Showing papers in "Journal of Heuristics in 2013"
TL;DR: The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase, which is the first ILS approach for the HFVRP.
Abstract: This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP is $\mathcal{NP}$ -hard since it is a generalization of the classical Vehicle Routing Problem (VRP), in which clients are served by a heterogeneous fleet of vehicles with distinct capacities and costs. The objective is to design a set of routes in such a way that the sum of the costs is minimized. The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase. To the best of our knowledge, this is the first ILS approach for the HFVRP. The developed heuristic was tested on well-known benchmark instances involving 20, 50, 75 and 100 customers. These test-problems also include dependent and/or fixed costs according to the vehicle type. The results obtained are quite competitive when compared to other algorithms found in the literature.
225 citations
TL;DR: It is shown that the algorithm outperforms all previously published metaheuristics for this problem class and finds the best solutions for all available benchmark instances.
Abstract: This paper considers a real world waste collection problem in which glass, metal, plastics, or paper is brought to certain waste collection points by the citizens of a certain region. The collection of this waste from the collection points is therefore a node routing problem. The waste is delivered to special sites, so called intermediate facilities (IF), that are typically not identical with the vehicle depot. Since most waste collection points need not be visited every day, a planning period of several days has to be considered. In this context three related planning problems are considered. First, the periodic vehicle routing problem with intermediate facilities (PVRP-IF) is considered and an exact problem formulation is proposed. A set of benchmark instances is developed and an efficient hybrid solution method based on variable neighborhood search and dynamic programming is presented. Second, in a real world application the PVRP-IF is modified by permitting the return of partly loaded vehicles to the depots and by considering capacity limits at the IF. An average improvement of 25% in the routing cost is obtained compared to the current solution. Finally, a different but related problem, the so called multi-depot vehicle routing problem with inter-depot routes (MDVRPI) is considered. In this problem class just a single day is considered and the depots can act as an intermediate facility only at the end of a tour. For this problem several instances and benchmark solutions are available. It is shown that the algorithm outperforms all previously published metaheuristics for this problem class and finds the best solutions for all available benchmark instances.
102 citations
TL;DR: All the heuristics and metaheuristics for finding near-optimal solutions for the MDP are reviewed and the new benchmark library MDPLIB is presented, which includes most instances previously used for this problem, as well as new ones, giving a total of 315.
Abstract: This paper presents extensive computational experiments to compare 10 heuristics and 20 metaheuristics for the maximum diversity problem (MDP). This problem consists of selecting a subset of maximum diversity from a given set of elements. It arises in a wide range of real-world settings and we can find a large number of studies, in which heuristic and metaheuristic methods are proposed. However, probably due to the fact that this problem has been referenced under different names, we have only found limited comparisons with a few methods on some sets of instances.
This paper reviews all the heuristics and metaheuristics for finding near-optimal solutions for the MDP. We present the new benchmark library MDPLIB, which includes most instances previously used for this problem, as well as new ones, giving a total of 315. We also present an exhaustive computational comparison of the 30 methods on the MDPLIB. Non-parametric statistical tests are reported in our study to draw significant conclusions.
75 citations
TL;DR: This paper reports on the application of a new Tabu Search algorithm to large scale Max-cut test problems, designed for the general unconstrained quadratic binary program (UBQP), and is not specialized in any way for the Max-Cut problem.
Abstract: In recent years many algorithms have been proposed in the literature for solving the Max-Cut problem. In this paper we report on the application of a new Tabu Search algorithm to large scale Max-cut test problems. Our method provides best known solutions for many well-known test problems of size up to 10,000 variables, although it is designed for the general unconstrained quadratic binary program (UBQP), and is not specialized in any way for the Max-Cut problem.
69 citations
TL;DR: A complex variant of the Container Loading Problem arising from a real-world industrial application that includes several features such as multiple containers, box rotation, and bearable weight, which is based on local search metaheuristics and shows clear improvement on the previous heuristic solution.
Abstract: We consider a complex variant of the Container Loading Problem arising from a real-world industrial application. It includes several features such as multiple containers, box rotation, and bearable weight, which are of importance in many practical situations. In addition, it also considers the situation in which boxes have to be delivered to different destinations (multi-drop).
Our solution technique is based on local search metaheuristics. Local search works on the space of sequences of boxes to be loaded, while the actual load is obtained by invoking, at each iteration, a specialized procedure called loader. The loader inserts the boxes in the container using a deterministic heuristic which produces a load that is feasible according to the constraints.
We test our solver on real-world instances provided by our industrial partner, showing a clear improvement on the previous heuristic solution. In addition, we compare our solver on benchmarks from the literature on the basic container loading problems. The outcome is that the results are in some cases in-line with the best ones in the literature and for other cases they also improve upon the best known ones. All instances and solutions are made available on the web for future comparisons.
60 citations
TL;DR: This paper considers a multi-depot periodic vehicle routing problem which is characterized by the presence of a homogeneous fleet of vehicles, multiple depots, multiple periods, and two types of constraints that are often found in reality, i.e., vehicle capacity and route duration constraints.
Abstract: In this paper, we consider a multi-depot periodic vehicle routing problem which is characterized by the presence of a homogeneous fleet of vehicles, multiple depots, multiple periods, and two types of constraints that are often found in reality, i.e., vehicle capacity and route duration constraints. The objective is to minimize total travel costs. To tackle the problem, we propose an efficient path relinking algorithm whose exploration and exploitation strategies enable the algorithm to address the problem in two different settings: (1) As a stand-alone algorithm, and (2) As a part of a co-operative search algorithm called integrative co-operative search. The performance of the proposed path relinking algorithm is evaluated, in each of the above ways, based on standard benchmark instances. The computational results show that the developed PRA performs well, in both solution quality and computational efficiency.
56 citations
TL;DR: A bilevel integer program (BIP) is formulated, in which the defender takes on the leader’s role and the attacker acts as the follower, and the results show that protection budget plays a significant role in maintaining the service accessibility of critical facilities in the worst-case interdiction scenario.
Abstract: The bilevel p-median problem for the planning and protection of critical facilities involves a static Stackelberg game between a system planner (defender) and a potential attacker. The system planner determines firstly where to open p critical service facilities, and secondly which of them to protect with a limited protection budget. Following this twofold action, the attacker decides which facilities to interdict simultaneously, where the maximum number of interdictions is fixed. Partial protection or interdiction of a facility is not possible. Both the defender's and the attacker's actions have deterministic outcome; i.e., once protected, a facility becomes completely immune to interdiction, and an attack on an unprotected facility destroys it beyond repair. Moreover, the attacker has perfect information about the location and protection status of facilities; hence he would never attack a protected facility. We formulate a bilevel integer program (BIP) for this problem, in which the defender takes on the leader's role and the attacker acts as the follower. We propose and compare three different methods to solve the BIP. The first method is an optimal exhaustive search algorithm with exponential time complexity. The second one is a two-phase tabu search heuristic developed to overcome the first method's impracticality on large-sized problem instances. Finally, the third one is a sequential solution method in which the defender's location and protection decisions are separated. The efficiency of these three methods is extensively tested on 75 randomly generated instances each with two budget levels. The results show that protection budget plays a significant role in maintaining the service accessibility of critical facilities in the worst-case interdiction scenario.
55 citations
TL;DR: This paper presents a general-purpose software framework dedicated to the design, the analysis and the implementation of local search metaheuristics: ParadisEO-MO, which has proven its efficiency and high flexibility by enabling the resolution of many academic and real-world optimization problems from science and industry.
Abstract: This paper presents a general-purpose software framework dedicated to the design, the analysis and the implementation of local search metaheuristics: ParadisEO-MO. A substantial number of single solution-based local search metaheuristics has been proposed so far, and an attempt of unifying existing approaches is here presented. Based on a fine-grained decomposition, a conceptual model is proposed and is validated by regarding a number of state-of-the-art methodologies as simple variants of the same structure. This model is then incorporated into the ParadisEO-MO software framework. This framework has proven its efficiency and high flexibility by enabling the resolution of many academic and real-world optimization problems from science and industry.
53 citations
TL;DR: This paper presents an integer programming model and describes a GRASP based algorithm to solve a vehicle routing and scheduling problem for the collection of Waste of Electric and Electronic Equipment (WEEE).
Abstract: This paper presents an integer programming model and describes a GRASP based algorithm to solve a vehicle routing and scheduling problem for the collection of Waste of Electric and Electronic Equipment (WEEE). The difficulty of this problem arises from the fact that it is characterized by four variants of the vehicle routing problem that have been studied independently in the literature, but not together. The experimental analysis on a large set of randomly-generated instances shows the good performance of the proposed algorithm. Moreover, computational results using real data show that the method outperforms real existing approaches to reverse logistics.
41 citations
TL;DR: The resolution approach proposed here is a sequential Ant Colony System (ACS)—Tabu Search algorithm that introduces a two pheromone trail strategy to accelerate agents’ (ants) learning process.
Abstract: This paper considers a practical variant of the Vehicle Routing Problem (VRP) known as the Heterogeneous Vehicle Routing Problem with Time Windows and Multiple Products (HVRPTWMP). As the problem is NP-hard, the resolution approach proposed here is a sequential Ant Colony System (ACS)--Tabu Search algorithm. The approach introduces a two pheromone trail strategy to accelerate agents' (ants) learning process. Its convergence to good solutions is given in terms of fleet size and travel time while completing tours and service to all customers. The proposed procedure uses regency and frequency memories form Tabu Search to further improve the quality of solutions. Experiments are carried out using instances from literature and show the effectiveness of this procedure.
40 citations
TL;DR: This paper develops a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and proposes two novel local search heuristics within the JPSO framework.
Abstract: This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches.
TL;DR: A new representation of the solutions of the FVSP (feedback sets) is suggested, able to design a local transformation (equivalent to a neighborhood) that changes a feedback set into a new one.
Abstract: The feedback vertex set problem (FVSP) consists in making a given directed graph acyclic by removing as few vertices as possible. In spite of the importance of this NP-hard problem, no local search approach had been proposed so far for tackling it. Building on a property of acyclic graphs, we suggest in this paper a new representation of the solutions of the FVSP (feedback sets). Thanks to this solution representation, we are able to design a local transformation (equivalent to a neighborhood) that changes a feedback set into a new one. Based on this neighborhood, we have developed a simulated annealing algorithm for the FVSP. Our experiments show that our algorithm outperforms the best existing heuristic, namely the greedy adaptive search procedure by Pardalos et al.
TL;DR: This paper proposes a three-phase matheuristic solution strategy for the capacitated multi-commodity fixed-cost network design problem with design-balance constraints that combines exact and neighbourhood-based methods.
Abstract: This paper proposes a three-phase matheuristic solution strategy for the capacitated multi-commodity fixed-cost network design problem with design-balance constraints. The proposed matheuristic combines exact and neighbourhood-based methods. Tabu search and restricted path relinking meta-heuristics cooperate to generate as many feasible solutions as possible. The two meta-heuristics incorporate new neighbourhoods, and computationally efficient exploration procedures. The feasible solutions generated by the two procedures are then used to identify an appropriate part of the solution space where an exact solver intensifies the search. Computational experiments on benchmark instances show that the proposed algorithm finds good solutions to large-scale problems in a reasonable amount of time.
TL;DR: The proposed backbone-guided tabu search algorithm for the Unconstrained Binary Quadratic Programming problem is capable of finding the best-known solutions for 21 large random instances with 3000 to 7000 variables and boosts the performance of the basic TS in terms of both solution quality and computational efficiency.
Abstract: We propose a backbone-guided tabu search (BGTS) algorithm for the Unconstrained Binary Quadratic Programming (UBQP) problem that alternates between two phases: (1) a basic tabu search procedure to optimize the objective function as far as possible; (2) a strategy using the TS notion of strongly determined variables to alternately fix and free backbone components of the solutions which are estimated likely to share values in common with an optimal solution. Experimental results show that the proposed method is capable of finding the best-known solutions for 21 large random instances with 3000 to 7000 variables and boosts the performance of the basic TS in terms of both solution quality and computational efficiency.
TL;DR: A bi-objective commercial territory design problem motivated by a real-world application from the bottled beverage distribution industry is addressed and a GRASP framework is proposed for tackling considerably large instances.
Abstract: A bi-objective commercial territory design problem motivated by a real-world application from the bottled beverage distribution industry is addressed. The problem considers territory compactness and balancing with respect to number of customers as optimization criteria. Previous work has focused on exact methods for small- to medium-scale instances. In this work, a GRASP framework is proposed for tackling considerably large instances. Within this framework two general schemes are developed. For each of these schemes two strategies are studied: (i) keeping connectivity as a hard constraint during construction and post-processing phases and, (ii) ignoring connectivity during the construction phase and adding this as another minimizing objective function during the post-processing phase. These strategies are empirically evaluated and compared to NSGA-II, one of the most successful evolutionary methods known in literature. Computational results show the superiority of the proposed strategies. In addition, one of the proposed GRASP strategies is successfully applied to a case study from industry.
TL;DR: A two stage framework for LTL carrier collaboration is introduced and it is indicated that distance savings of 7–15 % can be achieved by collaborating at the entrance to the city and integrating integer programming with local search results in at least an order of magnitude speed up in the second stage problem.
Abstract: Less-Than-Truckload (LTL) carriers generally serve geographical regions that are more localized than the inter-city line-hauls served by truckload carriers. That localization can lead to urban freight transportation routes that overlap. If trucks are traveling with less than full loads, there typically exist opportunities for carriers to collaborate over such routes. We introduce a two stage framework for LTL carrier collaboration. Our first stage involves collaboration between multiple carriers at the entrance to the city and can be formulated as a vehicle routing problem with time windows (VRPTW). We employ guided local search for solving this VRPTW. The second stage involves collaboration between carriers at transshipment facilities while executing their routes identified in phase one. For solving the second stage problem, we develop novel local search heuristics, one of which leverages integer programming to efficiently explore the union of neighborhoods defined by new problem-specific move operators. Our computational results indicate that integrating integer programming with local search results in at least an order of magnitude speed up in the second stage problem. We also perform sensitivity analysis to assess the benefits from collaboration. Our results indicate that distance savings of 7---15 % can be achieved by collaborating at the entrance to the city. Carriers involved in intra-city collaboration can further save 3---15 % in total distance traveled, and also reduce their overall route times.
TL;DR: This work addresses the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions and proposes a hybrid heuristic to solve it, proving that the HACO algorithm is a very good alternative approach to solve these problems.
Abstract: In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-Hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an ant colony optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search (LS) procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the LS is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.
TL;DR: An integer programming formulation for the handover minimization problem is described and it is shown that state-of-the-art integer programming solvers can solve only very small instances of the problem.
Abstract: A mobile device connects to the cell tower (base station) from which it receives the strongest signal. As the device moves it may connect to a series of towers. The process in which the device changes the base station it is connected to is called handover. A cell tower is connected to a radio network controller (RNC) which controls many of its operations, including handover. Each cell tower handles an amount of traffic and each radio network controller has capacity to handle a maximum amount of traffic from all base stations connected to it. Handovers between base stations connected to different RNCs tend to fail more often than handovers between base stations connected to the same RNC. Handover failures result in dropped connections and therefore should be minimized. The Handover Minimization Problem is to assign towers to RNCs such that RNC capacity is not violated and the number of handovers between base stations connected to different RNCs is minimized. We describe an integer programming formulation for the handover minimization problem and show that state-of-the-art integer programming solvers can solve only very small instances of the problem. We propose several randomized heuristics for finding approximate solutions of this problem, including a GRASP with path-relinking for the generalized quadratic assignment problem, a GRASP with evolutionary path-relinking, and a biased random-key genetic algorithm. Computational results are presented.
TL;DR: This paper studies a robust graph coloring problem, which is a variant of the classical graph coloring Problem, where penalties are charged for non-adjacent vertices that are assigned the same color.
Abstract: This paper studies a robust graph coloring problem, which is a variant of the classical graph coloring problem, where penalties are charged for non-adjacent vertices that are assigned the same color. The problem can be formulated as an unconstrained quadratic programming problem, and has many applications in industry. Since the problem is known to be strongly NP-complete, we develop a number of metaheuristics for it, which are based on various encoding schemes, neighborhood structures, and search algorithms. Extensive experiments suggest that our metaheuristics with a partition based encoding scheme and an improvement graph based neighborhood outperform other methods tested in our study.
TL;DR: This paper proposes a new algorithm for dynamic continuous optimization based on several coordinated local searches and on the archiving of the optima found by these local searches, which is used when the environment changes.
Abstract: Many real-world optimization problems are dynamic (time dependent) and require an algorithm that is able to track continuously a changing optimum over time. In this paper, we propose a new algorithm for dynamic continuous optimization. The proposed algorithm is based on several coordinated local searches and on the archiving of the optima found by these local searches. This archive is used when the environment changes. The performance of the algorithm is analyzed on the Moving Peaks Benchmark and the Generalized Dynamic Benchmark Generator. Then, a comparison of its performance to the performance of competing dynamic optimization algorithms available in the literature is done. The obtained results show the efficiency of the proposed algorithm.
TL;DR: This paper analyzes the solvability of a railway network design problem and its robust version of GRASP heuristics, and indicates that the results obtained in a computational experience indicate that theGRASP algorithms are suitable for railway networkDesign problems.
Abstract: This paper analyzes the solvability of a railway network design problem and its robust version. These problems are modeled as integer linear programming problems with binary variables, and their solutions provide topological railway networks maximizing the trip coverage in the presence of a competing mode, both assuming that the network works fine and that links can fail, respectively. Since these problems are computationally intractable for realistic sizes, GRASP heuristics are proposed for finding good feasible solutions. The results obtained in a computational experience indicate that our GRASP algorithms are suitable for railway network design problems.
TL;DR: A bi-objective mixed-integer linear model for the problem is formulated and two methodologies of solution are presented, based on a series of linked variable neighborhood searches and the second one is based on NSGA-II provided of specific operators.
Abstract: This work is motivated by a problem proposed to the authors by a bakery company in Northern Spain. The objective is to design the daily routes over the week in order to minimize the total traveled distance. For reducing this total distance, some flexibility in the dates of delivery is introduced, which will cause a stock. Therefore, we study the problem under the bi-objective perspective, "minimizing" simultaneously the total traveled distance and the stock. A bi-objective mixed-integer linear model for the problem is formulated and two methodologies of solution are presented. The first one is based on a series of linked variable neighborhood searches and the second one is based on NSGA-II provided of specific operators. Numerical results showing the obtained estimated Pareto front in both cases are presented.
TL;DR: Theoretical results characterizing binary local maxima in terms of certain induced subgraphs of the given graph are developed and these results are used to develop an efficient local search algorithm that provides considerable speed-up over a typical local search algorithms for the binary Hamming distance-2 neighborhood.
Abstract: This article investigates the local maxima properties of a box-constrained quadratic optimization formulation of the maximum independent set problem in graphs. Theoretical results characterizing binary local maxima in terms of certain induced subgraphs of the given graph are developed. We also consider relations between continuous local maxima of the quadratic formulation and binary local maxima in the Hamming distance-1 and distance-2 neighborhoods. These results are then used to develop an efficient local search algorithm that provides considerable speed-up over a typical local search algorithm for the binary Hamming distance-2 neighborhood.
TL;DR: The proposed framework to tackle mixed integer programming problems based upon a “constrained” black box approach was effective, in terms of solution quality as well as computational time, when compared with a commercial MIP solver and the best algorithm from the literature.
Abstract: In this paper we present a framework to tackle mixed integer programming problems based upon a "constrained" black box approach. Given a MIP formulation, a black-box solver, and a set of incumbent solutions, we iteratively build corridors around such solutions by adding exogenous constraints to the original MIP formulation. Such corridors, or neighborhoods, are then explored, possibly to optimality, with a standard MIP solver. An iterative approach in the spirit of a hill climbing scheme is thus used to explore subportions of the solution space. While the exploration of the corridor relies on a standard MIP solver, the way in which such corridors are built around the incumbent solutions is influenced by a set of factors, such as the distance metric adopted, or the type of method used to explore the neighborhood. The proposed framework has been tested on a challenging variation of the lot sizing problem, the multi-level lot sizing problem with setups and carryovers. When tested on 1920 benchmark instances of such problem, the algorithm was able to solve to near optimality every instance of the benchmark library and, on the most challenging instances, was able to find high quality solutions very early in the search process. The algorithm was effective, in terms of solution quality as well as computational time, when compared with a commercial MIP solver and the best algorithm from the literature.
TL;DR: This work proposes several versions of the DDT constructive heuristic based on the alternative representation of the quadratic function and presents an efficient implementation of local search using one-flip and two-Flip moves that simultaneously change the values of one or two binary variables.
Abstract: The unconstrained binary quadratic minimization problem is known to be NP-hard and due to its computational challenge and application capability, it becomes more and more considered and involved by the recent research studies, including both exact and heuristic solution approaches. Our work is in line with what was suggested by Glover et al. (in Eur. J. Oper. Res. 137, 272---287, 2002) who proposed one pass heuristics as alternatives to the well-known Devour Digest Tidy-up procedure (DDT) of Boros et al. (in RRR 39-89, 1989). The "devour" step sets a term of the current representation to 0 or 1, and the "tidy-up" step substitutes the logical consequences derived from the "digest" step into the current quadratic function. We propose several versions of the DDT constructive heuristic based on the alternative representation of the quadratic function. We also present an efficient implementation of local search using one-flip and two-flip moves that simultaneously change the values of one or two binary variables. Computational experiments performed on instances up to 7000 variables show the efficiency of our implementation in terms of quality improvement and CPU use enhancement.
TL;DR: This paper analyzes the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapes’ theory and proves that the problem can be written as the sum of two elementary components and gives the exact expressions for these components.
Abstract: Landscapes' theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of an especial kind of landscape called elementary landscape. The elementary landscape decomposition of a combinatorial optimization problem is a useful tool for understanding the problem. Such decomposition provides an additional knowledge on the problem that can be exploited to explain the behavior of some existing algorithms when they are applied to the problem or to create new search methods for the problem. In this paper we analyze the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapes' theory. We prove that the problem can be written as the sum of two elementary components and we give the exact expressions for these components. We use the landscape decomposition to compute autocorrelation measures of the problem, and show some practical applications of the decomposition.
TL;DR: The variable objective search framework for combinatorial optimization utilizes different objective functions used in alternative mathematical programming formulations of the same combinatorially optimization problem in an attempt to improve the solutions obtained using each of these formulations individually.
Abstract: This paper introduces the variable objective search framework for combinatorial optimization. The method utilizes different objective functions used in alternative mathematical programming formulations of the same combinatorial optimization problem in an attempt to improve the solutions obtained using each of these formulations individually. The proposed technique is illustrated using alternative quadratic unconstrained binary formulations of the classical maximum independent set problem in graphs.
TL;DR: Express (Explore and Repair Stochastic Solution) heuristic as discussed by the authors is a tailored heuristic approach based on alternating phases of exploration and feasibility repairing which is called Express heuristic.
Abstract: Integer problems under joint probabilistic constraints with random coefficients in both sides of the constraints are extremely hard from a computational standpoint since two different sources of complexity are merged. The first one is related to the challenging presence of probabilistic constraints which assure the satisfaction of the stochastic constraints with a given probability, whereas the second one is due to the integer nature of the decision variables. In this paper we present a tailored heuristic approach based on alternating phases of exploration and feasibility repairing which we call Express (Explore and Repair Stochastic Solution) heuristic. The exploration is carried out by the iterative solution of simplified reduced integer problems in which probabilistic constraints are discarded and deterministic additional constraints are adjoined. Feasibility is restored through a penalty approach. Computational results, collected on a probabilistically constrained version of the classical 0---1 multiknapsack problem, show that the proposed heuristic is able to determine good quality solutions in a limited amount of time.
TL;DR: Tests show that the developed ALNS algorithm is significantly outperforming both Gurobi and a currently applied heuristic for the Parental Consultation Timetabling Problem, and is therefore available for approximately 95 % of the Danish high schools.
Abstract: In the different stages of the educational system, the demand for efficient planning is increasing. This article treats the $$\mathcal NP $$ NP -hard Consultation Timetabling Problem, a recurrent planning problem for the high schools in Denmark, which has not been described in the literature before. Two versions of the problem are considered, the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Problem (SCTP). It is shown that both problems can be modeled using the same Integer Programming model. Solutions are found using the state-of-the-art MIP solver Gurobi and Adaptive Large Neighborhood Search (ALNS), and computational results are established using 300 real-life datasets. These tests show that the developed ALNS algorithm is significantly outperforming both Gurobi and a currently applied heuristic for the PCTP. For both the PCTP and the SCTP, it is shown that the ALNS algorithm in average provides results within 5 % of optimum. The developed algorithm has been implemented in the commercial product Lectio, and is therefore available for approximately 95 % of the Danish high schools.
TL;DR: This work shows how to express the problem of searching for D-optimal matrices as a Linear and Quadratic Integer Optimization problem, and describes some additional combinatorial and number-theoretic characteristics that a solution of the D-Optimal matrix problem must possess.
Abstract: We show how to express the problem of searching for D-optimal matrices as a Linear and Quadratic Integer Optimization problem. We also focus our attention in the case where the size of the circulant submatrices that are used to construct a D-optimal matrix is a multiple of 3. In this particular case, we describe some additional combinatorial and number-theoretic characteristics that a solution of the D-optimal matrix problem must possess. We give some solutions for some quite challenging D-optimal matrix problems that can be used as benchmarks to test the efficiency of Linear and Quadratic Integer Optimization algorithms.