Iterative approaches for a dynamic memory allocation problem in embedded systems

Memory allocation has a significant impact on energy consumption in embedded systems. In this paper, we are interested in dynamic memory allocation for embedded systems with a special emphasis on time performance. We propose two mid-term iterative approaches which are compared with existing long-term and short-term approaches, and with an ILP formulation as well. These approaches rely on solving a static version of the allocation problem and they take advantage of previous works for addressing the static problem. A statistic analysis is carried out for showing that the mid-term approach is the best one in terms of solution quality.     

Advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) knapsack and covering problems, in which the constraints are exploited by means of surrogate constraint strategies. In addition, we provide a new graduated-probe strategy for improving the selection of variables to be assigned values. Going beyond the greedy and advanced greedy frameworks, we describe ways to utilize these algorithms with multi-start and strategic oscillation metaheuristics. Finally, we identify how surrogate constraints can be utilized to produce inequalities that dominate those previously proposed and tested utilizing linear programming methods for solving multi-constraint knapsack problems, which are responsible for the current best methods for these problems. While we focus on 0–1 problems, our approaches can readily be adapted to handle variables with general upper bounds.     

POPMUSIC for the travelling salesman problem

POPMUSIC— Partial OPtimization Metaheuristic Under Special Intensification Conditions — is a template for tackling large problem instances. This metaheuristic has been shown to be very efficient for various hard combinatorial problems such as p-median, sum of squares clustering, vehicle routing, map labelling and location routing. A key point for treating large Travelling Salesman Problem (TSP) instances is to consider only a subset of edges connecting the cities. The main goal of this article is to present how to build a list of good candidate edges with a complexity lower than quadratic in the context of TSP instances given by a general function. The candidate edges are found with a technique exploiting tour merging and the POPMUSIC metaheuristic. When these candidate edges are provided to a good local search engine, high quality solutions can be found quite efficiently. The method is tested on TSP instances of up to several million cities with different structures (Euclidean uniform, clustered, 2D to 5D, grids, toroidal distances). Numerical results show that solutions of excellent quality can be obtained with an empirical complexity lower than quadratic without exploiting the geometrical properties of the instances.     

New neighborhood structures for the Double Traveling Salesman Problem with Multiple Stacks

The changing requirements in transportation and logistics have recently induced the appearance of new vehicle routing problems that include complex constraints as precedence or loading constraints. One of these problems that have appeared during the last few years is the Double Traveling Salesman Problem with Multiple Stacks (DTSPMS), a vehicle routing problem in which some pickups and deliveries must be performed in two independent networks, verifying some precedence and loading constraints imposed on the vehicle. In this paper, four new neighborhood structures for the DTSPMS based on reinsertion and permutation of orders to modify both the routes and the loading planning of the solutions are introduced and described in detail. They can be used in combination with any metaheuristic using local search as a subprocedure, guiding the search to unexplored zones of the solution space. Some computational results obtained using all proposed neighborhood structures are presented, providing good quality solutions for real sized instances.      

A variable neighborhood search based algorithm for finite-horizon Markov Decision Processes

This paper considers the application of a variable neighborhood search (VNS) algorithm for finite-horizon (H stages) Markov Decision Processes (MDPs), for the purpose of alleviating the “curse of dimensionality” phenomenon in searching for the global optimum. The main idea behind the VNSMDP algorithm is that, based on the result of the stage just considered, the search for the optimal solution (action) of state x in stage t is conducted systematically in variable neighborhood sets of the current action. Thus, the VNSMDP algorithm is capable of searching for the optimum within some subsets of the action space, rather than over the whole action set. Analysis on complexity and convergence attributes of the VNSMDP algorithm are conducted in the paper. It is shown by theoretical and computational analysis that, the VNSMDP algorithm succeeds in searching for the global optimum in an efficient way.     

Exact and heuristic solutions of the global supply chain problem with transfer pricing

We examine the example of a multinational corporation that attempts to maximize its global after tax profits by determining the flow of goods, the transfer prices, and the transportation cost allocation between each of its subsidiaries. Vidal and Goetschalckx [Vidal, C.J., Goetschalckx, M., 2001. A global supply chain model with transfer pricing and transportation cost allocation. European Journal of Operational Research 129 (1), 134–158] proposed a bilinear model of this problem and solved it by an Alternate heuristic. We propose a reformulation of this model reducing the number of bilinear terms and accelerating considerably the exact solution. We also present three other solution methods: an implementation of Variable Neighborhood Search (VNS) designed for any bilinear model, an implementation of VNS specifically designed for the problem considered here and an exact method based on a branch and cut algorithm. The solution methods are tested on artificial instances. These results show that our implementation of VNS outperforms the two other heuristics. The exact method found the optimal solution of all small instances and of 26% of medium instances.     

Evolutionary,constructive and hybrid procedures for the bi-objective set packing problem

The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge and surprise, this problem has not yet been studied whereas several applications have been reported. Unfortunately, solving the problem exactly in a reasonable time using a generic solver is only possible for small instances. We designed three alternative procedures for approximating solutions to this problem. The first is derived from the original ‘Strength Pareto Evolutionary Algorithm’, which is a population-based metaheuristic. The second is an adaptation of the ‘Greedy Randomized Adaptative Search Procedure’, which is a constructive metaheuristic. As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics. Thus, the third alternative, which is the primary subject of this paper, is an original hybridization of the previous two metaheuristics. The algorithmic aspects, which differ from the original definition of these metaheuristics, are described, so that our results can be reproduced. The performance of our procedures is reported and the computational results for 120 numerical instances are discussed.     

Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

The classical Differential Evolution (DE) algorithm, one of population-based Evolutionary Computation methods, proved to be a successful approach for relatively simple problems, but does not perform well for difficult multi-dimensional non-convex functions. A number of significant modifications of DE have been proposed in recent years, including very few approaches referring to the idea of distributed Evolutionary Algorithms. The present paper presents a new algorithm to improve optimization performance, namely DE with Separated Groups (DE-SG), which distributes population into small groups, defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities. The performance of DE-SG is compared to that of eight algorithms belonging to the class of Evolutionary Strategies (Covariance Matrix Adaptation ES), Particle Swarm Optimization (Comprehensive Learning PSO and Efficient Population Utilization Strategy PSO), Differential Evolution (Distributed DE with explorative-exploitative population families, Self-adaptive DE, DE with global and local neighbours and Grouping Differential Evolution) and multi-algorithms (AMALGAM). The comparison is carried out for a set of 10-, 30- and 50-dimensional rotated test problems of varying difficulty, including 10- and 30-dimensional composition functions from CEC2005. Although slow for simple functions, the proposed DE-SG algorithm achieves a great success rate for more difficult 30- and 50-dimensional problems.     

A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem

We present a variable neighborhood search approach for solving the one-commodity pickup-and-delivery travelling salesman problem. It is characterized by a set of customers such that each of the customers either supplies (pickup customers) or demands (delivery customers) a given amount of a single product, and by a vehicle, whose given capacity must not be exceeded, that starts at the depot and must visit each customer only once. The objective is to minimize the total length of the tour. Thus, the considered problem includes checking the existence of a feasible travelling salesman’s tour and designing the optimal travelling salesman’s tour, which are both NP-hard problems. We adapt a collection of neighborhood structures, k-opt, double-bridge and insertion operators mainly used for solving the classical travelling salesman problem. A binary indexed tree data structure is used, which enables efficient feasibility checking and updating of solutions in these neighborhoods. Our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best-known algorithms in terms of both the solution quality and computational efforts. Moreover, we improve the best-known solutions of all benchmark instances from the literature (with 200 to 500 customers). We are also able to solve instances with up to 1000 customers.     

Instance-specific multi-objective parameter tuning based on fuzzy logic

Finding good parameter values for meta-heuristics is known as the parameter setting problem. A new parameter tuning strategy, called IPTS, is proposed that is a novel instance-specific method to take the trade-off between solution quality and computational time into consideration. Two important steps in the method are an a priori statistical analysis to identify the factors that determine heuristic performance in both quality and time for a specific type of problem, and the transformation of these insights into a fuzzy inference system rule base which aims to return parameter values on the Pareto-front with respect to a decision maker’s preference.Applied to the symmetric Travelling Salesman Problem and the meta-heuristic Guided Local Search, the approach is consistently faster than a traditional non-instance-specific parameter tuning strategy without significantly affecting solution quality; optimised for speed, computational times are shown to be on average 20 times faster while producing solutions of similar quality. A number of interesting areas for further research are discussed.