In this paper, we study the problem of makespan minimization for the multiprocessorscheduling problem in the presence of communication delays. The communication delaybetween two tasks i and j depends on the distancebetween the two processors on which these two tasks are executed. Lahlou shows that asimple polynomial-time algorithm exists when the length of the schedule is at most two(the problem becomes 𝒩𝒫-complete when the length of the scheduleis at most three). We prove that there is no polynomial-time algorithm with a performanceguarantee of less than 4/3 (unless 𝒫 = 𝒩𝒫) to minimizethe makespan when the network topology is a chain or ring and the precedence graph is abipartite graph of depth one. We also develop two polynomial-time approximation algorithmswith constant ratio dedicated to cases where the processor network admits a limited orunlimited number of processors.

This paper presents a hybrid schedule generation scheme for solving theresource-constrained project scheduling problem. The scheme, which is called the PolarizedAdaptive Scheduling Scheme (PASS), can operate in a spectrum between two poles, namely theparallel and serial schedule generation schemes. A polarizer parameter in the rangebetween zero and one indicates how similarly the PASS behaves like each of its two poles.The presented hybrid is incorporated into a novel genetic algorithm that neverdegenerates, resulting in an effective self-adaptive procedure. The key point of thisgenetic algorithm is the embedding of the polarizer parameter as a gene in the genomesused. Through this embedding, the procedure learns via monitoring its ownperformance and incorporates this knowledge in conducting the search process. Thecomputational experiments indicate that the procedure can produce optimal solutions for alarge percentage of benchmark instances.

The two-dimensional bin packing problem is a well-known problem for which several exact and approximation methods were proposed. In real life applications, such as in Hazardous Material transportation, transported items may be partially incompatible, and have to be separated by a safety distance. This complication has not yet been considered in the literature. This paper introduces this extension called the two-dimensional bin packing problem with partial conflicts (2BPPC) which is a 2BP with distance constraints between given items to respect, if they are packed within a same bin. The problem is NP-hard since it generalizes the BP, already NP-hard. This study presents a mathematical model, two heuristics and a multi-start genetic algorithm for this new problem.

This paper addresses a Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines a three-dimensional loading problem and vehicle routing problemin distribution logistics. The problem requires the combinatorial optimization of afeasible loading solution and a successive routing of vehicles to satisfy client demands,where all vehicles must start and terminate at a central depot. In spite of its clearpractical significance in the real world of distribution management, 3L-CVRP in literatureis very limited for its high combinatorial complexity. We solve this problem by a hybridapproach which combines Genetic Algorithm and Tabu Search (GATS). Genetic algorithm isdeveloped for vehicle routing and tabu search for three-dimensional loading, while thesetwo algorithms are integrated for the combinatorial problem. We computationally evaluatethis hybrid genetic algorithm on all publicly available test instances, and obtain newbest solutions for several instances.

The paper concerns a model of influence in which agents make their decisions on a certainissue. We assume that each agent is inclined to make a particular decision, but due to apossible influence of the others, his final decision may be different from his initialinclination. Since in reality the influence does not necessarily stop after one step, butmay iterate, we present a model which allows us to study the dynamic of influence. Aninnovative and important element of the model with respect to other studies of thisinfluence framework is the introduction of weights reflecting the importance that oneagent gives to the others. These importance weights can be positive, negative or equal tozero, which corresponds to the stimulation of the agent by the ‘weighted’ one, theinhibition, or the absence of relation between the two agents in question, respectively.The exhortation obtained by an agent is defined by the weighted sum of the opinionsreceived by all agents, and the updating rule is based on the sign of the exhortation. Theuse of continuous variables permits the application of differential equations systems tothe analysis of the convergence of agents’ decisions in long-time. We study the dynamic ofsome influence functions introduced originally in the discrete model,e.g., the majority and guru influence functions, but the approachallows the study of new concepts, like e.g. the weighted majorityfunction. In the dynamic framework, we describe necessary and sufficient conditions for anagent to be follower of a coalition, and for a set to be the boss set or the approval setof an agent. equations to the influence model, we recover the results of the discretemodel on on the boss and approval sets for the command games equivalent to some influencefunctions.