Memetic Search for the Generalized Quadratic Multiple Knapsack Problem

The generalized quadratic multiple knapsack problem (GQMKP) extends the classical quadratic multiple knapsack problem with setups and knapsack preference of the items. The GQMKP can accommodate a number of real-life applications and is computationally difficult. In this paper, we demonstrate the interest of the memetic search approach for approximating the GQMKP by presenting a highly effective memetic algorithm (denoted by MAGQMK). The algorithm combines a backbone-based crossover operator (to generate offspring solutions) and a multineighborhood simulated annealing procedure (to find high quality local optima). To prevent premature convergence of the search, MAGQMK employs a quality-and-distance (QD) pool updating strategy. Extensive experiments on two sets of 96 benchmarks show a remarkable performance of the proposed approach. In particular, it discovers improved best solutions in 53 and matches the best known solutions for 39 other cases. A case study on a pseudo real-life problem demonstrates the efficacy of the proposed approach in practical situations. Additional analyses show the important contribution of the novel general-exchange neighborhood, the backbone-based crossover operator as well as the QD pool updating rule to the performance of the proposed algorithm

Iterated responsive threshold search for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) consists in assigning objects with both individual and pairwise profits to a set of limited knapsacks in order to maximize the total profit. QMKP is a NP-hard combinatorial optimization problem with a number of applications. In this paper, we present an iterated responsive threshold search (IRTS) approach for solving the QMKP. Based on a combined use of three neighborhoods, the algorithm alternates between a threshold-based exploration phase where solution transitions are allowed among those satisfying a responsive threshold and a descent-based improvement phase where only improving solutions are accepted. A dedicated perturbation strategy is utilized to ensure a global diversification of the search procedure. Extensive experiments performed on a set of 60 benchmark instances in the literature show that the proposed approach competes very favorably with the current state-of-the-art methods for the QMKP. In particular, it discovers 41 improved lower bounds and attains all the best known results for the remaining instances. The key components of IRTS are analyzed to shed light on their impact on the performance of the algorithm

The bi-objective quadratic multiple knapsack problem: Model and heuristics

The single objective quadratic multiple knapsack problem (QMKP) is a useful model to formulate a number of practical problems. However, it is not suitable for situations where more than one objective needs to be considered. In this paper, we extend the single objective QMKP to the bi-objective case such that we simultaneously maximize the total profit of the items packed into the knapsacks and the ’makespan’ (the gain of the least profit knapsack). Given the imposing computational challenge, we propose a hybrid two-stage (HTS) algorithm to approximate the Pareto front of the bi-objective QMKP. HTS combines two different and complementary search methods — scalarizing memetic search (first stage) and Pareto local search (second stage). Experimental assessments on a set of 60 problem instances show that HTS dominates a standard multi-objective evolutionary algorithm (NSGA II), and two simplified variants of HTS. We also present a comparison with two state-of-the-art algorithms for the single objective QMKP to assess the quality of the extreme solutions of the approximated Pareto front

A NOVEL METHOD FOR THE M-TERMS OF SHIP WITH FORWARD SPEED

One of the major difficulties in linear wave-induced ship motion problem with forward speed is how to solve the m-terms accurately. This paper proposes a novel numerical method (Taylor Expansion Boundary Element Method, TEBEM) to compute the m-terms for arbitrary floating bodies. This method treats the m-terms as the Dirichlet type, uses the first-order derivatives terms on the right-handed side of boundary value problem, which is solved by TEBEM method. Numerical studies are performed for the hemisphere, mounted cylinder, and modified KVLCC2 ship models. Compared to the analytical solutions and other numerical results, a good agreement can be obtained by the TEBEM method

Dynamic thresholding search for minimum vertex cover in massive sparse graphs

A number of important applications related to complex network analysis require finding small vertex covers in massive graphs. This paper proposes an effective stochastic local search algorithm called DTS_MVC to fulfill this task. Relying on a fast vertex-based search strategy, DTS_MVC effectively explores the search space by alternating between a thresholding search phase during which the algorithm accepts both improving and non-improving solutions that satisfy a dynamically changing quality threshold, and a conditional improving phase where only improving solutions are accepted. A novel non-parametric operation-prohibiting mechanism is introduced to avoid search cycling. Computational experiments on 86 massive real-world benchmark graphs indicate that DTS_MVC performs remarkably well by discovering 7 improved best known results (new upper bounds). Additional experiments are conducted to shed light on the key ingredients of DTS_MVC

A hybrid metaheuristic approach for the capacitated arc routing problem

The capacitated arc routing problem (CARP) is a difficult combinatorial optimization problem that has been intensively studied in the last decades. We present a hybrid metaheuristic approach (HMA) to solve this problem which incorporates an effective local refinement procedure, coupling a randomized tabu thresholding procedure with an infeasible descent procedure, into the memetic framework. Other distinguishing features of HMA include a specially designed route-based crossover operator for solution recombination and a distance-and-quality based replacement criterion for pool updating. Extensive experimental studies show that HMA is highly scalable and is able to quickly identify either the best known results or improved best known results for almost all currently available CARP benchmark instances. In particular, it discovers an improved best known result for 15 benchmark instances (6 classical instances and 9 large-sized instances whose optima are unknown). Furthermore, we analyze some key elements and properties of the HMA-CARP algorithm to better understand its behavior

An evolutionary path relinking approach for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) is a challenging combinatorial optimization problem with numerous applications. In this paper, we propose the first evolutionary path relinking approach (EPR) for solving the QMKP approximately. This approach combines advanced features both from the path relinking (PR) method and the responsive threshold search algorithm. Thanks to the tunneling property which allows a controlled exploration of infeasible regions, the proposed EPR algorithm is able to identify very high quality solutions. Experimental studies on the set of 60 well-known benchmarks and a new set of 30 large-sized instances show that EPR outperforms several state-of-the-art algorithms. In particular, for the 60 conventional benchmarks, it discovers 10 improved results (new lower bounds) and matches the best known result for the remaining 50 cases. More significantly, EPR demonstrates remarkable efficacy on the 30 new larger instances by easily dominating the current best performing algorithms across the whole instance set. Key components of the algorithm are analyzed to shed lights on their impact on the proposed approach

Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5

The residual interaction between composite fermions (CFs) can express itself through higher order fractional Hall effect. With the help of diagonalization in a truncated composite fermion basis of low-energy many-body states, we predict that quantum Hall effect with partial spin polarization is possible at several fractions between $\nu=1/3$ and $\nu=2/5$. The estimated excitation gaps are approximately two orders of magnitude smaller than the gap at $\nu=1/3$, confirming that the inter-CF interaction is extremely weak in higher CF levels.Comment: 4 pages, 3 figure

Stress field around arbitrarily shaped cracks in two-dimensional elastic materials

The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are based on either perturbative approaches or on combinations of analytic and numerical techniques. We present here a general solution of this problem for any arbitrary crack. Along the way we develop a method to compute the conformal map from the exterior of a circle to the exterior of a line of arbitrary shape, offering it as a superior alternative to the classical Schwartz-Cristoffel transformation. Our calculation results in an accurate estimate of the full stress field and in particular of the stress intensity factors K_I and K_{II} and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR