Mahdi Khemakhem

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

In this paper we propose a new hybrid heuristic approach that combines the Quantum Particle Swarm Optimization technique with a local search method to solve the Multidimensional Knapsack Problem. The approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problems. Experimental results obtained on a wide set of benchmark problems clearly demonstrate the competitiveness of the proposed method compared to the state-of-the-art heuristic methods.

A hybrid heuristic for the 0-1 Knapsack Sharing Problem

A new hybrid method based on ILPH and QPSO is proposed and validated on the KSP.The proposed approach can be easily adapted to other variants of knapsack problems.New valid constraints are used to speed up the reduced problems solved inside ILPH.A local search is incorporated in ILPH as an intensification process.QPSO starts with the best solutions provided by ILPH where infeasibility is allowed. The Knapsack Sharing Problem (KSP) is a variant of the well-known NP-hard knapsack problem that has received a lot of attention from the researches as it appears into several real-world problems such as allocating resources, reliability engineering, cloud computing, etc. In this paper, we propose a hybrid approach that combines an Iterative Linear Programming-based Heuristic (ILPH) and an improved Quantum Particle Swarm Optimization (QPSO) to solve the KSP. The ILPH is an algorithm conceived to solve 0-1 mixed integer programming. It solves a series of reduced problems generated by exploiting information obtained through a series of linear programming relaxations and tries to improve lower and upper bounds on the optimal value. We proposed several enhancements to strengthen the performance of the ILPH: (i) New valid constraints are introduced to speed up the resolution of reduced problems; (ii) A local search is incorporated as an intensification process to reduce the gap between the upper and the lower bounds. Finally, QPSO is launched by using the k best solutions encountered in the ILPH process as an initial population. The proposed QPSO explores feasible and infeasible solutions. Experimental results obtained on a set of problem instances of the literature and other new harder ones clearly demonstrate the good performance of the proposed hybrid approach in solving the KSP.

A dynamic programming algorithm for the Knapsack Problem with Setup

The Knapsack Problem with Setup (KPS) is a generalization of the classical Knapsack problem (KP), where items are divided into families. An individual item can be selected only if a setup is incurred for the family to which it belongs. This paper provides a dynamic programming (DP) algorithm for the KPS that produces optimal solutions in pseudo-polynomial time. In order to reduce the storage requirements of the algorithm, we adopt a new technique that consists in converting a KPS solution to an integer index. Computational experiments on randomly generated test problems show the efficiency of the DP algorithm compared to the ILOGs commercial product CPLEX 12.5. HighlightsA conversion method of binary solution to an integer index is proposed for the KPS.A new storage reduction technique is used to improve a DP algorithm performance.Computational experiments show the efficiency of the proposed DP algorithm.

A quantum particle swarm optimization for the 0---1 generalized knapsack sharing problem

This study proposes a new hybrid heuristic approach that combines the quantum particle swarm optimization (QPSO) technique with a local search phase to solve the binary generalized knapsack sharing problem (GKSP). The approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problems. This study is the first to report on the application of the QPSO method to the GKSP. The efficiency of our proposed approach was tested on a large set of instances, and the results were compared to those produced by the commercial mixed integer programming solver CPLEX 12.5 of IBM-ILOG. The Experimental results demonstrated the good performance of the QPSO in solving the GKSP.

A unified matheuristic for solving multi-constrained traveling salesman problems with profits

In this paper, we address a rich Traveling Salesman Problem with Profits encountered in several real-life cases. We propose a unified solution approach based on variable neighborhood search. Our approach combines several removal and insertion routing neighborhoods and efficient constraint checking procedures. The loading problem related to the use of a multi-compartment vehicle is addressed carefully. Two loading neighborhoods based on the solution of mathematical programs are proposed to intensify the search. They interact with the routing neighborhoods as it is commonly done in matheuristics. The performance of the proposed matheuristic is assessed on various instances proposed for the Orienteering Problem and the Orienteering Problem with Time Window including up to 288 customers. The computational results show that the proposed matheuristic is very competitive compared with the state-of-the-art methods. To better evaluate its performance, we generate a new testbed including instances with various attributes. Extensive computational experiments on the new testbed confirm the efficiency of the matheuristic. A sensitivity analysis highlights which components of the matheuristic contribute most to the solution quality.

A tree search based combination heuristic for the knapsack problem with setup

We propose a tree search heuristic to the Knapsack Problem with Setup (KPS).We demonstrate the benefit of a new technique to avoid solutions duplication.Computational experiments show the efficiency of the proposed heuristic. Knapsack Problems with Setups (KPS) have received increasing attention in recent research for their potential use in the modeling of various concrete industrial and financial problems, such as order acceptance and production scheduling. The KPS problem consists in selecting appropriate items, from a set of disjoint families of items, to enter a knapsack while maximizing its value. An individual item can be selected only if a setup is incurred for the family to which it belongs. In this paper, we propose a tree search heuristic to the KPS that generates compound moves by a strategically truncated form of tree search. We adopt a new avoid duplication technique that consists in converting a KPS solution to an integer index. The efficiency of the proposed method is evaluated by computational experiments involving a set of randomly generated instances. The results demonstrate the impact of the avoiding duplication technique in terms of enhancing solution quality and computation time. The efficiency of the proposed method was confirmed by its ability to produce optimal and near optimal solutions in a short computation time.

Solving constrained optimization problems by solution-based decomposition search

Solving constrained optimization problems (COPs) is a challenging task. In this paper we present a new strategy for solving COPs called solve and decompose (or

Design factors analysis for instances of rich vehicle routing problem

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