cQAP elements. Numerical and analytical techniques that measure the difficulty of the composite QAP instances in comparison with other QAPs from the literature are introduced. These methods point out that some cQAP instances are difficult for local search with many local optimum of various values, low epistasis and non-trivial asymptotic behaviour.

In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the multiobjective generalized assignment problem (mGAP), which is basically concerned with finding the optimal assignment of jobs to agents such that each job is assigned to exactly one agent, subject to capacity constraint of agents, and aims to optimize multiple objective functions simultaneously, such as minimizing cost, minimizing time, and maximizing profit. First, the mGAP is described and a standard multi-objective mathematical programming model for mGAP is given. Second, the DDE is presented, in which individuals are represented as the integer encoding scheme, and a novel integer-encoding-based dynamic mutation operator is employed to generate new candidate solutions. Furthermore, a sequential selection operator for dealing with multiple objectives is embedded in the proposed DDE. Finally, an extensive computational study is carried out by comparison with the enumeration algorithm and genetic algorithm, the results show that the proposed DDE is an effective algorithm for mGAP.

The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experiment...

In this paper, we consider the quadratic assignment problem (QAP), one of the hardest NP-hard combinatorial optimization problems. We first present a new reformulation of the problem. Then a Lexisearch Algorithm (LSA) is developed for obtaining exact optimal solution to the problem. Finally, a comparative study has been carried out to show the efficiency of the algorithm against an existing algorithm for some medium sized instances from the quadratic assignment problem library, QAPLIB. The comparative study shows the efficiency of the proposed LSA based on the reformulation.

A differential improvement modification to Hybrid Genetic Algorithms is proposed. The general idea is to perform more extensive improvement algorithms on higher quality solutions. Our proposed Differential Improvement (DI) approach is of rather general character. It can be implemented in many different ways. The paradigm remains invariant and can be easily applied to a wider class of optimization problems. Moreover, the DI framework can also be used within other Hybrid metaheuristics like Hybrid Scatter Search algorithms, Particle Swarm Optimization, or Bee Colony Optimization techniques. Extensive experiments show that the new approach enables to improve significantly the performance of Hybrid Genetic Algorithms without adding extra computer time. Additional experiments investigated the trade-off between the number of generations and the number of iterations of the improvement algorithm. These experiments yielded six new best known solutions to benchmark quadratic assignment problems. Many other variants of the proposed algorithm are suggested for future research.

Obtaining exact results for larger problem instances of the intractable problems is still an important issue. Genetic algorithms can provide good solutions for such problems by using appropriate recombination and mutation operators to search the solution space, provided that they are given a sufficient population size of individuals and enough time to iterate through generations. There are numerous proposed recombination operators that programmers use for this purpose. Most of the time, one of these operators are randomly selected to solve a problem without knowing its capabilities. In this study, we analyze the most used recombination operators and propose a new swap-based operator, Bubble Recombination Operator (BRX), for the intractable permutation problems. The proposed operator swaps iteratively and outperforms most of the well-known permutation recombination operators. BRX provides either the optimum or very close to the best available solutions reported so far for the problem instances of the Quadratic Assignment Problem.

This paper is concerned with automated classification of Combinatorial Optimization Problem instances for instance-specific parameter tuning purpose. We propose the CluPaTra Framework, a generic approach to CLUster instances based on similar PAtterns according to search TRAjectories and apply it on parameter tuning. The key idea is to use the search trajectory as a generic feature for clustering problem instances. The advantage of using search trajectory is that it can be obtained from any local-search based algorithm with small additional computation time. We explore and compare two different search trajectory representations, two sequence alignment techniques (to calculate similarities) as well as two well-known clustering methods. We report experiment results on two classical problems: Travelling Salesman Problem and Quadratic Assignment Problem and industrial case study.

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems, which models many real-life problems. However, it is considered as one of the most difficult NP-hard problems, which means that no polynomial-time algorithm is known to solve this intractable problem effectively. Even small instances of QAP may require vast computation time. In this work, a uniform cellular solution to QAP is proposed in the framework of membrane computing by using a family of recognizer tissue P systems with cell division. In the design of the solution, we encode the given instances in binary notations. The paper can be considered as a contribution to the study of considering a binary encoding of the information in P systems.

Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of permutation matrices, we relax the variable to be the more tractable doubly stochastic matrices and add an $L_p$-norm ($0 < p < 1$) regularization term to the objective function. The optimal solutions of the $L_p$-regularized problem are the same as the original problem if the regularization parameter is sufficiently large. A lower bound estimation of the nonzero entries of the stationary points and some connections between the local minimizers and the permutation matrices are further established. Then we propose an $L_p$ regularization algorithm with local refinements. The algorithm approximately solves a sequence of $L_p$ regularization subproblems by the projected gradient method using a nonmontone line search with the Barzilai-Borwein step sizes. Its performance can be further improved if it is combined with certain local search methods, the cutting plane techniques as well as a new negative proximal point scheme. Extensive numerical results on QAPLIB and the bandwidth minimization problem show that our proposed algorithms can often find reasonably high quality solutions within a competitive amount of time., This paper has been accepted for publication in SIAM Journal on Optimization

The vector assignment p-median problem (VAPMP) and the ordered p-median problem (OMP) are important extensions of the classic p-median problem. The VAPMP extends the p-median problem by allowing assignment of a demand to multiple facilities, and a wide variety of multi-assignment and backup location problems are special cases of this problem. The OMP optimizes a weighted sum of service distances according to their relative ranks among all demands. The OMP is well known as it represents a generalization of both the p-median and the p-center problems. In this article, a new model is developed which extends both the VAPMP and OMP problems. In addition, beyond median, center, and vector assignment, this new model can resolve problems where the system objective involves maximizing distance. The new model also gives rise to meaningful special-case problems, such as a “reliable p-center” problem. Different integer linear programming (ILP) formulations of the new problem are presented and tested. It is demonstrated that an efficient formulation for a special case of the VAOMP problem can solve medium sized problems optimally in a reasonable amount of time.

Ant-Colony Optimization (ACO) is a popular swarm intelligence scheme known for its efficiency in solving combinatorial optimization problems. However, despite some extensions of this approach to continuous optimization, high-dimensional problems remain a challenge for ACO. This paper presents an ACO-based algorithm for numerical optimization capable of solving high-dimensional real-parameter optimization problems. The algorithm, called the Differential Ant-Stigmergy Algorithm (DASA), transforms a real-parameter optimization problem into a graph-search problem. The parameters' differences assigned to the graph vertices are used to navigate through the search space. We compare the algorithm results with the results of previous studies on recent benchmark functions and show that the DASA is a competitive continuous optimization algorithm that solves high-dimensional problems effectively and efficiently.

This paper introduces a new variable depth search method for the Quadratic Assignment Problem. The new method considers the cost of edges assignment as the criterion to decide which vertices to exchange during local search moves. It also presents the results of an extensive experimental study that compares the performance of local search and variable depth search algorithms for the Quadratic Assignment Problem. The investigation presented here contributes to a better understanding of the potential of these techniques, which are widely used as intensification tools in more sophisticated heuristic methods, such as evolutionary algorithms. Different algorithms presented in the literature were implemented and compared to the proposed methods. The results of a computational experiment with 161 benchmark instances are reported. Different statistical tests are applied in order to analyze the results provided by the experiments.

Evaluation of system reliability in stochastic flow networks under time constraints depends on the transmission time of minimal paths. The lead-time of a minimal path plays an important role in calculating the transmission time. Component assignments not only affect on the lead-time of a path but also the reliability value. Components assignment problem subject to total lead-time is never discussed. Thus, this paper focuses on solving this problem under total-lead time constraint, in which each component has an assignment lead-time. Subsequently an optimization method based on genetic algorithm is proposed to search the optimal components for a minimum total lead-time that maximizes the system reliability. The mathematical programming formulation for the assignment problem with optimal network reliability subject to total lead-time is formulated and solved by the presented genetic algorithm. The presented algorithm is applied on two given examples with different number of available components to assert its efficiency in solving the given assignment problem.

The cuttlefish optimization algorithm is a new combinatorial optimization algorithm in the family of metaheuristics, applied in the continuous domain, and which provides mechanisms for local and global research. This paper presents a new adaptation of this algorithm in the discrete case, solving the famous travelling salesman problem, which is one of the discrete combinatorial optimization problems. This new adaptation proposes a reformulation of the equations to generate solutions depending a different algorithm cases. The experimental results of the proposed algorithm on instances of TSPLib library are compared with the other methods, show the efficiency and quality of this adaptation.

Metaheuristics form a family of optimization algorithms for solving combinatorial optimization problems by applying the research procedures to quickly find a good approximation of the best solution. In this paper we proposed a new metaheuristic novel hybrid penguins search optimization algorithm (NPeSOA) which is based on the combination of penguins search optimization algorithm (PeSOA) and harmony search algorithm (HS) to solve the Travelling Salesman Problem. The search for harmony was added to improve the research technique of PeSOA method. The results of this experience are tested by the instances of TSPLib, and compared with the methods of PeSOA and HS to show the efficiency of NPeSOA.

A new method for solving the assignment problem based on the decomposition of the original problem into a number of two-dimensional optimization problems is proposed. The integer-valuedness and monotonicity of the iterative procedure with respect to the objective function ensures that the algorithm is finite. As a result, either a unique optimal solution of the original assignment problem or a system of constraints is obtained. In the latter case, the system of constraints can be used to obtain all optimal solutions. Examples illustrating the algorithm are discussed.

An instance of the quadratic assignment problem (QAP) with cost matrix Q is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix C such that for each assignment, the QAP and LAP objective function values are identical. Several sufficiency conditions are known that guarantee linearizability of a QAP. However, no polynomial time algorithm is known to test if a given instance of QAP is linearizable. In this paper, we give a necessary and sufficient condition for an instance of a QAP to be linearizable and develop an O(n4) algorithm to solve the corresponding linearization problem, where n is the size of the QAP.

A direct cut-off method to solve combinatorial optimization problems on polyarrangements with additional constraints is proposed and justified. The method allows obtaining a feasible solution at each stage without constructing the linear hull of the set of polyarrangements.

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.

The Combinatorial problems are real world decision making problem with discrete and disjunctive choices. When these decision making problems involve more than one conflicting objective and constraint, it turns the polynomial time problem into NP-hard. Thus, the straight forward approaches to solve multi-objective problems would not give an optimal solution. In such case evolutionary based meta-heuristic approaches are found suitable. In this paper, a novel particle swarm optimization based meta-heuristic algorithm is presented to solve multi-objective combinatorial optimization problems. Here a mapping method is considered to convert the binary and discrete values (solution encoded as particles) to a continuous domain and update it using the velocity and position update equation of particle swarm optimization to find new set of solutions in continuous domain and demap it to discrete values. The performance of the algorithm is compared with other evolutionary strategy like SPEA and NSGA-II on pseudo-Boolean discrete problems and multi-objective 0/1 knapsack problem. The experimental results confirmed the better performance of combinatorial particle swarm optimization algorithm.

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Kunzli in 2004, where the opti- mization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contri- bution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experi- mental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.

This paper addresses the application of the principles of feedback and self-controlling software to the tabu search algorithm. We introduce two new reaction strategies for the tabu search algorithm. The first strategy treats the tabu search algorithm as a target system to be controlled and uses a control-theoretic approach to adjust the algorithm parameters that affect search intensification. The second strategy is a flexible diversification strategy which can adjust the algorithm's parameters based on the search history. These two strategies, combined with tabu search, form the Self Controlling Tabu Search (SC-Tabu) algorithm. The algorithm is implemented and tested on the Quadratic Assignment Problem (QAP). The results show that the self-controlling features of the algorithm make it possible to achieve good performance on different types of QAP instances.